Multiple Substrate Kinetics of Ribonuclease P: Relative Rate Constant Determination Through Internal Competition

Home , Ribonuclease P

MULTIPLE SUBSTRATE KINETICS OF RIBONUCLEASE P: RELATIVE RATE CONSTANT DETERMINATION THROUGH INTERNAL COMPETITION

LINDSAY ELYSE YANDEK

Submitted in partial fulfillment of the requirements

For the degree of Doctor of Philosophy

Dissertation Advisor: Dr. Michael Harris

Department of Biochemistry

CASE WESTERN RESERVE UNIVERSITY

August 2013

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the thesis/dissertation of Lindsay E. Yandek candidate for the Ph.D. Degree*

(signed) William Merrick (chair of the committee)

Michael Harris

Eckhard Jankowsky

Pieter deHaseth

Blanton Tolbert

(date) 13 May 2013

*We also certify that written approval has been obtained for any proprietary material contained therein.

Table of Contents

List of Tables ……………………………………………………………………………..6

List of Figures …………………………………………………………………………….7

Acknowledgements ……………………………………………………………………….8

Abstract …………………...………………………………………………………………9

Chapter 1: Introduction ……..……………….…………………………………………..11

RNase P and pre-tRNA interactions …………………………………………….12

E. coli transfer RNA …………………………………………………………….18

Apparent Kinetic Mechanism …………………………………………………...21

Uniformity and thermodynamic compensation in substrate binding by

RNase P ………………………………………………………………………….24

Facing the biological context ……………………………………………………25

Chapter 2: Molecular Recognition in tRNA Processing by the RNase P Ribonucleoprotein ……………………………………………………………………….28

Results and Discussion ………………………………………………………….33

Comparison of the multiple turnover kinetics of pre-tRNAMET82 and pre- tRNAMETf47 processing by E. coli RNase ………………………………………..37

Pre-steady state kinetic analyses to evaluate the reaction step that limits V……..46

Single turnover kinetics to evaluate the reaction step that is rate limiting

for V/K …………………………………………………………………………...46

Competitive alternative substrate kinetics of pre-tRNAMET82 and pre-tRNAMETf47 processing by RNase P …………………………………………………………..51

Determination of relative rate constants for pre-tRNAs in complex substrate populations by internal competition……………………………………………...56

Chapter 3: Simultaneous Determination of Processing Rate Constants for All Individual RNA Species Processed by RNase P…………………………………………………….65

Experimental Design …………………………………………………………….74

Results and Discussion…………………………………………………………..79

Competitive Multiple Turnover Kinetics of the Randomized Pool …….……….79

Effects of N(-3) to N(-8) randomization and N(-1) to N(-6) randomization on the kinetics of processing of these populations by RNase P …….…………………..82

Competitive Multiple Turnover Reactions of L1-L5 against pre-tRNAMET82+2 – Shortened Sequence …………………………………………………………..…83

Chapter 4: Discussion …………………………………………………………………...86

Comparison of the multiple turnover kinetic schemes of representative canonical and non-canonical pre-tRNA substrates…………………………………………87

Testing the fundamental features of a simple alternative substrate kinetic model for RNase P processing of multiple pre-tRNAs in vitro…………………………89

Comparison of relative V/K values for selected alternative substrates………..…90

Parallels between RNase P processing and alternative substrate recognition by other enzymes……………………………………………………………………93

Application of internal competition kinetics to the analysis of complex substrate populations…………………………………………………………………….…94

Validation of results from HTS-KIN reveals apparent effects of kinetic mechanism on sensitivity to substrate variation…………………………………95

Chapter 5: Future Directions …………………………………………………………….97

Single turnover HTS-KIN kinetics comparing two different +21 extended sequence of the randomized pool in the N(-1) to N(-6) position………………..97

Competitive Multiple Turnover Reactions– Varying Mg2+ Concentrations….....97

Explore possibility of in vivo experiments………………………………………98

Chapter 6: Experimental Procedures …………………………………………………..100

Appendix: Expansion on the mathematical properties of alternative substrate kinetics………………………………………………………………………………….108

References………………………………………………………………………………112

List of Tables

Table 2-1. Multiple turnover rate constants for processing of pre-tRNAMET82 and pre- tRNAMETf47 by RNase P……………...………………..…………………………………42

Table 2-2. Single turnover rate constants for processing of pre-tRNAMET82 and pre- tRNAMETf47 by RNase P………………………………………………………………….42

Table 3-2. Multiple turnover data for randomized pre-tRNAMET82 against RNase P……81

Table 3-3. Non-competitive multiple turnover data for L1-L5 against RNase P Holoenzyme……………………………………………………………………………...81

Table 3-4. Single turnover reaction rates of a uniform pre-tRNA controls and two different randomized pools of pre-tRNAs……………………………………………….83

Table 3-5.rk values determined for L1-L5+21 variants to pre-tRNAMET82+2……………85

Table 3-6.rk values determined for L1-L5 substrates lacking the additional +21 leader nucleotides relative to pre-tRNAMET82+2………………………………………………...85

List of Figures

Figure 1-1. Pre-tRNA cleavage by RNase P Holoenzyme……………………………………….13

Figure 1-2. Schematic of E. coli RNase P…………………………………………………….….14

Figure 1-3. Secondary structure representation of E. coli RNase P……………………………...17

Figure 1-4. RNase P and pre-tRNA interactions at the cleavage site………………………….…20

Figure 2-1. Secondary structure and sequence conservation of E.coli pre-tRNAs…………….…30

Figure 2-1. Secondary structure and sequence representative pre-tRNAs……………………..…39

Figure 2-3. Multiple turnover and pre-steady state kinetics of pre-tRNAMET82 and pre- tRNAfMET47by RNase P…………………………………………………………………………...43

Figure 2-4. Progress curve analysis of pre-tRNAMET82 and pre-tRNAMETf47 multiple turnover kinetics…………………………………….……………………………………………….……..45

Figure 2-5. Single turnover kinetics of pre-tRNAMET82 and pre-tRNAMETf47 processing by RNase P………………………………………………………………………………………………...... 49

Figure 2-6. Competitive multiple turnover reactions containing both pre-tRNAMETf47 and pre- tRNAMET82+2……………….……………………………………………………………………..52

Figure 2-7. Analysis of the relative rate constant for processing of pre-tRNALEU76 by internal competition……………………………………………………………………...... 58

Figure 2-8. Determination of relative rate constants for pre-tRNASER80 cleavage and miscleavage by internal competition…………………………………………………………………………...62

Figure 2-9. Histogram of rk values for different pre-tRNA substrates…………………………...64

Figure 3-1. Crystal structure of the RNase P and leader sequence interactions………………….68

Figure 3-2. Hydroxyl radical protection analysis of pre-tRNA binding to E. coli RNase P……..71

Figure 3-3. The randomized leader sequence of pre-tRNAMET82…………………………………72

Figure 3-4. Difference between random pool and single substrate multiple turnover kinetics…..75

Figure 3-5. Histogram of distribution of random population in comparison to pre-tRNAMET82…77

Figure 3-6. The sequence logo of fastest sequences analyzed through HTS-KIN……………….78

Acknowledgements

For the successful completion of my tenure here at Case Western Reserve University I owe a great many thanks to a number of individuals including mentors, colleagues, friends and family.

I owe Dr. Michael Harris a world of thanks for being an incredible advisor and mentor. Through his guidance I have grown as a scientist in ways I never thought possible. I will be eternally grateful to him for bringing me into his laboratory, helping me to develop my independent thinking, and allowing me to see all aspects of what it takes to be a successful scientist, which I think he has accomplished quite extraordinarily.

When I joined the Harris Laboratory, it was Mike, Dr. Frank Campbell, Dr. Eric Christian and myself. I could not have asked for a better introduction to my Ph.D. studies. These men, all accomplished scientists, patiently taught me the ropes and spent endless hours talking with me about science, politics and life. Even though we have gone our separate ways, I think of those years as the fondest of my graduate career, largely in part to them and will be forever grateful for all their advice and ideas.

I would like to acknowledge the Biochemistry Department who has provided me with a wonderful education and learning environment. I am very grateful to my committee members Drs. Eckhard Jankowsky, Pieter deHaseth and Blanton Tolbert for participating on my committee and spending time giving thoughtful feedback on my project. I would like to give a special thank you to my committee chair Dr. William Merrick for not only participating on my committee, but being a support system to me and all of the graduate students by acting as our always supportive and helpful academic advisor.

Last but not least I would like to thank my family and friends who have supported my tirelessly. From my friends at Case Western Reserve University that are now spread far and wide perusing their scientific careers, to my non-science friends, thank you for countless hours of commiserating, having scientific discussions and of course beer drinking and department gossip. I am extremely lucky to have a sister, Amy, who is perusing a doctorate degree at the same time. Although our degrees are in very different fields, we can always talk to each other about our successes and road blocks with understanding. I have been very lucky to have such a solid support system in Kevin Reilly. Without his tireless patience and understanding I do not know if I could have made it through this. And of course, I would like to thank my parents, Edward and Catherine Yandek, who have been with me every step of the way offering endless support through my 25 years of schooling. Without the love and support they have always provided I would never be where I am today.

Multiple Substrate Kinetics of Ribonuclease P: Relative Rate Constant Determination

through Internal Competition

Abstract

LINDSAY ELYSE YANDEK

A single enzyme, ribonuclease P (RNase P), processes all precursor tRNA (pre-tRNA) in cells and organelles that carry out tRNA biosynthesis. This substrate population includes over 80 different competing pre-tRNAs in Escherichia coli. While the reaction kinetics and molecular recognition of a few individual model substrates of bacterial RNase P have been well described, the competitive substrate kinetics of the enzyme are comparatively unexplored. To understand the factors that determine how different pre-tRNA substrates compete for processing by E. coli RNase P, we compared the steady state reaction kinetics of two pre-tRNAs that differ at sequences that are contacted by the enzyme. For both pre-tRNAs, we demonstrated that substrate cleavage is fast relative to dissociation such that there is a large commitment to catalysis. As a consequence, V/K, the rate constant for the reaction at limiting substrate concentrations, reflects the substrate association step for both pre-tRNAs. Reactions containing two or more pre-tRNAs follow simple competitive alternative substrate kinetics in which the relative rates of

processing are determined by pre-tRNA concentration and their relative V/K values. The

relative V/K values for eight different pre-tRNAs, that were selected to represent the

range of structure variation at sites contacted by RNase P, were determined by internal

competition in reactions in which all eight substrates are present simultaneously. The

results reveal a relatively narrow range of V/K values suggesting rates of pre-tRNA processing by RNase P are tuned for uniform specificity and consequently optimal coupling to precursor biosynthesis. To evaluate this further, we developed a new, scalable method in order to study larger and more complex populations of pre-tRNAs.

We examined all sequence variants in the cognate site of the RNA substrate for the C5 protein subunit of E. coli RNase P, which binds pre-tRNA leaders non-specifically. A high-throughput sequencing kinetics approach (HITS-KIN) reveals pronounced discrimination of C5 between sequence variants, determinants for discrimination that cannot be delineated by analysis of cellular substrates, and a distribution of substrate affinities of C5 that is very similar to specific DNA binding proteins.

Chapter 1: Introduction

Ribonucleoproteins (RNPs) are some of the most highly conserved and important

catalysts in biology. Ribonuclease P (RNase P) is an essential RNP enzyme that is

responsible for catalyzing the maturation of the 5' end of transfer RNAs (tRNAs) through

site-specific hydrolysis of a phosphodiester bond in precursor tRNAs (pre-tRNAs) (1).

The products resulting from the reaction are a tRNA with a mature 5' end and an RNA corresponding to the pre-tRNA 5’ leader sequence (2,3,4). Although the P RNA subunit is catalytic, RNase P differs from other ribozymes in two important ways. First, its biological role is to perform multiple turnover reactions, whereas other ribozymes typically undergo single turnover self-splicing or self-cleavage. The only other ribozyme known to have this ability is the ribosome and potentially the spliceosome (1). Second,

RNase P has the ability to process multiple RNA substrates, including all pre-tRNAs in the cell. However, the basis for RNase P substrate specificity is not well understood; therefore, a better understanding of steady-state reaction kinetics for different substrates is essential. Since the discovery of the catalytic property of the RNA subunit, most detailed kinetic studies limited their focus to reactions involving the RNA alone, and consequently, significantly less is known regarding the multiple turnover kinetics of the biologically relevant ribonucleoprotein holoenzyme. Because, RNase P functions as the

holoenzyme in vivo, an understanding of the kinetics of this enzyme form is essential for

understanding its function in tRNA processing. Recent evidence indicates that RNase P

Abbreviations used are: RNase P, ribonuclease P; tRNA, transfer RNA; pre-tRNA, precursor tRNA; HTS-

KIN, High Through-Put Sequencing Kinetics.

binds pre-tRNAs with uniform affinity and cleaves with an essentially identical rate

constant (5).

Extensive previous studies of essential RNPs such as the ribosome, snRNPs, and

RNase P, give us a detailed understanding of the structures of the free and bound RNA and proteins, and the function and regulation of the assembled complexes. Much less is known about the structural dynamics, kinetics, and thermodynamics that underlie molecular recognition of complex substrates, and these are the areas of interest in the field currently. For that reason, my goal has been to study RNase P structure and function in a manner that will provide better understanding of the cooperative function of the P

RNA and P protein subunits in molecular recognition by the RNase P holoenzyme.

Learning how the RNA and protein subunits function and coordinate activities in enzyme

specificity and catalysis is necessary for achieving an accurate understanding of their

function in normal cell growth and development as well as in human disease.

RNase P and pre-tRNA interactions - RNase P is a pH and metal-dependent enzyme

responsible for catalyzing the maturation of the 5' end of pre-tRNAs (Fig. 1-1). It has been shown that the protein subunit enhances cleavage rates when metal and substrate are subsaturating (6-8). While many RNase P holoenzymes consist of more than one protein subunit, bacterial RNase P has a simple configuration, consisting of one protein and one

RNA subunit. We study E. coli RNase P (Fig 1-2) which consists of a single RNA (~400 nt) and a single small protein subunit (~100 aa) which is easily reconstituted in vitro. For this reason, studying E. coli RNase P allows for more a precise and simplified study of the role of each subunit and their role in pre-tRNA processing.

Figure 1-1. A) Pre-tRNA cleavage by RNase P holoenzyme. On the left is a cartoon of a generic pre-tRNA, and on the right are the products of the phosphodiester bond cleavage, a 5’precursor sequence and a tRNA with a mature 5’ end. The red sphere represents the cleavage site. B) The proposed mechanism of the reaction based on biochemical studies.

On the left is a putative structure of the transition state of the reaction. On the right are the reaction products (1). Figure permission license number: 3138251263368.

Figure 1-2. Schematic of E. coli RNase P as adapted by Dr. Michael Harris. The red portion represents the small protein subunit. The green represents the pre-tRNA, with the dashed line representing the leader sequence. The gold star represents the cleavage site.

In bacteria, RNase P secondary structure falls into two classes, the more common

A type, of E. coli is an example, and the B type, which is found only in gram-positive bacteria (9-12) (Fig 1-3). The tertiary structure of bacterial RNase P RNA is formed by coaxially stacked helical domains which are stabilized by long range docking interactions

(13,14). Bacterial RNase P has its most evolutionarily conserved sequences in the substrate binding pocket, while the periphery of the RNA contains the most variation between species (13,15). Even though there is significant sequence and structure variation between the A type and B type RNA, both have a single, essential and homologous protein subunit. The presence of the protein subunit in E. coli RNase P stabilizes the tertiary structure of the corresponding RNA and decreases the Mg2+ dependence (16-20). There are currently three structures of the protein component of bacterial RNase P, one of the A type and 2 of the B type, which are have a strikingly similar crystal structure despite their overall very different sequences. This is not exceptionally surprising as early studies have shown that the protein subunits are interchangeable between species, which is thought to be largely in part due to their highly conserved hydrophobic core (12,21). But the structure of the protein alone provides limited information on the mechanism without the accompanying RNA component (22-

24). The three dimensional structure of the RNA component was initially investigated on a smaller scale, and then by domain (25-28), but more recently the structure of the entire

RNA component was solved (13,14). There are two distinct structural domains in bacterial RNase P that are responsible for two different actions. The S domain, or specificity domain recognizes the TΨC-loop of pre-tRNA while the catalytic (C) domain recognizes the acceptor stem and the 3’ CCA and catalyzes the hydrolysis of the 5’ leader

(13,14). The protein itself interacts primarily with the 5’leader sequence of pre-tRNA that is eventually removed to make a mature tRNA. These discoveries have been very useful in figuring out the RNase P mechanism, but ideally we would have a structure of the holoenzyme bound to pre-tRNA and to date, this has not been accomplished.

Fig 1-3. A secondary structure representation of type-A E. coli RNase P. Paired regions are labeled as P1, P2, etc. A linker joining two helices is labeled J11/12, and the loop capping P18 is called L18 (29).

E. coli Transfer RNA - Transfer RNA is a small RNA molecule essential for protein

synthesis in all organisms where is serves as the adaptor between the genetic code

contained in the mRNA and the peptidyl transfer center of the ribosome. In bacterial

cells, tRNA accounts for 20% of the total RNA. Transfer RNA steady-state levels in

bacteria are necessarily a function of four processes: transcription of tRNA genes,

processing of tRNA precursors, degradation of tRNA precursors, and degradation of

mature tRNAs (30). In E. coli there are 87 genes encoding for tRNAs and RNase P has to

process all of them. Many experiments have been done to understand the principles that

govern molecular recognition that are essential for pre-tRNA processing using P RNA

alone. These experiments have led to the elucidation of recognition elements in the pre-

tRNA sequence and structure that can greatly affect processing efficiency. The

recognition elements that are near the cleavage site are a 3’ RCCA sequence, a

G(+1)/C(+72) as the first base pair in the acceptor stem (cleavage takes place between N-

1 and N+1), and U(-1) (Fig.1-4). Another recognition element present in pre-tRNAs that

interacts with the substrate binding domain in P RNA are the 2’-OH groups in the T

stem-loop. Changes in all of the recognition elements have an effect on cleavage

efficiency except the 2’-OH groups, which only appear to affect binding efficiency.

Roughly half of all E. coli pre-tRNAs have these recognition elements (consensus pre- tRNAs) whereas the others lack one or more of these elements (non-consensus pre- tRNAs). Mutations in individual recognition elements, greatly affect cleavage by P

RNA alone in vitro, but with respect to the holoenzyme, the binding affinities and cleavage rates of both consensus and non-consensus substrates are essentially uniform, showing that it is not sensitive to changes in these elements of pre-tRNA sequence or

18 structure (5,31). Understanding how this uniformity is achieved is important in order to better understand how RNase P processes pre-tRNAs in a biological context.

RNA production is an essential process in all cells for their successful growth, of which tRNA is a major component. In E. coli cells, the production of tRNA is regulated by the stringent response, which senses an increase of uncharged tRNA and negatively regulates the initiation of transcription of tRNA operons (32). E. coli has 87 tRNA genes coding for the different amino acids, however the steady state distribution of these tRNA species is not uniform (2). The tRNAs that are present at higher concentrations are those that recognize the most commonly used codons for highly expressed proteins, with the overall abundance being largely due to gene copy number (33,34). This correspondence of codon usage and tRNA abundance is believed to increase translational efficiency and therefore growth rates of the organism (35).

Figure 1-4. RNase P and pre-tRNA interactions at the cleavage site indicating the recognition elements. A) Cartoon diagram of the RNase P enzyme–substrate complex. P RNA is depicted as a series of cylinders that indicate the positions of individual helices. The C5 protein subunit is shown as a sphere of approximate size relative to that of P RNA. The pre-tRNA substrate is shown as a black ribbon, with the leader sequence shown as a broken line. The site of processing by RNase P is indicated by an arrow. The nucleobase residues that are identified as important determinants for substrate recognition are shown as circles. B) Details of the interactions between P RNA and the pre-tRNA cleavage site. The 5′ R(73)C(74)C(75) 3′ sequence located at the 3′ terminus of pre-tRNA pairs with G292, G293, and U294 in the L15 region of P RNA; this interaction helps to align the correct phosphodiester bond in the active site. A pyrimidine (predominantly a U) is present 5′ to the cleavage site in about 80% of E. coli pre-tRNAs, and this residue contacts A248 in the J5/15 region of P RNA. Figure from Sun et. al (36).

Kinetic Mechanism of RNase P – RNase P has the ability to recognize and process many different substrates, but as introduced above, its native substrate, pre-tRNA, has a wide variability including the sequence and structure around the cleavage site. Both protein and RNA components are needed in vivo, but in vitro, the P RNA can catalyze RNA cleavage in the absence of the protein under conditions of high salt and divalent ion concentrations. RNase P was one of the first discovered ribozymes and initial studies focused almost exclusively on the P RNA alone. These early experiments showed that the P RNA reaction was pH-dependent, divalent metal ion-dependent and that substrate binding affinity is increased by increasing the salt concentration in addition to the structural recognition elements on the pre-tRNA mentioned above. The majority of the steady-state experiments showed tRNA product release to be the rate limiting step and not pre-tRNA cleavage (1,6-8,37). While these results were revealing, mechanistically these studies were limited as all other reaction steps are not visible. Because of this limitation, pre-steady state kinetics have been integral to acquiring more detailed information on the kinetic and catalytic mechanism of RNase P.

Steady-state and pre-steady-state kinetics have recently been executed on not only the P RNA subunit, but the holoenzyme with the latter experiments showing that the C5 protein enhances the rate constant for catalysis in addition to increasing pre-tRNA binding affinity (2,5,19,36,38). In order to understand the recognition of different pre- tRNAs by RNase P a simple kinetic model is applied allowing basic kinetic parameters for steady state and pre-steady state kinetics to be quantitatively related. The current model is a two-step mechanism for substrate binding (Scheme 1-1). This scheme is supported by data and previous observations from our laboratory and others, and includes

the adjustment of thermodynamic contributions of substrate interactions to catalysis

through threshold effects. In this scheme, substrate binding begins with a low affinity

complex (ES) resulting from initial enzyme and substrate collision, and a second

conformational change or ‘docking step’ where the substrate recognition elements are

contacted (ES*). Previous [32P] 5’-end labeled steady-state and transient kinetic experiments from our laboratory and others determined that the cleavage step (kc) is irreversible (5,31,36,39-41). A more minimal scheme (Scheme 1-2) in which compresses the two step binding mechanisms into a single equilibrium can fit most of the same data, and is more useful to quantitatively compare RNase P holoenzyme and P

RNA kinetics, as well as kinetics of RNase P components from different species.

Henceforth we will apply the convention of using V and V/K as the fundamental multiple

turnover kinetic parameters, where V is the rate constant for reaction of ES to form products and regenerate free enzyme and is equivalent to kcat, whereas V/K is the second

order rate constant at limiting substrate concentrations, equivalent to kcat/Km.

Scheme 1-1. Two-step RNase P substrate association mechanism. E (RNase P); S

(pre-tRNA) ES (RNase P * pre-tRNA complex); EP (RNase P*leader*mature tRNA); P

(5’ leader and mature tRNA). Substrate binding begins with a low affinity complex (ES) resulting from initial enzyme and substrate collision followed by a conformational change or ‘docking step’ where the substrate recognition elements are contacted (ES*).

The first two steps are considered to be in equilibrium (K), whereas the cleavage step and product release are essentially irreversible.

Scheme 1-2. Minimal kinetic scheme for pre-tRNA cleavage by RNase P. This simplified scheme that includes only initial binding, cleavage and product release if sufficient to fit most kinetic data. This is a more ideal scheme for comparing and contrasting different substrate mechanisms.

Uniformity and thermodynamic compensation in substrate binding by RNase P - As mentioned above, the absence of one or more consensus recognition elements decreases processing rates by the catalytic P RNA subunit in vitro. The presence of these elements varies among pre-tRNAs, and it has often been proposed that these differences might influence the steady state abundance of individual tRNAs via effects on RNase P processing based in studies of the P RNA alone (42-44). However, recent holoenzyme analyses from our laboratory suggest otherwise. Quantitative kinetic and equilibrium binding analyses of the molecular recognition properties of the reconstituted RNase P holoenzyme suggest that it has evolved to be insensitive to variation in pre-tRNA sequence and structure. Previously, the holoenzyme had been proposed to be sensitive to changes in pre-tRNA structure like the P RNA alone (5,36). Holoenzyme experiments have shown uniformity in binding affinity and catalysis with pre-tRNAs that vary significantly in the cognate recognition elements at the cleavage site (5,36,45). An interpretation of this result is that RNase P should optimally process the 5’ ends of all pre-tRNAs at a high uniform rate. This would make the overall rate of biosynthesis linked to transcription (46). Some new observations are that weak tRNA binding may be compensated by tight leader sequence binding (4) and that the thermodynamic contribution of different contacts is non-additive (4,5,36) and appear to be controlled by threshold effects leading to uniformity. This observation raises two questions; What are the optimal leader sequences for a particular substrate? and, How are variations in non- consensus sequences accommodated? Insight into the question is provided by the identification of the first sequence specific contact between leader sequence and protein subunits (47). We suggest, since pre-tRNAs have multiple recognition elements, that

24 variations at individual contacts may be tolerated due to thermodynamic coupling between the remaining contacts, reducing the apparent contribution of individual contacts to binding when multiple interactions are present, resulting in apparent uniform binding and catalysis for all substrates (2,4,5,36).

With the information presented above and our current understanding of RNase P association kinetics and bacterial tRNA biosynthesis, we hypothesize that uniformity in multiple substrate recognition is due to different thermodynamic contributions from C5 protein interactions with pre-tRNA leader sequences. This sets the stage for us to determine the mechanistic basis for multiple substrate recognition, through comparison of rate constants from our simple association model for a number of sequence varying substrates.

Facing the Biological Context - A large part of the substrate recognition studies of

RNase P have focused on dissecting the determinants for high binding affinity and fast cleavage rate by changing the structure of a “model” substrate (44,48,49). In some instances this model substrate was not even from the same organism from which the

RNase P was extracted (50,51). These types of experiments make the incorrect assumption that all tRNAs are the same. A majority of these earlier experiments were also done under single turnover conditions whereas RNase P holoenzyme is capable and works in multiple turnover capacity in vivo. For this reason we strive to develop a series of experiments that will bring us closer to understanding the kinetics of the enzyme that are relevant to biological context. The first step in developing a framework for understanding RNase P kinetics in vivo has been to compare in detail the kinetic schemes

for canonical versus non-canonical pre-tRNAs in order to provide a background for understanding how binding uniformity is achieved and to begin analysis of competitive multiple turnover kinetics. The experiments to date provide a framework for testing the basic model of substrate processing uniformity by RNase P. Because substrate binding is essentially irreversible relative to cleavage, it predicts that two substrates will compete at the level of the association step, which will be discussed in detail in Chapter 2. This

observation predicts that substrates in a population will similarly compete with their

relative rates determined by their concentration and their relative V/K values. Once the

relevant kinetic perspective for understanding the processing of substrates in vivo has

been established, we will be in a position to more effectively test the uniformity

hypothesis for pre-tRNA processing by RNase P.

It has been established that the bacterial RNase P protein, C5, interacts with the leader sequence of pre-tRNA. This interaction is thought to compensate for weakened binding from sequence and structural variation in pre-tRNAs. To further investigate and test this idea we are currently utilizing a novel high-throughput deep sequencing method

(high throughput sequencing kinetics, HTS-KIN) for determining the relative rate constants of all members of a large population of RNA sequence variants in collaboration with the laboratory of Dr. Eckhard Jankowsky which will be discussed in detail in chapter 3. Importantly, the interpretation of HTS-KIN data takes advantage of the simple competitive substrate inhibition model developed and validated, above. We are using this approach to identify the effect of pre-tRNA leader sequences variation on the interaction with C5 protein. We hope the results from these experiments will not only give insight

26 into protein-RNA interactions that control catalytic efficiency, but also will optimize this method for many future experiments.

Chapter 2: Molecular Recognition in tRNA Processing by the RNase P

Ribonucleoprotein1,2

Ribonuclease P (RNase P) is an essential ribonucleoprotein enzyme that is responsible for catalyzing the maturation of the 5' end of transfer RNAs (tRNAs) through site-specific hydrolysis of a phosphodiester bond in precursor tRNAs (pre-tRNAs) (52-

54). The RNA subunit, termed P RNA, contains the active site (17,55) while the smaller protein subunit (C5 in E. coli) is required for optimal molecular recognition and catalysis in vitro and is essential in vivo (6,19,39,48,56,58,59). Although P RNA is a ribozyme, its mode of molecular recognition differs from other catalytic RNAs in two important ways.

First, its biological role in pre-tRNA processing requires that it act in trans as a multiple turnover enzyme whereas, other ribozymes, with the exceptions of the ribosome and spliceosome, undergo single turnover self-splicing or self-cleavage reactions (46,60-62).

Second, RNase P processes multiple RNA substrates, including all pre-tRNAs in the cell, whereas other ribozymes, again with the exceptions of the ribosome and spliceosome, have one specific substrate (63,64). These characteristics are essential to RNase P function as they are to the ribosome and spliceosome, and are common to many enzymes involved in RNA metabolism (65-68). Therefore, understanding the multiple substrate recognition properties of RNase P can shed light on general principles of molecular recognition by other ribonucleoproteins and multi-substrate enzymes.

1Yandek, L.E., Lin, HC., and M.E. Harris (2013) Alternative substrate kinetics of Escherichia coli

Ribonuclease P: Determination of relative rate constants by internal competition. J Biol Chem.

288(12):8342-8354

2Further explanation of rational behind the equations published is discussed in the appendix.

The pre-tRNA nucleotides contacted by RNase P have been determined by chemical interference and structure-function studies (Fig. 2-1) (31,46,63,69). The recognition elements near the cleavage site include the 3’ RCCA sequence, a

G(+1)/C(+72) as the first base pair in the acceptor stem, and the 2’OH and nucleobase of a U(-1) residue 5’ to the cleavage site. The substrate binding domain of P RNA also contacts 2’-OH groups in the T stem-loop (70,71). The spacing of these contacts in the T stem-loop in relation to the cleavage site results in an overall shape recognition of the substrate (72-75).

Figure 2-1: Secondary structure and sequence conservation of E. coli (K12) pre-tRNAs at regions contacted by RNase P. A) the conserved secondary structure of tRNA is shown. The RNase P ribonucleoprotein interacts with the acceptor stem and TψC stem and loop of tRNA (black circles). The enzyme also contacts in the 5’ leader (gray circles). The sequences identified as forming RNA-RNA contacts with the RNase P enzyme are shown as letters and include a U at N(−1), a G(1)-C(73) base pair at the top of the acceptor stem, and the 3’-RCCA sequence as described in the Introduction. B) the linear sequences of tRNA involved in substrate binding are separated into three regions for presentation of sequence variation. Genomic tRNA sequences and alignments were obtained from the genomic tRNA database (64). Sequence logos for regions I, II, and III were created using WebLogo (76). Region I (N(−10 to N(−1)) includes the protein binding site in the 5’ leader and the nucleotide at N(−1) that contacts P RNA. Region II (N(1) to N(7)) is the 5’ side of the acceptor step including the RNase P cleavage site 5’ to N(1). Region III (N(66) to N(76)) includes the 3’ side of the acceptor stem and the conserved RCCA sequence that interacts with P RNA.

Comparative analysis of E. coli tRNA gene sequences shows significant variation

among the nucleotides identified as contact points with the enzyme. As shown in Fig. 2-

1, alignment of the 87 pre-tRNA genes of E. coli K12 (64) reveals that the leader sequences (Region I) and the acceptor stem (Regions II and III) show only minimal sequence conservation. An exception is the 3’CCA sequence that is recognized by the ribosome (77), aminoacyl-tRNA synthetases (78,79) and EF-Tu (80). Only two thirds of

E. coli pre-tRNAs (66/87) contain a G(+1)/C(+72) and a similar fraction (63/87) have an optimal U at the N(-1) position (64). The population of pre-tRNAs that contain all of the recognition elements is significantly smaller (~50%; 42/87). These pre-tRNAs make up a canonical sequence, whereas a non-canonical pre-tRNA is missing one or more of these recognition elements. The adjacent basepair to these recognition elements is often a

G(+2)/C(+71), however, this position is not known to contact RNase P. The 5’ leader sequence shows no conserved motif, nevertheless, both binding and cleavage of model substrates by E. coli RNase P are sensitive to changes in the sequence of the 5’ leader

(2,36). Indeed, recent studies identified a protein-RNA interaction between the leader sequence and the Bacillus subtilis RNase P (47). A structure from Mondragon and coworkers of the Thermotoga maritima RNase P bound to tRNA and leader products (75) is consistent with the experimentally defined interface between enzyme and substrate drawn from biochemical studies. Although specific leader contacts are not resolved in the crystal structure, it generally corresponds with the perspective from crosslinking and structure-function studies.

Central to achieving a complete understanding of multiple substrate recognition by

RNase P is the observation that catalysis by P RNA alone is sensitive to natural structural

variation among pre-tRNAs that results in the loss of RNA-RNA contacts between P

RNA and pre-tRNA (5,36,40,49). Catalysis by the ribonucleoprotein holoenzyme, which

forms additional leader sequence interactions, is less sensitive to sequence and structure

variation among endogenous pre-tRNAs (36). A conformational change during substrate recognition has been documented for B. subtilis RNase P, where the protein subunit facilitates via leader sequence contacts (31,39). This two-step mechanism for substrate binding may give rise to threshold effects resulting in similar rate constants for catalysis for substrates lacking optimal contacts with the enzyme (5,36,40,80).

Thus, detailed in vitro structure-function studies measuring binding and catalysis for model substrates have revealed basic principles of molecular recognition by RNase P.

Nonetheless, information on the competition between different alternative substrates is needed to understand RNase P function in vivo. Here, we test a simple competitive model to describe the relative rates of pre-tRNA processing by RNase P, and apply this model to evaluate the effect of natural, genomic variation in pre-tRNA substrate sequence on relative processing rates. The results provide insight into the features of the kinetic mechanism of RNase P that may govern its function in vivo. These insights could potentially be relevant for other multiple substrate enzymes.

Results and Discussion

Application of competitive alternative substrate kinetics to pre-tRNA processing by

RNase P- As illustrated in Scheme 2-1, a simple competitive multiple turnover mechanism allows the competition between different pre-tRNA substrates for processing by RNase P to be quantified (85-87). A single population of RNase P (E) combines with

multiple pre-tRNA substrates (S1, S2, S3 . . . SN) to form individual RNase P-pre-tRNA complexes (ES1, ES2, ES3 . . . ESN) that react with rate constants V1, V2, V3 . . . VN to form

tRNA and leader products that together are represented by P1, P2, P3 . . . PN. We apply

the convention of using V and V/K as the fundamental multiple turnover kinetic

parameters. The parameter V is the rate constant for reaction of ES to form products and

regenerate free enzyme and is equivalent to kcat. The V/K is the second order rate constant

at limiting substrate concentrations (i.e. kcat/Km) (88,89). Importantly, both S1 and S2

must compete with the remaining population of substrates which act as competitive

inhibitors (85-87,90). As a result the expression for the ratio of the rates for conversion

of S1 and S2 to products simplifies to,

vobs1 / vobs2 = (V1/K1)[S1] / (V2/K2)[S2] Equation 1

Thus, the ratio of the observed rates of product formation for the two substrates depends on the ratio of their V/K values and their concentrations. The designation rk is used, below, to refer to the ratio of the V/K values for an experimental or unknown

r substrate relative to a reference substrate ( k = (V/K) /(V/K)reference) (90). As indicated in

Experimental Procedures the pre-tRNAMET82(+2) substrate is used as the primary

reference in this study.

There are two key consequences of Scheme 2-1 and consequently Eq. 1 that are

important in considering the in vivo function of RNase P (85-87,90). First, the relative

V/K values and consequently the observed rates of any two substrates will be independent of the presence or concentration of alternative substrates. The reason for this is that the

34 additional substrates act essentially as competitive inhibitors decreasing the concentration of free enzyme available for all substrates equally. Second, the relative processing rates will depend on the V/K values of the two substrates regardless of the enzyme concentration, or whether either substrate concentration is saturating. These considerations highlight that the second order rate constant at limiting substrate as an essential parameter in understanding the biological function of RNase P as it is with other enzymes.

K V 1 1 E + S E·S E + P 1 1 1

K V 2 2 + S E·S E + P 2 2 2

K V 3 3 + S E·S E + P 3 3 3

K V N N + S E·S E + P N N N

Scheme 2-1

Accordingly, we set out to test whether this simple competitive model describes the

relative rates of pre-tRNA processing by RNase P, and to evaluate the effect of natural,

genomic variation in pre-tRNA substrate structure on the kinetics of competition

reactions containing multiple substrates. As described in the following sections, we first

measured the V and V/K values for two well-characterized canonical and non-canonical

pre-tRNAs using standard steady state reactions of uniform RNA populations. We used

pre-steady state and single turnover kinetic analysis to determine the reaction steps that

limit V and V/K. Reactions containing mixtures of both substrates were analyzed, and the

simple competitive model described above was validated. Using an internal competition

approach based on this model, we determined the relative rate constants for eight

different pre-tRNAs representing the range of pre-tRNA structural variation at sites of

RNase P contact occurring in the E. coli genome.

Comparison of the multiple turnover kinetics of pre-tRNAMET82 and pre-

tRNAMETf47 processing by E. coli RNase P- The substrates pre-tRNAMET82 and pre-

tRNAMETf47 (Fig. 2-2) were selected as representative examples of canonical and non- canonical pre-tRNAs, respectively. Both pre-tRNAs have similar sequence length and base composition; however, they differ significantly in the nucleotides contacted by the P

RNA subunit of RNase P. The pre-tRNAMETf47, an initiator tRNA, has an A instead of an

optimal U at N(-1) and a C(+1)-A(+72) pair at the cleavage site that results in a >900- fold decrease in the rate of catalysis by the P RNA subunit alone (36). In contrast, the

RNase P holoenzyme binds both pre-tRNAMET82 and pre-tRNAMETf47 with equivalent

equilibrium binding constants and processes them with similar single turnover rate

constants (36). The metal ion and pH dependence of the single turnover reactions of

both substrates are also comparable (2). In order to isolate the effects of tRNA sequence and structure that contact RNase P from secondary effects due to flanking sequences that are idiosyncratic to individual pre-tRNAs we use a standard substrate structure containing the tRNA and ten additional nucleotides to make up the leader sequences (Fig. 2-2).

Figure 2-2: Sequence and secondary structure of representative pre-tRNAs. The location of the RNase P cleavage site between nucleotides N(−1) and N(+1) is indicated by an arrow for each pre-tRNA. The N(+1)/N(+72) base pair is boxed, and the N(−1) position is indicated by a gray circle.

To evaluate the V/K for processing of pre-tRNAMET82 and pre-tRNAMETf47 by RNase

P the observed initial rates for both substrates are plotted against their concentrations and

fit to the Michaelis-Menton equation (Fig. 2-3).

vobs = VEtotal / (1 + K/[S]) Equation 2

The steady-state kinetic parameters V and K for both substrates are highly similar (VMET82

-1 -1 = 0.11 + 0.01 s ; VMETf47 = 0.14 + 0.01 s and KMET82 = 310 + 60 nM; KMETf47 = 280 +

40 nM) resulting in a rk ratio near unity (ca. 0.9, where rk =

(VMETf47/KMETf47)/(VMET82/KMET82)) (Table 1). Fitting complete time courses of the multiple turnover reactions of pre-tRNAMET82 and pre-tRNAMETf47 to the integrated

Michaelis-Menton equation shows evidence of product inhibition (Fig. 2-4.). An

additional approach to measure V/K from multiple turnover reactions is to analyze

progress curve data using the integrated Michaelis-Menton equation:

t = (K/V)(ln(S0/St) + (1/V)(S0 - St) Equation 3

Although the multiple turnover time courses for RNase P cleavage of pre-tRNAMET82 and

pre-tRNAMETf47 fit well to the above equation, the value of V/K determined using initial

rate data do not predict the observed time courses for either substrate (dotted lines in Fig.

2-4). It is observed that the kinetics are significantly slower and a much larger K value is

obtained from fitting. These features are hallmarks of product inhibition, and thus we fit

the progress curve data to the integrated equation including product inhibition:

t = (K/V)(1 + S0/Ki)(ln(S0/St) + (1/V)(1-K/Ki)(St - S0) Equation 4

Equilibrium binding studies as well as competitive single-turnover inhibition

MET82 METf47 experiments indicate that the Kd for the tRNA is 150 nM and tRNA is 100 nM

(5,36). Using these values for Ki in the above equations provides a much improved fit of

the data (solid line in Fig. 2-4). The values of V and K for the two substrates obtained by

this method are ca. 2-fold lower than those obtained from analysis of the initial rate data,

however, the values of V/K are highly similar.

The multiple turnover kinetic parameters, V and V/K, estimated by both approaches

are highly similar for both substrates despite their significant difference in structure

(Table 1). Next, we asked whether the similar V and V/K values for the two substrates

reflect the same or different rate limiting steps.

______Table 2-1. Rate constants for processing of pre-tRNAMET82 and pre-tRNAMETf47 by RNase P ______substrate V (s-1) K (nM) V/K (M-1s-1 x 106)

______pre-tRNAMET82 MM1 0.11 + 0.01 300 + 60 0.3 + 0.1 PC 0.06 + 0.01 110 + 5 0.6 + 0.1 pre-tRNAMETf47 MM 0.14 + 0.01 290 + 40 0.5 + 0.1

PC 0.05 + 0.01 130 + 10 0.4 + 0.1 ______

1MM, Michaelis-Menton; PC, progress curve.

______

Table 2-2. Rate constants for processing of pre-tRNAMET82 and pre-tRNAMETf47 by RNase P ______

2+ 1 k1 k-1 Km, calc Kd, calc Kd, obs (Ca ) (M-1s-1 x 106) (s-1 x 104) nM nM nM pre-tRNAMET82 1.9 + 0.1 2.4 + 0.7 57 +172 0.8 + 1.7 0.5 + 0.4 pre-tRNAMETf47 1.5 + 0.4 9.1 + 0.4 71 + 117 5.7 + 6.4 0.3 + 0.2 ______1From Sun et al., 2006 (5)

Figure 2-3: Multiple turnover and pre-steady state kinetics of pre-tRNAMET82 and pre- tRNAMETf47 processing by RNase P. A) the observed initial rates for pre-tRNAMETf47 (open symbols) and pre-tRNAMET82 (filled symbols) processing by E. coli RNase P were determined and normalized to the total enzyme concentration, (v/[E]total) as described under “Experimental Procedures.” These data are plotted as a function of the initial substrate concentration and fit to the Michaelis-Menten equation as described below. Note that the substrate concentrations are shown on a log scale to better display the range of concentrations tested. Error bars indicate S.D. B) pre-steady state kinetics of pre- tRNAMETf47 (open symbols) and pre-tRNAMET82 (filled symbols) at 5 and 10 nm RNase P concentration. The maximal predicted burst amplitudes for these two reaction conditions are indicated on the y axis.

Figure 2-4: Progress curve analysis of pre-tRNAMET82 and pre-tRNAMETf47 multiple turnover kinetics. The kinetics of substrate depletion from reactions containing 400 nm pre-tRNAMET82 (A) or pre-tRNAMETf47 (B) substrate and 2 nm RNase P were analyzed by fitting to the integrated Michaelis-Menten equation as described below. Simulations in which the V and V/K determined from analysis of initial rate data are shown as dotted lines. The solid lines show fitting the data to a model assuming product inhibition as described below.

Pre-steady state kinetic analyses to evaluate the reaction step that limits V- The kinetics of pre-tRNA cleavage at increasing concentrations of RNase P were examined to determine the predominant form of the enzyme that is populated at steady state (ES or

EP, in Scheme 2-1). As shown in Fig.2-3B, for reactions in which RNase P (5 nM and

10 nM) and the pre-tRNA substrate (500 nM) are both present at concentrations in excess of Kd (> 1 nM), there is a linear increase in product concentration that extrapolates back

to the origin. Reactions with either 5 or 10 nM RNase P result in product formation that

increases linearly with no evidence for a pre-steady state burst. A simple interpretation

of this result is that the net rate constant for dissociation of products and regeneration of

free enzyme (k3 in Scheme 2-2) is faster than substrate cleavage (k2). Therefore, ES is the predominate form of the enzyme that accumulates at steady state. This result contrasts with the kinetic mechanism of B. subtilis RNase P which is limited by product release for a canonical pre-tRNAASP substrate (7).

Single turnover kinetics to evaluate the reaction step that is rate limiting for V/K-

An important observation relevant to the reaction mechanism of E. coli RNase P is that

the observed K (where K = (koff + V)/kon in Scheme 2-1; i.e. Km) (53) from multiple turnover kinetic analyses is greater than the independently measured equilibrium

MET82 dissociation constant, Kd (310 nM versus 0.5 nM for pre-tRNA and 280 nM versus

0.3 nM for pre-tRNAMETf47) (Tables 1 & 2). This result implies that the net rate constant

for cleavage to regenerate free enzyme (V = k2k3/k2+k3) in Scheme 2-2) is fast relative to

substrate dissociation (k-1) (91-93). It follows that at limiting substrate concentration the

rate of multiple turnover could therefore be limited by substrate association (89).

To test these predictions we determined the relative magnitudes of the rate constant

for catalysis, k2, and the rate constant for substrate dissociation, k-1 using a ‘sequential

mixing’ or ‘isotope trapping’ experiment (84). The RNase P-pre-tRNA complex was formed by mixing limiting substrate (1-2 nM) with a saturating concentration of enzyme

(100 nM). At an intermediate time an excess of non-radiolabeled substrate is added. If k2

is fast relative to k-1, then there will be little dissociation of the remaining RNase

P-pre-tRNA complexes over the remaining time course of the reaction, and

correspondingly no effect on the accumulation of product. Alternatively, if substrate

dissociation is fast relative to catalysis (k-1 >> k2), then the addition of non-radiolabeled

substrate will quench the formation of radiolabeled product.

The dependence of the observed pseudo first order rate constant on enzyme

concentration showed saturable behavior as predicted based on Scheme 2-1 (data not shown). These data allowed reaction conditions to be determined under which all of the radiolabeled pre-tRNA is present in the ES complex. As shown in Fig. 2-5A & B,

addition of a cold substrate chase after formation of ES did not result in quenching or a

change in reaction kinetics. In contrast, addition of the excess non-radiolabeled substrate

at the start of the reaction resulted in the expected slow, multiple turnover kinetics.

Therefore, we concluded that substrate dissociation is negligible over the remaining time

course of the reaction (k2 >> k-1).

An important implication of this result is that the substrate association rate constant, k1, can be measured from the concentration dependence of the single turnover reaction

(kobs versus [E]) (54). Fitting the dependence of kobs to [E] at concentrations below K1/2

permits k1 and k-1 to be estimated as the slope and intercept (Fig. 2-5C). The kinetic

parameters for both substrates are similar (1.9 + 0.1 x 106 M-1s-1 and 1.5 + 0.4 x 106 for

MET82 METf47 pre-tRNA and pre-tRNA , respectively) (Table 2). The estimates for k-1 from

second order analyses are less than the V for both substrates. In this case the observed K

for the multiple turnover reaction will be approximated by V/k1 (91). The experimentally measured values of these kinetic parameters result in calculated K values of 57-172 nM for pre-tRNAMET82 and 71-117 nM for pre-tRNAMET47. These calculated values are within 2-fold of the experimentally observed K determined from analysis of initial rate data (Tables 1 and 2). It is possible that differences in the reaction pH or errors in the determination of concentrations of substrate and enzyme account for this difference.

From the definitions for V and K, above, it follows that V/K = k2k1/(k-1 + k2) (89).

Thus, when k2 >> k-1 then V/K ≈ k1. Therefore, the most simple interpretation of the

presteady state and single turnover results is that the cleavage step (k2) is rate limiting for

V (i.e. at saturating substrate concentrations) and that V/K reflects the association step (k1)

for both pre-tRNAs at limiting substrate concentrations.

Figure 2-5: Single turnover kinetics of pre-tRNAMET82 and pre-tRNAMetf47 processing by RNase P. A) single turnover sequential mixing experiment with initial concentrations of 1 nM pre-tRNAMET82 and 100 nM RNase P. At the time indicated by the vertical dotted line, the reaction was divided, and one fraction was combined with a high concentration (5 μM) of nonradiolabeled pre-tRNA (circles). Time points were continuously collected from the remaining fraction (squares). As a control, an identical reaction was combined with nonradiolabeled substrate before the addition of enzyme

(triangles). B) single turnover sequential mixing experiment using pre-tRNAMetf47 performed as described in panel A. C) second order analysis of RNase P binding of pre- tRNAMET82 and pre-tRNAMetf47 to increasing concentrations of RNase P. The pseudo-first order rate constants (kobs) determined for a single turnover reaction containing 2.5–10 nM

RNase P concentrations are plotted versus [E]. These data are fit to a linear function kobs

= k1[E] + k−1 to determine the rate constants reported in Table 2. Error bars indicate S.D.

Competitive alternative substrate kinetics of pre-tRNAMET82 and pre-tRNAMETf47

processing by RNase P- As introduced above, in competitive multiple turnover reactions

the relative rates for two competing pre-tRNAs are expected to be determined by their

r relative V/K values ( k = (V/K)/(V/K)reference) and their concentrations (46-48,51). Also, it

follows that the presence of additional substrates will decrease the observed rates for all

substrates in the reaction due to competition for free enzyme, but should not affect the rk

value for any two substrates (85,94,95). We tested the competitive alternative substrate

model for RNase P by analyzing the competitive kinetics of reactions containing both

pre-tRNAMET82 and pre-tRNAMETf47.

To simultaneously measure the reaction kinetics of two pre-tRNAs in the same reaction we used a reference substrate in which two additional G residues are added to the 5' end of the leader sequence. This modification allows the products of the pre- tRNAs to be distinguished by their mobility on denaturing PAGE and quantified individually. An example of the primary data from this approach for pre-tRNAMET82(+2)

and pre-tRNAMETf47 is shown in Fig. 2-6A. The precursor band contains both substrates

as these species are not resolved under these gel conditions. However, the products from

the two substrates are readily distinguished and quantified allowing relative rates of

product formation to be measured. To address the effect of the additional nucleotides on

pre-tRNA processing the relative rate constants for comparison of pre-tRNAMET82 to pre-

tRNAMET82(+2) and comparison of pre-tRNAMETf47 to pre-tRNAMETf47(+2) were also

measured (data not shown) and were observed to be 0.9-1.3. Thus, the presence of the

additional nucleotides required to distinguish the products from two substrates has

essentially no effect on the rate of RNase P processing.

Figure 2-6: Competitive multiple turnover reactions containing both pre-tRNAMetf47 and pre-tRNAMET82(+2). A) PAGE analysis of the products of a reaction containing 5′32P end-labeled pre-tRNAMetf47 and pre-tRNAMET82(+2). The two precursors run as a single band indicated by a bracket denoting the presence of both substrates. The two leader sequence products are indicated by lines with or without the additional guanosines that identify the product from pre-tRNAMET82(+2). B) plot of the observed multiple turnover Metf47 MET82 rate constants (vobs) for pre-tRNA (open symbols) and pre-tRNA (filled symbols) as a function of the relative concentrations of the two substrates. The data are fit to the log form of Equation 2 (Equation 5). C) plot of the observed multiple turnover rate Metf47 MET82 constants (vobs) for pre-tRNA (open symbols) and pre-tRNA (filled symbols) as a function of the concentration of the third substrate pre-tRNALEU76. The data are fit to a mechanism in which pre-tRNALEU76 acts as a competitive inhibitor (Equation 6). The inset shows the individual rk values determined from dividing the observed rate for pre- tRNAMetf47 by the observed rate for pre-tRNAMET82 at each of the different pre-tRNALEU76 concentration. The solid line and dashed lines represent the average and standard deviation, respectively, calculated from this data set.

To compare the competitive kinetics of pre-tRNAMETf47 and pre-tRNAMET82 the

observed rates of product formation were determined for reactions containing substrate

concentration ratios (in nM) of 10:100, 100:10 10:10 and 100:100 (pre-tRNAMETf47:pre-

tRNAMET82). The product ratios from at least three time points taken under steady state conditions were averaged and then corrected for the relative substrate concentrations.

Additionally, the collection of data for the observed rates as a function of the relative rates of the two substrates were fit to the logarithmic form of Eq. 1,

r log(v2/v1) = log k + log (S2/S1) Equation 5

METf47 where v2/v1 is the ratio of the observed initial rates for pre-tRNA relative to pre-

tRNAMET82(+2). Analysis of the data in this manner allows determination rk from the

combined data set. As shown in Fig. 2-6B the data for both the pre-tRNAMETf47/pre-

tRNAMET82(+2) and the pre-tRNAMETf47(+2)/pre-tRNAMET82 combination of substrates

fits this relationship as predicted. Fitting to Eq. 3 yields an rk value of 0.5

MET82 ((V/K)MET47/(V/K)MET82) for the reaction in which the pre-tRNA was modified to contain the additional two leader nucleotides. As a control, the rk was measured in competitive reactions in which pre-tRNAMETf47 instead of pre-tRNAMET82 was lengthened

in order to distinguish the products from the two substrates. A similar value of 0.6 was

observed consistent with the value measured in which the pre-tRNAMET82(+2) was used

for the reference substrate.

An additional prediction of the internal competition model is that the addition of a

third substrate will not affect the rk value for these two substrates. Accordingly, we

tested the effect of increasing concentrations of a third substrate on the observed rates of

pre-tRNAMET82(+2) and pre-tRNAMETf47 product formation. In Scheme 2-1 additional

substrates act as competitive inhibitors that decrease the observed rate of processing of

both substrates by competing for free enzyme. In Fig. 2-6C, pre-tRNALEU76 is added as a

competitive alternative third substrate in reactions containing pre-tRNAMETf47 and pre-

tRNAMET82(+2) as the reference substrate. Increasing concentrations of non-radiolabeled

pre-tRNALEU76, which binds to RNase P with similar affinity as the other two pre-tRNAs

in the reaction, decreases the observed rates of pre-tRNAMETf47 and pre-tRNAMET82(+2)

processing as expected. The data fit to a simple competitive inhibition model derived

from Scheme 1,

vobs = V1Etotal/(1 + K1/S1 + S2/K2 + S3/K3) Equation 6

where S1 is the concentration of the labeled substrate, S2 and S3 are the concentrations of

the competitive alternative, non-labeled substrates in Fig. 2-6C. Analysis of the observed rates data for pre-tRNAMET82 and pre-tRNAMETf47 in the presence of 10 nM to 3000 nM

pre-tRNALEU76 allows the K value for pre-tRNALEU76 to be estimated. A value of ca. 300

nM is obtained, which is similar to the values measured by analysis of initial rate data for

reactions containing pre-tRNAMET82 or pre-tRNAMETf47 alone (Table 1). Nonetheless, as

demonstrated in the inset in Fig. 2-6C the ratio of the observed rates, the rk for pre-

tRNAMETf47 referenced to pre-tRNAMET82(+2) is independent of the presence and

concentration of a competing substrate. Since the rk value for two competing substrates

is insensitive to a third competing substrate, the internal competition approach could be

used to determine the rk values for substrates in reactions containing more complex

populations.

Determination of relative rate constants for pre-tRNAs in complex substrate populations by internal competition- It follows from Scheme 1 and the observations documented above, that the presence of additional substrates, regardless of their number or concentration, should also have no effect on the relative rates of processing of any two substrates in the population. To test this concept, we generated five pre-tRNA substrates in addition to pre-tRNAMET82, pre-tRNAMETf47 and pre-tRNALEU76. Substrates were

selected to span the range of pre-tRNA structure variation encountered by E. coli RNase

P in vivo, and their secondary structures are shown in Fig. 2-2. Among these similar pre- tRNAHIS and pre-tRNASER substrates have served as substrates for analyzing the determinants of specificity adjacent to the site of 5’ processing (96).

We used the same approach, described in the preceding section, of distinguishing between the products of two substrates by analyzing the relative rate constants of pre- tRNAMET82(+2) and pre-tRNAMETf47. Since the two substrates of interest are the only

species that are radiolabeled, their products alone are detected. As shown in Fig. 2-9, the

rk determined by this method (0.3) is within error of the value of 0.5 determined by

analysis of the two substrates alone. Thus, the presence of additional competing

substrates in the reaction does not have an appreciable effect on the magnitude of the

relative V/K for pre-tRNAMETf47 and pre-tRNAMET82(+2).

Next, we determined the rk values for the remaining seven substrates using the pre-

tRNAMET82(+2) as the reference substrate. As shown in Fig. 2-7, the rk value for the pre-

tRNALEU76 substrate is readily determined by this approach. This substrate has an rk of

3.5 indicating faster processing of pre-tRNALEU76 over the reference pre-tRNAMET82 when they compete for RNase P processing. For this particular substrate the pre-tRNA can be resolved from the unreacted reference pre-tRNAMET82(+2). This allows the change in the

relative concentrations of the residual substrates to be quantified as well. As shown in

Fig. 2-7B, we took advantage of internal competition analyses typically used to measure the relative rate constants for isotope effect measurements (90). The slower reacting pre-

tRNA will become progressively enriched in the residual substrate population and the

relative rate constant can be determined by analyzing the change in substrate ratio as a

function of the fraction of reaction. Using the ratio of residual precursor concentrations

derived from the ratio of radiolabeled precursor bands the rk for pre-tRNALEU76 was determined by fitting to,

r ln(Rs) = ( k – 1)ln(1- f) – ln(R0) Equation 7

where R0 is the ratio at the start of the reaction and Rs is the ratio at fraction of reaction

(f) of the reference substrate (Fig. 2-7C) (90,97). The fraction of reaction for pre-

tRNAMET82(+2) is determined from the intensity of its precursor and product bands. As expected the faster rate constant for the pre-tRNALEU76 substrate results in faster depletion

of this substrate from the residual precursor population relative to the slower reacting pre-

tRNAMET82(+2). As a result the pre-tRNALEU76/pre-tRNAMET82(+2) ratio becomes

progressively smaller as the reaction progresses. An essentially identical rk value of 3.4 is obtained from the fitting of the data shown in Fig. 2-7B.

Figure 2-7: Analysis of the relative rate constant for processing of pre-tRNALEU76 by internal competition. A) PAGE analysis the observed rates of processing determined by quantification of both precursor and product bands in a background population of 100 nm each of the eight pre-tRNAs shown in Fig 2-2. Note that in this case, the larger tRNA of pre-tRNALEU76 results in sufficient separation of the two substrates such that the precursor bands can be distinguished. B) determination of the rk value for pre-tRNALEU76 by internal competition kinetic analysis of the depletion of the faster reacting substrate in the residual precursor population. The graph shows the natural log of the ratio of the two substrates plotted as a function of the total fraction of reaction. These data are fit to an integrated form of the relative rate constant equation (90,97).

Interestingly, in the course of experiments to determine the rk for pre-tRNASER80 we

detected two cleavage products in addition to correct RNase P cleavage at the mature

tRNA 5’ end. As shown in Fig. 2-8A the reaction of pre-tRNAMET82(+2) yields a single

product as expected, while the pre-tRNASER80 substrate gives rise to three products

(labeled P1, P2 and P3 in Fig. 2-8). The P1 product maps to the expected site for RNase

P processing between N(-1) and N(1). The P2 product is derived from miscleavage one nucleotide 5’ to the authentic site yielding a product one nucleotide smaller. Cleavage to give the P3 product occurs five nucleotides upstream of the correct site. RNase P cleavage in the leader sequence is not expected, although several studies have demonstrated the ability of the RNase P holoenzyme to cleave unstructured RNA, but with sequence or structure specificity that is not yet well defined (73,98). Alternatively, cleavage may result from alternative RNA folding (99,100). The rk for the miscleavage at P2 occurs at essentially the same rate as P1 (both have an rk of ca. 0.6). Surprisingly,

the rk value for miscleavage of the pre-tRNASER80 substrate at P3 occurs with an rk that is

significantly higher (2.2). Although the precursors of both substrates can be resolved, the

fact that pre-tRNASER80 reacts to form multiple products precludes determination of its

relative rate constant by analysis of precursor ratios by Eq. 5.

Nonetheless, as demonstrated in Fig. 2-8B the relative rates of accumulation of the

three products of pre-tRNASER80 are readily distinguished. For the pre-tRNAGLY62, pre-

tRNAILE1, pre-tRNAHIS37, and pre-tRNAGLN85 substrates the rk values were determined relative to pre-tRNAMET82(+2) from analyzing the initial rates of formation of the

products. The rk values for all eight substrates, shown as the natural log to provide a

linear scale, are compared in Fig. 2-9 together with the values for the alternative products for pre-tRNASER80.

In this study we have taken a new approach to analyzing substrate recognition by

RNase P by applying the perspective of alternative substrate kinetics. In addition to

providing insight into the enzymatic behavior that underlies its biological function, the

framework described here is useful for extracting relative rates by internal competition.

With the simple competitive substrate kinetics of RNase P established, more broad

application of competitive kinetics may be considered. In principle, internal competition

methods are applicable to very large populations of substrates so long as reaction

progress and the ratios of their precursors or products can be quantified as will be seen in

the following chapter.

Figure 2-8: Determination of relative rate constants for pre-tRNASER80 cleavage and miscleavage by internal competition. A) PAGE analysis of the precursor and products of the competitive cleavage reaction containing 5’ end-labeled pre-tRNASER80 and pre- tRNAMET82(+2) in a background of the eight different E. coli pre-tRNA shown in Fig. 2. The large variable arm of pre-tRNASER80 results in a substrate that is 15 nucleotides longer than pre-tRNAMET82(+2), which can be resolved under these gel conditions (15% PAGE). The pre-tRNASER80 substrate is cleaved by RNase P to give three products: the correct cleavage product resulting from cleavage 5’ to N(+1) (SER P1), miscleavage one nucleotide 5’ into the leader sequence (SER P2), and miscleavage four nucleotides 5’ to the correct cleavage site (SER P3). All of these products are resolved from the single cleavage product resulting from processing at the authentic 5’ end of pre-tRNAMET82 (MET82). B) plot of product accumulation versus time for the products indicated in panel A showing the initial rates of product formation for the Ser P1 (open circles), Ser P2 (filled circles), and Ser P3 (open triangles) products relative to the accumulation of the product from pre-tRNAMET82 processing (squares). C) secondary structure of pre- tRNASER80 with arrows indicating the location of the three cleavage sites in pre- tRNASER80 by RNase P.

Figure 2-9: Histogram of rk values for different pre-tRNA substrates. The individual rk values are presented as their natural log so that the length of the bar is linearly proportional to the difference from the reference substrate for substrates that are faster and slower than the reference pre-tRNAMET82(+2). For the pre-tRNAMETf47 substrate, the bar indicating the rk determined by calculation from the individually measured V/K values is indicated by an asterisk. The rk values for the three cleavage products of pre-tRNASER80 are indicated by P1–P3.

Chapter 3 - Simultaneous Determination of Processing Rate Constants for All

Individual RNA Species Processed by RNase P

Introduction

Typically RNA binding proteins bind their specific proteins based on distinct structures, sequences or both (101,102). Despite this general property, some proteins bind RNAs in a non-specific manner, in which distinct sequence and structure motifs are not apparent from analysis of known physiological substrates. To date it is unclear how substrate affinities for non-specific RNA binding proteins are impacted by sequences or structure variation at cognate sites, aside from effects of RNA structure (102-105).

There are currently many detailed models that link affinities to RNA sequence or structure variation for specific RNA binding proteins. These models show the highest affinities for distinct physiological binding sites (106-108). Based on this idea, it is assumed, but not proven, that an absence of specific sequence or structure for non- specific RNA binding proteins reflects an inability to discriminate between different

RNA sequences. This difference between specific binding sites and non-specific binding sites for RNA binding proteins has recently become a topic of great interest due to the emerging importance of RNA binding proteins with broad specificity. Many studies have been performed on specific RNA binding proteins but the binding modes and determinants of affinity non-specific RNA binding proteins is not as clear. Therefore, the

C5 subunit of E.coli RNase P, which functions essentially as a non-specific RNA binding protein, will be used to systematically probe substrate discrimination for this class of macromolecular associations (31).

The C5 subunit of E. coli RNase P is a useful model system for addressing mechanisms of multiple substrate recognition by RNA binding proteins. E. coli RNase P is responsible for processing the 87 genomically encoded pre-tRNA leader sequences. It has been established that the bacteria RNase P protein, C5, interacts with the leader sequence of pre-tRNA (Fig 3-1). Previous studies have shown conserved residues in the leader sequence (47) but where the C5 protein binds, there does not appear to be any specificity among genomically encoded pre-tRNAs. The C5-5’leader sequence interaction is thought to compensate for weakened binding from sequence and structural variation in pre-tRNA sequence. To further investigate this idea, we are currently utilizing a novel high-throughput deep sequencing method (high throughput sequencing kinetics, HTS-KIN) in collaboration with the laboratory of Dr. Eckhard Jankowsky, for

determining the relative rate constants of all members of a large population of RNA

sequence variants. Importantly, the interpretation of HTS-KIN data takes advantage of

the simple competitive substrate inhibition model developed and validated in the previous

chapter. We are using this approach to identify pre-tRNA leader sequences that interact

with the C5 protein. We anticipate that the results from these experiments will not only

give insight into protein-RNA interactions that control catalytic efficiency, but also will

optimize this method for many future experiments directed at understanding RNA

binding specificity.

HTS-KIN was developed based on a publication by Ferre-D’Amare (109) in

which the change in distribution of sequences of a ribozyme in a large population over

the course of several rounds of in vitro selection was followed. We adapted this approach to permit the measurement of relative rate constants of different sequences in a

population simultaneously. In a mixed population of RNA with different sequences, the

faster reacting (or binding) sequences will become progressively depleted in the

unreacted substrate population, and the slower reacting sequences will become

progressively enriched. Using this principle the basic strategy of HTS-KIN involves: 1.

Synthesis of a population of RNA (pre-tRNA leader sequence variants in this case) in

which specific nucleotides comprising a potential recognition site are randomized; 2.

Reaction or binding of the randomized population followed by purifying the residual,

unreacted substrate from various intervals of time or concentration; 3. Determination of

the distribution of each sequence in the residual pre-tRNA population by Illumina

sequencing; and, 4. Quantitative analysis of the concentration or time dependence of the

distribution of each sequence in the residual, unreacted population to calculate the

relative rate or binding constants for all members of the population simultaneously. My

contribution has been in the validation of initial HTS-KIN experiments by analysis of

individual sequence variants and continued application of HTS-KIN to further analyze the interaction between pre-tRNA sequence and processing rate.

Figure 3-1: The pre-tRNA 5′ leader (purple, with purple and orange spheres for the phosphorous and non-bridging oxygens, respectively) was modeled as a polyphosphate chain with five phosphates (P−1 to P−5). The leader follows a highly conserved patch in the protein extending from the 5′ end of the mature tRNA (red) and away from the P RNA. The addition of a 5′ leader with metal (Sm3+) reveals a second metal ion (M2) (75). Figure permission License Number: 3138270926001

We applied the general HTS-KIN approach to understand the molecular recognition properties of the C5 protein and its contribution to RNase P processing of pre-tRNA in the following way. It has previously been determined that the leader sequence between positions N(-3) and N(-7) are in contact with the C5 protein (6,47,58)

(Fig 3-2). Investigation of the pre-tRNA genomic sequences did not reveal any significant conservation between sequences that would be responsible for tight or weak binding. Further information obtained by determining specific leader sequences responsible for uniformity in pre-tRNA processing has the potential therefore to advance our understanding of RNase P biology in two ways. First, it will provide a more comprehensive model for substrate association, and second, it will provide a better understanding of the fundamental principles that govern enzyme specificity in general.

My contribution to this collaborative project has been to further characterize the kinetics of 5 chosen hexamers, known henceforth as L1-L5. These results were then matched to the results obtained through the HTS-KIN analysis as a verification of the method.

In addition to the initial HTS-KIN experiments, I have continued this project in order to both improve the methodology and advance the scope of our research. In continuing to characterize the five chosen hexamers past the initial experiments, we executed multiple turnover kinetics on the individual hexamers as a single species population. Interestingly, as single uniform populations, the relative rates of the variants do not replicate the results of HTS-KIN while in reactions where they are in competition, the results conform precisely to the expectations from the relative rate constants measured using the new method. The simplest explanation consistent with the alternative substrate kinetic model used to describe the reaction is that HTS-KIN measures effects on

V/K since substrates are in competition whereas for reactions performed at saturating,

uniform substrate concentrations the observed rate is determined by V. As described in

Chapter 3, the kinetic parameters V and V/K represent different rate limiting steps in the

E. coli RNase P kinetic scheme. These discoveries and the results explained in more

detail below, led to our interest in repeating the HTS-KIN experiment using single

turnover kinetics in which the effects of substrate variation on V and V/K can be

distinguished.

A complicating factor in the initial application of this method is that the pre-

tRNAs have additional nucleotides on their 5’ end that are used in subsequent RT-PCR

and Illumina sequencing steps. Because of the potential for these sequences to influence

the outcome of the experiment by forming alternative, inhibitory RNA structures, it is of

utmost importance to further investigate the effects of substrate structure and sequence on

an individual substrate basis in the course of future HTS-KIN experiments. Several

factors argue that the extended 5’ leader sequences are unlikely to interfere with RNase P

processing. First, pre-tRNAs can be encoded in polycistronic genes along with rRNA

and mRNA, as well as in single tRNA genes. These pre-tRNAs are separated from

transcripts containing mRNAs and other tRNAs primarily by RNase E (110,111).

Additionally, analysis of the bacterial genome sequences and the structures of pre-tRNA

precursors in vivo demonstrate that the leader sequence length can vary among precursor

tRNAs. Nonetheless, the potential for formation of alternative structures is fundamental

to the molecular biology of RNA and thus this issue needs to be properly evaluated.

Accordingly, we analyzed the multiple turnover kinetics of the L1-L5 leader sequence

variants, without the extended sequences and compare their processing rates.

P protein

protection

Figure 3-2: Hydroxyl radical protection analysis of pre-tRNA binding to E. coli P RNA and RNase P holoenzyme. Compiled protection data for nucleotides −10 to +35 shown on the secondary structure for pre-tRNA. Each nucleotide is displayed as a circle. The data for protection by P RNA are indicated by blue circles, and the data for RNase P holoenzyme are indicated by red circles. Adapted from Sun et al. 2010 (36).

Figure 3-3. The randomized portion of the pre-tRNAMET82 leader sequence, N(-3)-N(-8).

Image courtesy of Drs. Michael Harris and Ulf-Peter Gunther.

Experimental Design – As introduced above, my contribution has been the analysis of individual substrate 5’ leader sequence variants, however, it is necessary to review how they were identified using HTS-KIN in collaboration with the laboratory of Dr. Eckhard

Jankowsky. Briefly, to examine how the C5 protein from E. coli RNase P discriminates

between all possible sequence variants of its binding site, a population of pre-tRNAMET82

was synthesized in which the nucleotides that interact with the C5 protein were

randomized (Fig 3-3). An initial test of the randomized pool consisted of simple multiple

turnover kinetics in which the processing of the random RNA was compared with the

kinetics of the reference pre-tRNA, pre-tRNAMET82, alone (Fig 3-4). This experiment

showed a difference in processing rates between the randomized pool and a uniform population of pre-tRNAMET82. The conclusion from this result is that there must be

sequences that react faster/slower/differently than pre-tRNAMET82 and thus developing the

HTS-KIN method is expected to reveal the identity of sequences with reaction kinetics

distinct from the genomically encoded sequence. The processing rates of this population

of over 4,000 sequences were then measured under multiple turnover reaction conditions.

Because the sequence variants under these conditions are in competition and therefore are

limited by each other’s V/K values, we were able to directly observe the discrimination

by C5 for certain sequence variants in the ongoing reaction as further described below.

Multiple turnover kinetics with the randomized population of pre-tRNAs were

performed and relative rate constants determined by quantifying the change in the

number of specific sequence variants over time by analysis of the distribution of varients

using high-throughput sequencing (112,113). Results are presented as rk as defined

above as the ratio of the V/K. In this case the rk is computed for each sequence variant

relative to the encoded leader sequence for pre-tRNAMET82 (AAAAAG). Thus, a rk of 1

means that a particular sequence has the same V/K as the reference sequence and variants

with an rk >1 have larger V/K and variants with rk < 1 have a lower V/K. Preliminary

results (Fig. 3-5) were displayed in a histogram relative to the native sequence, pre-

tRNAMET82. It is apparent from these results that a significant number of sequence variants (~1/3) reacted faster than the pre-tRNAMET82 leader sequence (rk >1). This indicates that the physiological leader sequence, or genomically encoded leader sequence, is not an optimal sequence for the C5 protein subunit. In the C5 protein distribution there is a clear sequence logo from the fastest sequences and a less clear sequence logo from the slowest sequences (Fig 3-6). What is interesting from the standpoint of in vivo RNase

P function, is that none of the genomic sequences for pre-tRNA fall into the fast sequences, instead they all fall near the median of rk values. These observations are

similar to those seen in specific RNA binding proteins, showing similarities between

classically defined non-specific RNA binding proteins and specific RNA binding proteins

as pointed out by our collaborators in the Jankowsky laboratory. The clear difference

seems to be that the high affinity sequences for the specific RNA binding proteins are

physiological whereas in the RNase P non-specific example, they are not (114,115).

From this data, 5 sequences were selected for further study as shown in Table 3-1

and Fig 3-5. My contribution has been to analyze these individual sequence variants with

different rk values and examine their processing kinetics directly in order to validate the

quantitative HTS-KIN analysis.

Figure 3-4 – Difference between random pool and single substrate multiple turnover kinetics. Figure adapted from Guenther, Yandek, Niland, Campbell, Anderson,

Anderson, Harris and Jankowsky. Hidden rules govern discrimination by a non-specific

RNA binding protein.

Table 3-1. Observed rk values for hexamers selected for further kinetic study.

*Ref Sequence is AAAAAG

“R” Timepoint 1 Timepoint 2

Hexamer Exp. 1 Exp. 2 Exp. 1 Exp. 2

(L)

TTATAT 4.078 3.751 3.270 2.592

(L1)

TCAGAC 2.049 2.105 2.161 1.889

(L2)

ATTCAA 0.893 0.962 1.003 0.951

(L3)

CGTCAG 0.265 0.457 0.300 0.296

(L4)

CTCCTG 0.183 -0.572 -0.536 -0.396

(L5)

Figure 3-5. Histogram of distribution of random population in comparison to pre- tRNAMET82. The boxed sequences are the five hexamers selected for further evaluation. Adapted figure courtesy of Drs. Ulf-Peter Gunther and Eckhard Jankowsky.

Figure 3-6: The sequence logo of the fastest 1% of all sequences analyzed through the

HITS-KIN method. Adapted figure courtesy of Drs. Ulf-Peter Gunther and Eckhard

Jankowsky.

Results and Discussion

Competitive Multiple Turnover Kinetics of the Randomized Pool – To test the expectations regarding the relative rate constants of different substrate variants from the

HTS-KIN method, I executed multiple turnover experiments under V/K conditions using the holoenzyme and the randomized pool with the addition of one individual [32P]-

labeled substrate (L1-L5). Under these conditions the multiple turnover rate for each of

the individual hexamers are interrogated separately since it is the only radiolabeled

species in the population. The reactions were run under standard reaction conditions of

o 37 C, pH 8, with optimal metal and salt conditions (0.1 M NaCl and 17.5 mM MgCl2)

for the E. coli RNase P holoenzyme. Time points are acquired and the reaction stopped by addition of EDTA. Precursor and product were resolved on a denaturing PAGE gel

and the fraction of reaction was determined by phosphorimager analysis. The first 10%

of substrate processed is fit to a linear equation where the slope of the line reflects the

-1 observed initial rate (vobs nM s ) which is normalized to enzyme concentration in order to

yield the initial multiple turnover rate constant (v s-1). The results from these experiments

(Table 3-2.) show that the trend of fast to slower sequences relative to the reference

sequence of pre-tRNAMET82 is consistent with the expectations from the HTS-KIN

experiment. This result led to the question of whether or not these non-physiological pre-

tRNAs with their extended leader sequences would have the same kinetic profile when

their processing rate was looked at individually, i.e. not within the pool.

As described in detail above and in Chapter 1, substrates compete for processing

by RNase P as a function of their relative V/K values. Accordingly, the relative rate

constants determined using HTS-KIN are effects on V/K. Therefore the results above

were obtained in the context of competition between the individual radiolabeled substrate

and the rest of the RNAs in the population. As expected, the rate constants determined

directly are consistent with the relative rate constants determined using HTS-KIN. It follows, therefore, that analysis of the individual substrates as uniform populations at

saturating concentrations will reveal effects on V rather than V/K. Since the rate limiting

steps for V and V/K are different as described in Yandek et al., 2013, to determine the effects of leader sequence variation on V for the L1-L5 substrates, we ran the reactions

identically to the experiments above, except that uniform populations of individual pre-

tRNAs were analyzed.

Remarkably, the results obtained are displayed in Table 3-3 show that there is

little correlation of the relative V values compared to the predicted processing kinetics

(V/K) as seen in the HTS-KIN data and the validation in Table 3-2. This observation

further supports the conclusion that the data in Table 3-2 is representing V/K conditions,

whereas the data in Table 3-3 is not. This realization has led to an idea for a future

selection, which would be to repeat HTS-KIN analysis of the randomized pool under

single turnover reaction conditions. The rational is that under saturating enzyme

concentrations the reaction rate will reflect the activation energy between the bound

substrate and the transition state whereas under multiple turnover conditions the rate

constant measures reaction from free substrate and enzyme to regeneration of free

enzyme. Since these parameters measure different rate limiting steps, we predict that

there will be differences in the sensitivity to sequence variation between experiments

performed under these two conditions.

Table 3-2. Multiple turnover data for 1 mM randomized leader pre-tRNAMET82 and a spike of 32P L1-L5 against RNase P.

~v (s-1) Standard Deviation

Pool & L1 0.30 0.13

Pool & L2 0.12 0.02

Pool & L3 0.08 0.04

Pool & L4 0.06 0.03

Pool & L5 0.02 0.01

Table 3-3. Non-competitive multiple turnover data for each L1-L5 against RNase P

~v (s-1) Standard Deviation

L1 0.70 0.35

L2 0.07 0.04

L3 0.30 0.10

L4 0.35 0.08

L5 0.14 0.05

Effects of N(-3) to N(-8) randomization and N(-1) to N(-6) randomization on the

kinetics of processing of these populations by RNase P- To set the stage for analysis of

individual rate constants, we first analyzed the kinetics of RNase P processing of the N(-

3) to N(-8) randomized pool under single turnover conditions similar to the experiment

described in Figure 3-4 for the multiple turnover reaction conditions. We once again are

using pre-tRNAMET82 as our reference sequence, as well as the initial randomized pool

with the 6 nucleotides varied being in the N(-3) to N(-8) position. In addition we initiated the analysis of a second randomized pool designed to analyze both RNA-RNA and RNA-protein interactions. Since we know that there are direct contacts with the P

RNA and the leader sequence closer to the tRNA body, we logically chose to randomize the N(-1) to N(-6) position. This randomization ensures that the randomized portion of the sequence will affect both C5 interactions (N(-3) to approximately N(-8)) and P RNA interactions at N(-1) and potentially N(-2).

We repeated the experiment at two different enzyme concentrations to ensure we were fully saturated. Interestingly, the results shown in Table 3-4 reveal a different result than observed in the previous multiple turnover experiments. In the single turnover experiments, the wild type sequence, or reference pre-tRNAMET82, has the same rate constant as the original randomized pool, whereas the second randomized pool (N(-1) to

N(-6) positions) encompassing both C5 and P RNA known interactions differed considerably. Therefore, we conclude that V is affected when these positions are altered in the sequence and we can move forward with the single turnover HTS-KIN analysis to obtain very useful information on the sequence effects on the cleavage step.

Interestingly, however, there is little effect of leader sequence randomization N(-3) to N(-

8) on the kinetics of the pool under single turnover conditions which contrasts to the large

effect under multiple turnover conditions. This result is consistent with the expectation

the primary effect of the protein subunit is on substrate association.

Table 3-4: Single turnover reaction rates of a uniform pre-tRNA control and pre-tRNA

pools randomized at the N(-1) to N(-6)1 and N(-3) to N(-8)2 positions. (1 nM substrate

and 100 nM RNase P Holoenzyme at pH 6).

Substrate 100 nM Holoenzyme 500 nM Holoenzyme

pre-tRNAMET82 0.06 s-1 + 0.01 0.05 s-1 + 0.01

pre-tRNAMET82R1_61 0.02 s-1 + 4e-3 0.02 s-1 + 6e-4

Pre-tRNAMET82R3_82 0.04 s-1 + 0.01 0.06 s-1 + 3e-3

Competitive Multiple Turnover Reactions of L1-L5 and pre-tRNAMET82+2 – Effects of leader sequence length on rk. - As described above, in order to analyze the sequence distribution of the remaining substrate population by Illumina sequencing an additional

21 nucleotide sequence was necessarily added to each pre-tRNA. To test whether there is

any interference due to this extended sequence, we compared the reaction kinetics of the

pre-tRNA L1-L5 containing the additional 21 nucleotides to that of the same substrates with shortened sequences. Both sets of experiments were performed under standard reaction conditions as described above with the results shown in Table 3-1 and Table 3-

2. These experiments are in fact, a simplified example of the HTS-KIN randomized

pool. Instead of looking at a population consisting of over 4,000 sequences, we are

looking at only two different sequences in competition with each other. Under these

conditions we are measuring the individual pre-tRNAs V/K, due to the competition of

relative rate constants as described more completely in Chapter 2. We once again are

utilizing the ability to attach two additional nucleotides to a sequence in order to clearly

separate two leader sequences through denaturing PAGE.

From these results two things are apparent; first, the L2 substrate lacking the 21 nucleotides does not conform to the relative rate constant expected from HTS-KIN and the direct measurement of its rate constant in competition with the random pool; second, the range of effects of leader sequence variation is smaller with differential effects for different leader variants. These initial results raise the question of whether some variants, such as L2, interact with other members of the population that influence their observed rate constant. Furthermore, the effect of the additional 5’ leader sequences in altering the effects of proximal leader sequence variation is unexpected and may reflect the contribution of secondary structure formation which is influenced by N(-3) to N(-8)

sequence identity.

TABLE 3-5: rk values determined for L1-L5+21 variants relative to pre- tRNAMET82+2

Substrate rk Standard deviation

pre-tRNAMET82 L1 0.61 0.05

pre-tRNAMET82 L2 0.05 8.0E-3

pre-tRNAMET82 L3 0.57 0.04

pre-tRNAMET82 L4 0.41 0.06

pre-tRNAMET82 L5 0.37 0.01

TABLE 3-6: rk values determined for L1-L5 substrates lacking the additional +21 leader nucleotides relative to pre-tRNAMET82+2

Substrate rk Standard deviation

pre-tRNAMET82 L1 1.5 0.2

pre-tRNAMET82 L2 1.9 0.8

pre-tRNAMET82 L3 0.7 0.2

pre-tRNAMET82 L4 1.3 0.6

pre-tRNAMET82 L5 0.6 5.0E-2

Chapter 4 - Discussion

Ribonuclease P had been used extensively as an experimental system to study

RNA folding, catalysis, molecular recognition and RNA-protein interactions. These studies have provided much insight into substrate recognition and the catalytic mechanism of this essential enzyme. The kinetic mechanisms for the processing of model substrates has been well established by the Fierke laboratory and other groups

(Hartmann, Kirsebom, Harris), and have provided insight into the role of both subunits of this enzyme. The roles of metal ions in folding and catalysis have been identified, as have high resolution three dimensional structures of both subunits of this enzyme.

Despite all these advances, we still lack a fundamental understanding of the functional properties of the enzyme that define its biological role. The purpose of this thesis project was to explore this aspect, and begin to transition RNase P research from using ideal model substrates and reaction conditions to a more biologically relevant understanding of how this enzyme functions as a multiple turnover enzyme in which numerous alternative substrates compete for processing. This is a general property of many enzymes involved in RNA processing and the information gained has shed light on multiple substrate recognizing properties of enzymes in general. We initially set out with the goal of defining the kinetic mechanism by which RNase P recognizes multiple substrates, and using that insight to understand how the kinetic parameters of different substrates affect their steady-state abundance with the hope that these studies would significantly advance our understanding of the regulation of tRNA processing and the role RNase P plays in it.

To achieve this goal, we first compared the multiple turnover reaction schemes of two representative canonical and non-canonical pre-tRNAs. Next, we adapted internal

competition kinetics to analysis of pre-tRNA processing by RNase P and tested several fundamental aspects of the simple internal competition kinetics model. We used this new approach to measuring relative processing rate constants to compare the V/K values for a

range of different canonical and non-canonical pre-tRNAs. The observation of near uniform V/K values throughout the pre-tRNAs tested despite variation in sequence and structure is related to similar properties of other multiple substrate reaction systems like the ribosome, helicases and in the function of splicing enhancers. The information gained refines our understanding of the potential effects of conformational changes on

RNase P substrate specificity. Building on this foundation we applied the internal competition model to a complex population of thousands of substrate variants in the process of testing the effect of 5’ leader sequence variation on processing efficiency. In the process of validating the results from this method by analysis of uniform substrate populations we discovered potential differences in the kinetic mechanisms of different substrate variants. Testing this hypothesis and understanding how kinetic complexity impacts the accuracy of internal competition kinetic analysis are important future directions. These advances and their implications for RNase P and more broadly RNA processing enzymes in general are discussed, in turn, in the following sections.

Comparison of the multiple turnover kinetic schemes of representative canonical and non-canonical pre-tRNA substrates - As described in Chapter 1, RNase P processed multiple, structurally distinct substrates which fall into two general categories, canonical and non-canonical. Nonetheless, RNase P must process all pre-tRNAs in a cell.

Therefore, understanding the kinetic mechanisms by which different substrates compete

for processing by RNase P is important for understanding its function in vivo. This point

is similarly true for the broad class of RNA processing enzymes that recognize multiple

cognate substrates, and so the insights gained are expected to be broadly applicable to

this general class of molecular recognition. In Chapter 2, steady state kinetic analyses of

two representative canonical and non-canonical pre-tRNA substrates were used to provide a framework for establishing a basic alternative substrate kinetic model for understanding pre-tRNA competition for processing by E. coli RNase P. Using a combination of steady state, pre-steady state and single turnover kinetic experiments, we determined that for both substrates the rate limiting step for V is the substrate cleavage step, however, the rate limiting step for V/K is substrate association. Because substrate binding is essentially irreversible relative to cleavage, both substrates compete for RNase

P processing based on their relative rates of association.

These results are important for the following reasons. The results reveal that

RNase P is a highly efficient enzyme. Since dissociation is slow relative to catalysis, every productive collision of the enzyme with the substrate results in product formation.

If substrate dissociation were fast relative to catalysis then the substrate may have to collide many times with the enzyme before being converted to product. Along these lines we observed that the V/K or second order rate constant for the E. coli RNase P enzyme has a magnitude (105 – 106 M-1s-1) that is similar to other RNase P enzymes and other

macromolecular RNA processing reactions. Importantly, we know that when substrates

compete, the competition is governed by the relative V/K values, so this predicts that both

the canonical and non-canonical substrates will be processed at equivalent rates in

reactions containing multiple substrates. Another important implication of the internal

competition kinetic model developed in Yandek et al., 2013, is that the presence of

additional substrates will similarly compete for association with RNase P and reduce the

observed rates of processing of all substrates in the population. However, the presence of

additional substrates should not affect the relative rate constants for any two substrates in

the reaction since both compete equally with the remaining population of alternative pre-

tRNAs. Testing these predictions became the essential next step in understanding the

alternative substrate kinetics of RNase P.

Testing the fundamental features of a simple alternative substrate kinetic model for

RNase P processing of multiple pre-tRNAs in vitro - Using internal competition reactions, in which two or more substrates are present in the same reaction, we set out to validate the basic features of the alternative substrate kinetic model. A key technical advance was the application of substrate with additional dinucleotide sequence ‘tags’ in the 5’ end which allowed the products of alternative substrates to be quantified independently by PAGE analysis of radiolabelled pre-tRNA followed by phosphorimager analysis. Extensive validation that the effects of these differences in substrate structure did not interfere with reaction kinetics was required as described in Chapter 2. This

system has proved to be highly valuable for scoring the accumulation of alternative

products in multiple substrate reactions and has now been adapted in several contexts for

alternative substrate kinetics in the laboratory.

The results with RNase P demonstrated that the relative rates of processing of two

substrates directly reflect their relative V/K values (i.e. the specificity constant) and their

concentrations as predicted. This result is important since it indicates that intrinsic V/K

values can be determined by simply comparing the kinetics of two alternative substrates

as long as the intrinsic V/K of one of the substrates is known. This issue becomes

essential in analyzing large populations in which one substrate is used as a reference.

Also, the presence of additional substrates reduced the observed rate of processing of

individual pre-tRNAs, but did not affect the observed rk for the two substrates being compared. This is a key prediction of the internal competition model since each alternative substrate should act as essentially a competitive inhibitor for all of the other substrates in the reaction by simply depleting the concentration of available enzyme.

However, it is critical that the presence of multiple alternative substrates not interfere with the kinetics of each other. If this were to be the case because of the ability of substrates to interact at a second enzyme binding site, or with each other, then the further application of internal competition in this system would likely be prohibitively complex.

Thus, for the set of substrates examined here, the E. coli RNase P enzyme follows simple alternative substrate kinetics; and, assuming the results for pre-tRNAMETf47 and pre-

tRNAMET82 are representative, the competition is governed by similar association rate constants. The results represent an important advance because they shed light on the biological function of RNase P in tRNA biosynthesis, and provide a framework for quantifying relative processing rates in complex populations of competing tRNA precursors.

Comparison of relative V/K values for selected alternative substrates - Using the internal competition kinetic model as a basis, we next compared the relative rate constants for a range of different canonical and non-canonical pre-tRNAs. As indicated above, this aspect of RNase P function is essential but poorly explored. Biosynthesis of

the translational machinery, including tRNA, consumes most of the resources in rapidly dividing cells (63). Importantly, the distribution of tRNA species is not uniform. The tRNAs that are present at higher concentrations are those that recognize the preferred codons of the genes encoding the highly expressed proteins of rapidly growing bacteria

(33,34). This correspondence of codon usage and tRNA abundance is believed to maximize translation efficiency and therefore growth rates (35,116). The turnover of

mature tRNA does not appear to be a major mechanism for the modulation of tRNA

abundance (30). Thus, the steady state levels of tRNAs are largely set at the

transcriptional level. In E. coli, tRNA and rRNA biosynthesis are tightly regulated by the

stringent response, which senses the accumulation of uncharged tRNA and negatively

regulates the initiation of transcription of tRNA and rRNA operons (32). The pre-tRNA

substrates for RNase P can be transcribed individually, or as part of polycistronic RNAs

containing additional pre-tRNAs, rRNA or mRNA (63,64). Precursors to individual

tRNAs that are part of a rRNA primary transcripts are thought to be released during the

course of rRNA maturation by endonculeolytic cleavage by RNase III or RNase E (117).

Separation of individual tRNA precursors from transcripts containing mRNAs or other

tRNAs is accomplished primarily by RNase E (110-111).

The narrow range of V/K values for the model pre-tRNA substrates observed in

our recent studies suggests that the relative rates of processing different pre-tRNAs in the

cell will be proportional to the abundance of each precursor, assuming minimal influence

of additional flanking RNA sequences. From this perspective, the alternative substrate

kinetics of RNase P are tuned to be directly and uniformly proportional to rates of

precursor biosynthesis. It follows that the enzyme has a negligible role in influencing the

steady state abundance, but rather functions to maintain the distribution set by precursor

biosynthesis despite significant differences in the structure and context of each individual

substrate.

This model is specific to pre-tRNA substrates and indeed, there may be

circumstances under which the rates of RNase P processing are modulated in order to

contribute to regulation of gene expression. There are non-pre-tRNA substrates of RNase

P including riboswitches (118-120) that are likely to have different kinetic properties

related to their unique function and so are not accounted for in the scenario described

above for pre-tRNA substrates. Additionally, the context of different RNase P substrates

within larger polycistronic transcripts may influence relative processing rates (64) and

clearly deserved further attention. For example, a suppressor tRNA substrate the length

of the leader sequence has an effect on cell growth potentially due to effects on in vivo

processing efficiency (121). Recently, Kushner and colleagues have identified two tRNA

polycistrons in which RNase P is the primary processing event separating the individual

tRNA units (122,123). RNase P cleaves 4-7 nucleotides downstream of the CCA determinant generating a substrate for additional processing nucleases in the substrate for pre-tRNALEU5 (124). The structures and binding modes that underlie RNase P cleavage at alternative sites in non-pre-tRNA substrates are poorly understood. Both bacterial

(73,98) and eukaryotic (125-126) RNase P have been observed to catalyze cleavage at multiple sites distinct from ‘authentic’ pre-tRNA processing sites, and these forms of alternative specificity clearly deserve further attention. For example, we note that the cleavages of the pre-tRNASER80 substrate demonstrated here occur at a V/K that is within

the range of processing at the correct site.

Parallels between RNase P processing and alternative substrate recognition by other enzymes - The results provide insight not only into issues specific to RNase P function, but also draws attention to parallels with the recognition capabilities of the ribosome.

Studies by Uhlenbeck and colleagues demonstrated uniform affinities, dominated by similar association constants, of EF-Tu for aminoacyl-tRNAs despite differences in tRNA and amino acid structure and chemical properties (127-128). Detailed analysis of misacylated tRNAs revealed thermodynamic compensation between the contributions of the amino acid and tRNA moieties of the aminoacyl-tRNA to binding. The ribosomal A- site shows specificity for both the amino acid and the tRNA portions of their aminoacyl- tRNA (aa-tRNA) substrates (129,130). Structure-function analysis of chimeric tRNAs indicated that each tRNA sequence has coevolved with its anticodon to tune ribosome affinity to a value that is the same for all tRNAs (131). Thus, the observation of similarly uniform rates of pre-tRNA processing by RNase P provides an additional example of the tuning of RNA recognition to accommodate the structural variation in tRNA necessary for its function in aminoacylation and translation.

Conformational changes are often a key component of molecular recognition by

RNA processing enzyme including RNase P. The impact of kinetic complexity on the internal competition model is therefore an important aspect of broadly considering the implication of the studies described herein. Fierke and colleagues demonstrated a conformational change during substrate binding by B. subtilis RNase P (39,132). Given the potential for the induced fit model to contribute to specificity, it is important to consider how the occurrence of a conformational change could impact alternative substrate competition. We assume that for cognate pre-tRNAs, any conformational

change upon binding is favorable, while for non-cognate RNAs this step is unfavorable.

As previously described, induced fit decreases the V/K for both a cognate and a non-

cognate substrate when the chemical step is rate limiting and therefore does not

intrinsically provide specificity (48). On the other hand, a conformational change can

provide specificity when a binding step or product release step is rate limiting for the

cognate substrate while the chemical step is rate limiting for a non-cognate RNA (48).

As suggested by our results, association is likely to be broadly rate limiting for pre-tRNA

processing by E. coli RNase P. Thus, the presence of a conformational change could

clearly enhance specificity over non-cognate substrates.

Application of internal competition kinetics to the analysis of complex substrate

populations - Many RNA binding proteins are non-specific in their association with their

biological substrates. RNase P is a prime example of this as in Chapter 2 it has been

shown to process substrates uniformly, with association to be the rate-limiting step.

Whether sequence variation has any effect on the way these non-specific proteins have affinity for their substrates is yet to be understood. Through collaboration with the

Jankowsky laboratory this has been looked at in great detail through the design of a novel assay, High Throughput Sequencing – Kinetics (HTS-KIN). A key component of this analysis is the determination of relative V/K values for a large population of pre-tRNA substrates using the internal competition model developed and described, above. This initial HTS-KIN experiment has established sequence determinants in the leader sequence of pre-tRNAs that represent a “fast” sequence and a “slow” sequence. That being said, it is unknown why E. coli C5 responds to these sequences. These sequence determinants are not found in physiological genomic pre-tRNA sequences. Do these

94 sequence determinants represent sequences now defunct from evolutionary growth? This question is unanswered as of yet, but it would seem that evolution has made processing rates the same for RNase P possibly because there are so many different substrates. This would allow for processing to be controlled at the transcriptional level, and not due to certain substrates binding too tightly or too weakly.

Validation of results from HTS-KIN reveals apparent effects of different rate limiting steps and RNA structure on sensitivity to substrate variation - The novel method outlined in Chapter 3 has given great insight into RNase P and its function as a non- specific RNA binding protein. Importantly, the results raise the question of whether differences in rate limiting step will affect the distribution of rate constants for individual sequences. Analysis of individual leader sequences as uniform populations show differences in the relative rate constants when measured under saturating substrate concentrations. Alternative substrate kinetics dictates that substrates compete relative to their V/K values while saturating substrate reactions measure effects on V. Since detailed kinetic analysis of both canonical and non-canonical pre-tRNAs showed that V/K is limited by substrate association step while V reflects the rate constant for catalysis.

Therefore, it follows that HTS-KIN experiments performed under single turnover experiments may yield different results. Indeed, initial experiments comparing the kinetics of the random population are consistent with this expectation. The effect of additional 5’ leader sequences on modulating the effects of proximal leader sequence variation points to the potential for RNA secondary structure to influence leader sequence recognition. Therefore, comparison of results obtained with different, additional 5’

95 leader sequences in order to better understand these effects is a focus of current experiments in the laboratory.

Chapter 5 – Future Directions

Single turnover HTS-KIN kinetics comparing two different +21 extended sequence of the randomized pool in the N(-1) to N(-6) position - The preliminary data obtained through single turnover experiments using two different randomized pools of pre-tRNA have given us reason to pursue this as our next iteration of HTS-KIN experiments.

Following up on this preliminary data is the first order of business for future experiments.

We hope to maximize the insight obtained from this experiment by changing not one, but two variables. First, we ideally want to explore the effect of the additional +21 nucleotides to the leader sequences that are required for Illumina sequencing. To do this, we want to completely redesign a new sequence that will essentially be the inverse of the current sequence. With the two different reference pre-tRNAs, we want to randomized the N(-1) through N(-6) positions. We saw in our single turnover controls that we were clearly able to distinguish between the randomized populations of this sequence from that

of the N(-3) to N(-8) position population as well as from the reference sequence. We

hypothesize this is because the randomized area encompasses both P RNA/pre-tRNA

interactions and C5 protein/pre-tRNA interactions. By examining the differences in results when measuring V vs V/K we think we will gain a much greater insight into how the enzyme is reacting with these competing substrates.

Competitive Multiple Turnover Reactions– Varying Mg2+ Concentrations - An

important observation from the kinetic work presented in Chapter 2 is that there is a large

commitment to catalysis for both non-canonical and canonical substrates. This indicates that effects of sequence variation observed in HTS-KIN experiments which measure

differences in V/K are effects on substrate association rate constants. In order to gain a

complete understanding of RNase P molecular recognition it will be necessary to

compare the effects of substrate structure variation on equilibrium substrate binding and

on the rate constant for catalysis. To reveal effects on equilibrium substrate binding

affinity we reasoned that lowering the divalent metal ion concentration could weaken

substrate binding and accordingly have a great effect on the results. Experiments from

the Fierke laboratory have shown tighter binding at higher divalent metal ion

concentrations and as expected more dramatic differences in kinetic properties are

present when reactions are performed under more natural MgCl2 concentrations, i.e., 2.5 mM versus 17.5 mM in standard in vitro assays (133).

Explore possibility of in vivo experiments – We are motivated to answer a simple question- Do the results in the test tube have any relationship to the behavior of the enzyme in vivo. Therefore, we have begun exploring the possibility of taking our HTS-

KIN experiments in vivo. To do this we need to consider a number of steps to ensure we

understand the results we are seeing. To begin, we would pick a portion of pre-tRNA to randomize, of which the most logical choice for initial experiments would be in the leader sequence. The rationale behind that we have already established results in the in vitro system and this would be an excellent way to validate our previous findings. The next step would be to choose a pre-tRNA to monitor through the reaction. This takes a bit more thought, but our initial idea would be to randomize a well characterized suppressor tRNA. This way we would have information on which steps of a cellular reaction we would be monitoring and more accurately track reaction progress than if we used an ordinary pre-tRNA.

Once we have figured out the logistics of which pre-tRNA to randomize and the exact location of mutation, we can proceed with designing the initial experiments and controls. First we need to design a plasmid that contains our mutated pre-tRNA, which we can successfully do by utilizing the well-developed ampicillin or kanamycin technique where we would insert in our plasmid an ampicillin resistant gene and grow up our cells on ampicillin resistant plates to ensure that any colonies grown would contain our mutated pre-tRNA. In order to further select our mutant pre-tRNA we would want to incorporate a temperature sensitive replicon (134). This whole process is referred to as

“chromosomal manipulation” (134). What this refers to is the knocking out of a wild type gene, in this case, the selected suppressor tRNA and replacing it with one we have designed with the optimal randomized sequence as well as a temperature sensitive replicon. We can then grow our E. coli cells that have been transformed at a non- permissive temperature to ensure that the only cells that survive have incorporated our desired pre-tRNA mutant. In this way we will be able to test the function of our mutant pre-tRNA in living cells. We can then evaluate our expression through northern blot analysis. Once we have established a system where we can monitor our mutant pre- tRNA we are confident we will be able to move our HTS-KIN experiment in vivo.

Chapter 6 - EXPERIMENTAL PROCEDURES

Methods in Chapter 2

RNA synthesis and RNase P holoenzyme reconstitution- E. coli P RNA and pre-tRNAs were generated by in vitro transcription from cloned DNA or PCR DNA templates. The pre-tRNAMETf47 and pre-tRNAMET82 substrates were synthesized from plasmids pre- tRNA605 and pre-tRNA608, respectively, as previously described (39). The pre-

tRNAHIS37, pre-tRNAGLN85, pre-tRNAGLY62, pre-tRNASER80, pre-tRNALEU76, and pre-

tRNAILE1 substrates were synthesized from PCR products generated from E. coli genomic

DNA using primers that introduce a T7 promoter and nine nucleotides of 5’ leader

sequence in order to generate the RNA sequences shown in Fig. 2-2:

pre-tRNAGLN85 F5’TAATACGACTCACTATA-GG-CCGGTTAT-TGGGGTATCGCC3’ R5’TGGCTGGGGTACCTGGATTCG3’ pre-tRNAGLY62 F5’TAATACGACTCACTATA-GG-ATCTCGAA-GCGGGCGTAGTTC3’ R5’TGGAGCGGGCGAAGGGAATCG3’

pre-tRNASER80 F5’TAATACGACTCACTATA-GG-GTCATTCC-GGAAGTGTGGCCG R5’TGGCGGAAGCGCAGAGATTCG3’ pre-tRNAILE1 F5’TAATACGACTCACTATA-GG-ACCTCTAC-AGGCTTGTAGCTC3’ R5’TGGTAGGCCTGAGTGGACTTG3’

PCR reactions contained 100 mM KCl, Tris pH 8, 5 mM MgCl2, 100 µM dNTP

and were performed at 95oC, 30 seconds, 60oC, 60 seconds, and 72oC, 90 seconds for

100

thirty cycles. The resulting DNA was purified by phenol and chloroform extraction and

precipitated with ethanol as described previously (40).

In vitro transcription reactions contained ca. 10 µg plasmid or PCR template, 5 mM

each NTP, 50 mM Tris-HCl pH 8, 17.5 mM MgCl2, 10 mM DTT, 2 mM spermidine, and

1 unit/µL T7 RNA polymerase (Ambion) and were incubated overnight at 37o C. The

resulting RNA products were recovered by phenol/chloroform extraction and ethanol

precipitation. The full length transcription products were purified by PAGE as described

(40).

Kinetic analyses of single pre-tRNA substrate reactions- The pre-tRNA substrates were 5’-end labeled with [γ-32P] ATP and T4 polynucleotide kinase after dephosphorylation by alkaline phosphatase. RNase P holoenzyme reaction kinetics were measured under the following conditions: 50 mM Tris-HCl pH 8, 100 mM NaCl, 17.5

32 mM MgCl2, and 0.005% Triton X-100. The P RNA and 5’- P-end labeled pre-tRNA

were renatured separately in the above buffer (omitting the Mg2+) by incubation at 95o C

o for 4 minutes followed immediately by incubation at 37 C for 10 minutes. MgCl2 was

added to a concentration of 17.5 mM and the incubation continued for an additional 10

minutes. C5 protein was purified and activity was tested by titrations into multiple

turnover reactions containing a constant concentration of P RNA as described previously

(82). C5 protein was added to a concentration equal to that of P RNA and the 37oC

incubation continued for an additional 10 minutes. Reactions were initiated by mixing

equal volumes of enzyme and substrate. Aliquots were removed at specific time intervals

and quenched with 50 mM EDTA. The residual pre-tRNA substrate and 5’ leader

cleavage product were resolved by denaturing PAGE (15%). The conversion of substrate

101

to product was quantified by phosphorimager analysis using a Molecular Dynamics

Storm system, and ImageQuant software. The fraction of reaction was determined as F =

[pre-tRNA]/([pre-tRNA] + [leader]) where [pre-tRNA] and [leader] are the intensity of

the pre-tRNA and leader bands, respectively. Data analysis and fitting were performed

using MSExcel and Origin 8.0 (OriginLab).

For multiple turnover reactions initial rates were measured and plotted versus pre-

tRNA concentration and fit to the Michaelis-Menton equation as described in Chapter 2.

Transient kinetic experiments were performed in a similar manner, with the substrate and

enzyme concentrations indicated in the Figure Legends. Single turnover kinetic analyses

were performed as previously described (83) using the following reaction conditions: 50 mM MES pH 6, 100 mM NaCl, 17.5 mM MgCl2 and 0.005% Triton X-100. F was

plotted versus time and fit to a single exponential function,

-kt F = Fo - Ae Equation 8

where Fo is the experiments were measured using the single turnover conditions

described above at pH 6 with either 1 nM pre-tRNAMETf47 or pre-tRNAMET82 and 100 nM

RNase P. At 30 seconds after initiating the reaction the volume was divided in half. One

aliquot was added to a tube containing a substrate quench giving a final concentration of

5 µΜ B. subtilis pre-tRNAASP. Both reactions were continued and the kinetic data both

pre- and post-chase were fit to Eq. 8 (84).

102

Determination of relative rate constants by internal competition- In order to detect the formation of products from two substrates independently in the same reaction, pre- tRNAMETf47 and pre-tRNAMET82 were modified by addition of two extra G nucleotides to

the 5’ end of the leader sequence giving rise to pre-tRNAMETf47(+2) and pre-

tRNAMET82(+2). The two additional residues allow their products to be separated on 15%

PAGE and quantified independently from the products of the other pre-tRNAs used in this study.

Internal competition reactions contained two, three or eight pre-tRNAs as indicated in the text and legends to Figs. 2-6-9. Reactions containing both pre- tRNAMETf47 and pre-tRNAMET82 at a range of concentrations from 10 – 100 nM were

performed with one or the other substrate containing the two extra G residues in the 5’

leader. Additional reactions containing pre-tRNAMETf47 and pre-tRNAMET82(+2) at 100

nM in the presence of increasing concentrations of non-radiolabeled pre-tRNALEU76 10 –

3000 nM were also analyzed by monitoring the formation of the 5’ end labeled pre-

tRNAMETf47 and pre-tRNAMET82(+2). Similarly, reactions containing all eight of the substrates shown in Fig. 2-2 were conducted with each pre-tRNA present at 100 nM (800 nM total). For these reactions, trace concentrations of radiolabeled reference substrate pre-tRNAMET82(+2) and one of the remaining seven substrates were included to follow

product formation.

Relative rate constants (rk = (V/K) / (V/K)reference; see below) were determined using analytical methods based on Eq. 1 and Scheme 2-1, as described in the following sections.

103

Methods in Chapter 3

E. coli RNase P holoenzyme and RNase P RNA were prepared and tested for integrity as

described (1,2). The pre-tRNAMET82 substrates contain 8 nucleotides of the genomically encoded leader and 21 nucleotides at the 5' end for the Illumina sequencing. These pre- tRNAMET82 were generated by in vitro transcription from DNA generated by PCR

amplification of the pre-tRNAMET82 gene (PMET82). The forward primer introduced the

T7 promoter sequence and the additional 21 nucleotides.

The pre-tRNAMET82 substrate population with randomized leader sequence N(-3) to N(-8)

was generated using a primer where this region (NNNNNN) was randomized.

The following PCR primers were used:

pre-tRNA Met82F

5’TAATACGACTCACTATA-GGGAGACCGGAATTCAGATTG-ATG-AAAAAG-

ATGGCTACGTAGCTCAGTTGG

pre-tRNA Met82FEco

5’GGGTTAACC-TAATACGACTCACTATA-GGGAGACCGGAATTCAGATTG-

ATG-AAAAAG-ATGGCTACGTAGCTCAGTTGG

pre-tRNAMet82Frandom

5’TAATACGACTCACTATA-GGGAGACCGGAATTCAGATTG-ATG-NNNNNN-

ATGGCTACGTAGCTCAGTTGG

pre-tRNAMet82R

5’TGGTGGCTACGACGGGATTC

104

pre-tRNAMet82 RBbs

5’CGGGATCCGAAGACAG-TGGTGGCTACGACGGGATTC

PCR protocol: 95° C, 2 min; 30 cycles (95° C, 30 s at 55° C, 45 s at 72° C), final

extension at 72° C for 5 min. The PCR products (142 bp) were extracted with phenol and

chloroform and recovered by ethanol precipitation. PCR products for the pre-tRNAMET82

DNA were amplified with the pre-tRNA Met82FEco and pre-tRNAMet82RBbs primers,

which include BamH1 and Eco R1 restriction sites. The PCR product was digested with

these enzymes and cloned into pUC19 that had been digested with EcoRI and BamH1.

The PCR product was digested with BamH1 and cloned into pUC19 that had been

digested with EcoRI and BamH1. The resulting plasmid, PRE-TRNAMET82(+21), was

digested with BbsI to yield the template for the in vitro transcription with the correct pre-

tRNAMET82 3’ end. In vitro transcription was performed in a volume of 400 μL with 20-

15 μg of PCR template or cloned plasmid DNA template, 400 units T7 RNA polymerase

(Ambion), 0.01 unit yeast pyrophosphatase, 0.5 mM rNTP, and the reaction buffer supplied by the polymerase manufacturer supplemented with 2.5 mM MgCl2. Reactions

were incubated overnight at 37° C. The full length RNA was purified on 8% denaturing

PAGE, as described (50,82). Recovered pre-tRNAs were dephosphorylated using calf

intestinal phosphatase and 5’ end labeled with 32P using [γ-32P]-ATP and T4 polynucleotide kinase. For the HITS-Kin experiments, the RNA was uniformly labeled by including [γ-32P]-GTP in the in vitro transcription reaction and reducing the rNTP concentrations to 100 μM.

105

RNase P processing reactions for HTS-KIN- Multiple turnover reactions were

performed in a buffer containing 50 mM Tris-HCl pH 8.0, 100 mM NaCl, 17.5 mM

MgCl2, 0.005% Triton x-100, with 1 μM pre-tRNA and 5 nM E. coli RNase P holoenzyme (1:1 ratio of P RNA and C5 protein). Equal volumes (40 μL) of enzyme and radiolabeled substrate at 2x their final concentrations were prepared in reaction buffer and combined to initiate the reaction. Aliquots (5 μL) were removed at the times indicated to achieve 5 % to 30 % substrate conversion. The reactions were quenched by addition of a buffer (5 μL) containing formamide and 100 mM EDTA. pre-tRNA and reaction products were resolved on 10% denaturing PAGE. The fraction product formed was determined with a PhosphorImager (GE) and the ImageQuant software. Precursor bands in the gel were located by exposure to X-ray film and were excised and eluted (50).

Eluted RNA was extracted with phenol and chloroform, and recovered by ethanol precipitation. Relative rate constants for defined pre-tRNAMET82 substrates were

determined in reactions containing 1 μM of the pool of randomized pre-tRNAMET82,

spiked with trace amounts (< 0.1 nM) of the respective radiolabeled L1-5 substrate. Time

courses of the reactions were followed as described above and apparent rate constants

were determined from plots of product accumulation over time (50). As outlined below,

the ratio of the observed rate constants is rk, since in competition kinetics substrates at

the concentrations used behave as V/K systems.

Primers Used for HTS-KIN Validation and Further Experiments:

Primers for PCR amplification of template for pre-tRNAMET82 leader sequence mutant

RNA transcription:

106

Basic primer design—

T7 Promoter randomized seq tRNA complementary seq

5’-TAA TAC GAC TCA CTA TA – GG – NNNNNN – AT – GGC TAC GTA GTT

CAG TTG GTT AGA G – 3’

DNA templates for substrates L1 to L5 contained the following C5 binding sites:

L1: TTATAT, L2: TCAGAC, L3: ATTCAA, L4: CGTCAG, L5: CTCCTG.

DNA PRIMERS:

PT608-L1; 5’TAATACGACTCACTATAGGTTATATATGGCTACGTAGTTCAGTTGGTTAGA G3’

PT608-L2; 5’TAATACGACTCACTATAGGTCAGACATGGCTACGTAGTTCAGTTGGTTAGA G3’

PT608-L3; 5’TAATACGACTCACTATAGGATTCAAATGGCTACGTAGTTCAGTTGGTTAGA G3’

PT608-L4; 5’TAATACGACTCACTATAGGCGTCAGATGGCTACGTAGTTCAGTTGGTTAGA G3’

PT608-L5; 5’TAATACGACTCACTATAGGCTCCTGATGGCTACGTAGTTCAGTTGGTTAGA G3’

Single turnover kinetics and multiple turnover kinetics were done the same as described in the Experimental Procedures section for Chapter 2. The pre-tRNAMET82 randomized in

N(-6) to N(-1) positions was generously donated by fellow graduate student Courtney

Niland.

107

Appendix

The definition of V and V/K in modern enzyme kinetics - The debate about “proper”

nomenclature for various kinetic terms in relation to enzyme kinetics has been around for

many decades. In particular, it can be noted that when Briggs and Haldane introduced

the steady-state hypothesis the confusion over what the and showed that the assumption

of rapid-equilibrium was not essential for the Michaelis-Menten equation to be applicable

to an enzymatic reaction (88,135,136). This lead to the question of what exactly the

Michaelis-Menten constant Km or K, really means in terms of fundamental properties of enzymes. The confusion over this issue is related to the meaning of kcat/Km, or V/K and

raised the further question of which definition is most useful for exploring the enzyme

kinetics of competition between alternative substrates by RNase P.

In order to understand the competition between alternative ptRNAs in a mechanistically consistent and quantitative manner, we needed to adapt to a more universal way of looking at kinetic parameters which has been clearly outlined by

Cleland (90,91,97,137). Here we have again two fundamental kinetic constants, which were deemed V/K and V which represent the apparent rate constants at very low and very high substrate concentration. Therefore, if we consider our kinetic scheme shown in

Chapter 1, scheme 1-2, the definition of V/K is determined by the rate limiting step from

free enzyme E up to and including the first irreversible step, product release, or

regeneration of free enzyme (88,137). V is defined by everything from the enzyme- substrate complex onwards to reformed free enzyme (137).

108

Alternative substrate kinetics - The simple model describing the kinetics of alternative substrates was developed in several sources (87,138). The equations for measuring

relative rate constants for two substrates from analysis of substrate and product ratios are

reproduced from Cleland where they are used to measure kinetic isotope effects (90).

The following description presents a consistent nomenclature for the equations used for

data analysis and their application to measure relative rate constants of RNA processing

reactions as described in Chapter 2. As seen in scheme 2-1, a single population of

enzyme (E) combines with multiple pre-tRNA substrates (S1, S2, S3 . . . Si) to form individual ES complexes (ES1, ES2, ES3 . . . ESi) that react with rate constants V1, V2, V3 .

. . Vi forming the corresponding products P1, P2, P3 . . . Pi and regenerating the free

enzyme. Here, the parameter Vi is the net first order rate constant for reaction of ESi with

release of the slowest dissociating product to regenerate active enzyme (139). For the

RNase P catalyzed processing of pre-tRNA the slowest dissociating product could be the

tRNA or the 5’ leader sequence product and the model does not distinguish between these

possibilities.

Under steady state reaction conditions the rate of processing of any individual

pre-tRNA substrate (vobs1) will be proportional to the fraction of total enzyme in the ES1

form according to:

= Equation 9

푣표푏푠1 푉1퐸푓퐸푆1 Where vobs1 is the observed reaction rate (e.g. nM/sec) for depletion of substrate

-1 S1, and V1 is the first order rate constant (s ) for the reaction of ES1 to yield free product,

P1, and free enzyme, and fES is the fraction of total enzyme that is in the form that reacts

with rate constant V1.

109

For two substrates the multiple turnover rate equation is essentially that for

competitive inhibition as illustrated in several primary sources (140,141).

= 1 + 1 + Equation 10 퐾1 푆2 푣표푏푠1 푉1퐸�� 푆1 � 퐾2�� = 1 + + Equation 11 푆1 푆1 푆2 푣표푏푠1 푉1퐸 퐾1�� 퐾1 퐾2� And by extension,

= 1 + + Equation 12 푆2 푆1 푆2 푣표푏푠2 푉2퐸 퐾2�� 퐾1 퐾2� Since the denominators of fES1 and fES2 are the same, the ratio of the two observed rates

simplifies to the following expression (87,140,141).

= Equation 13 푉 푣표푏푠2 � �퐾�2 푆2 표푏푠1 푉 1 푣 � �퐾�1 �푆 � Thus, the relative rate constant, or the ratio of the two individual rate constants for

the two competing substrates, is the ratio of their respective V/K values multiplied by the

ratio of their concentrations. This ratio is defined as rk where the substrate considered in

the denominator is the wildtype, control or reference substrate. A substrate with a larger

V/K relative to the reference substrate will have an rk > 1, while an rk of <1 indicates that

the substrate has a correspondingly lower V/K.

This basic relationship has been arrived in several different places in the literature

and in fact is the classic, quantitative definition of ‘enzyme specificity’. With respect to

practical application of competitive alternative substrate kinetics for structure-function

experiments these key issues that follow from equation 13 include the following.

Regardless of the substrate concentrations, even if one or both are greater than their

110

respective Km, both substrates will behave as V/K systems. This is because both

substrates must compete for the available free enzyme in order to react and form product.

Thus, the association step contributes to the relative population of ES1 and ES2 and

therefore the observed rates while the rk remains constant. Direct measurements of rate constants is therefore the only way to determine rk values for V. However, if V reflects the same rate constant as that measured under single turnover conditions (E>>S), then it

should be possible to measure relative effects on V by internal competition kinetics

performed under these conditions. Additionally, since the enzyme concentration occurs

in the rate equations for vobs1 and vobs2 it cancels out in their ratio. So long as the steady

state conditions are maintained the ratio of observed rates and the ratio of V/K values are

independent of enzyme concentration. It is also evident that the individual step or steps

in the reaction scheme that is rate limiting for V/K does not have to be the same for the

two substrates. Application of competitive kinetics will therefore report on the relative

V/K values for the two substrates and provided that the V/K of the reference substrates is

known the other can be calculated.

111

References

1. Kazantsev A.V. and N.R. Pace. (2006) Bacterial RNase P: a new view of an

ancient enzyme. Nat Rev Micr Biol 4: 729-740

2. Sun L. and M.E. Harris. (2007) Evidence that binding of C5 protein to P RNA

enhances ribozyme catalysis by influencing active site metal ion affinity. RNA 13: 1505-

1515.

3. GoBringer M. and R.K. Hartmann. (2007) Function of heterologous and truncated

RNase P proteins in Bacillus subtilis. Mol Micro 66 (3):801-813.

4. Zahler, N.H., Christian, E.L., and M.E. Harris. (2003) Recognition of the 5'

leader of pre-tRNA substrates by the active site of ribonuclease P. RNA 9: 734-745.

5. Sun, L., Campbell, F.E., Zahler, N.H. & Harris, M.E. (2006) Evidence that

substrate‐specific effects of C5 protein lead to uniformity in binding and catalysis by

RNase P. EMBO J 25:3998‐4007

6. Kurz, J.C., Niranjanakumari, S. & Fierke, C.A. (1998) Protein component of

Bacillus subtilis RNase P specifically enhances the affinity for precursor‐tRNAAsp.

Biochemistry 37:2393‐2400

7. Beebe, J.A. and Fierke C. A. (1994) A kinetic mechanism of precursor tRNAAsp

catalyzed by the RNA component of Bacillus subtilis Ribonuclease P. Biochemistry

33:10294-10304

8. Beebe, J.A., Kurz, J.C. & Fierke, C.A. (1996) Magnesium ions are required by

Bacillus subtilis ribonuclease P RNA for both binding and cleaving precursor tRNAAsp.

Biochemistry 35:10493‐10505

112

9. Brown, J.W., Haas, E.S., James, B.D., Hunt, D.A., Liu, J.S., and Pace N.R. (1991)

Phylogenetic analysis and evolution of RNase P RNA in proteobacteria. J Bacteriol

173(12):3855-3863.

10. Brown, J.W., Haas, E.S., and Pace, N.R. (1993) Characterization of ribonuclease

P RNAs from thermophilic bacteria. Nucleic Acids Res 21(3):671-679.

11. Brown, J.W., Nolan, J.M. Haas, E.S., Rubio, M.A., Major, F., and Pace N.R.

(1996) Comparative analysis of ribonuclease P RNA using gene sequences from natural

microbial populations reveals tertiary structural elements. Proc Natl Acad Sci U S A

93(7):3001-3006.

12. Haas, E.S., Banata, A.B., Harris, J.K., Pace, N.R. and Brown, J.W. (1996)

Structure and evolution of ribonuclease P RNA in Gram-positive bacteria. Nucleic Acids

Res 24(23):4775-4782.

13. Kazantsev, A.V., Krivenko, A.A., Harrington, D.J., Holbrook, S.R., Adams, P.D., and Pace, N.R.(2005) Crystal structure of a bacterial ribonuclease P RNA. Proc Natl

Acad Sci U S A 102(38):13392-13397.

14. Torres-Larios, A., Swinger, K.K., Krasilnikov, A.S., Pan, T., and Mondragon A.

(2005) Crystal structure of the RNA component of bacterial ribonuclease P. Nature

437(7058):584-587.

15. Kakuta, Y., Ishimatsu, I., Numata, T., Kimura, K., Yao, M., Tanaka, I., and

Kimura, M. (2005) Crystal structure of a ribonuclease P protein Ph1601p from

Pyrococcus horikoshii OT3: an archeal homolog of human nuclear ribonuclease P protein

Rpp 21. Biochemistry 44(36): 12086-12093.

113

16. Haas, E.S. and J.W. Brown. (1998) Evolutionary variation in bacterial RNase P

RNAs. Nucleic Acids Res 26(18): 4093-4099

17. Guerrier-Takada, C., Gardinera, K., Marsh, T., Pace, N., and Altman, S. (1983)

The RNA moiety of ribonuclease P is the catalytic subunit of the enzyme. Cell 35(3):849-

857

18. Westhof, E., Wesolowski, D. and Altman, S. (1996) Mapping in three dimensions of regions in a catalytic RNA protected from attack by an Fe(II)-EDTA reagent. J Mol

Biol 258(4):600-613

19. Buck, A.H., Dalby, A.B., Poole, A.W., Kazantsev, A.V. & Pace, N.R. (2005)

Protein activation of a ribozyme: the role of bacterial RNase P protein. EMBO J

24(19):3360-3368

20. Loria, A. and T. Pan. (1996) Domain structure of the ribozyme from eubacterial

ribonuclease P. RNA 2(6):551-563

21. Waugh, D.S., and Pace N.R. (1990) Complementation of an RNase P RNA (rnpB)

gene deletion in Escherichia coli by homologous genes from distantly related eubacteria.

172:6316-6322

22. Stams, T., Niranjanalumari, S., Fierke, C.A., and Christianson D.W. (1998)

Ribonuclease P protein structure: evolutionary origins in the translational apparatus.

Science 280:752-755

23. Spitzfaden, C., Nicholson, N., Jones, J.J., Guth, S., Lehr, R., Prescott, C.D., Hegg,

L.A., and Eggleston DS. (2000) The structure of ribonuclease P protein from

Staphylococcus aureus reveals a unique binding site for single-stranded RNA. J Mol Biol.

295:105-115

114

24. Kazantsev, A.V., Krivenko, A.A., Harrington, D.J., Carter, R.J., Holbrook, S.R.,

Adams, P.D., and Pace N.R. (2003) High-resolution structure of a bacterial ribonuclease

P RNA protein from Thermotoga maritime. Proc Natl Acad Sci U S A 100:7497-9502

25. Leeper, T.C., Martin, M.B., Kim, H., Cox, S., Semenchenko, V., Schmidt, F.J.,

and Van Doren, S.R. (2002). Strucutre of the UGAGAU hexaloop that braces Bacillus

RNase P for action. Nat Struc Biol 9:397-403

26. Getz, M.M., Andrews, A.J., Fierke, C.A., and Al-Hashimi HM (2007) Structural

plasticity and Mg2+ binding properties of RNase P P4 from combined analysis of NMR

residual dipolar couplings and motionally decoupled spin relaxation. RNA 13:251-266

27. Krasilnikov, A.S., Yang, X., Pan, T., and Mondragon A (2003) Crystal strucutre

of the specificity domain of ribonuclease P. Nature 421:760-764

28. Krasilnikov, A.S., Xiao, Y., Pan, T., and Mondragon A. (2004) Basis for

structural diversity in homologous RNAs. Science 306:104-107

29. McClain, W.H., Lai, L.B. and Gopalan, V. (2010) Trials, Travails and Triumphs:

An Account of RNA Catalysis in RNase P. J Mol Biol. 397: 627-646

30. Dittmar, K.A., Mobley, E.M., Radek, A.J., and T. Pan. (2004) Exploring the

regulation of tRNA distribution on the genomic scale. J. Mol. Biol.337:31-47

31. Smith, K.J., Hsieh, J., and C.A. Fierke. (2007) Importance of RNA-protein interactions in bacterial Ribonuclease P structure and catalysis. Biopolymers.87 (5-6):

329-338

32. Potrykus, K., and M. Cashel (2008). (p)ppGpp: still magaical? Annu Rev

Microbiol 62:35-51

115

33. Ikemura, T. (1981). Correlation between the abundance of Escherichia coli

transfer RNAs and the occurrence of the respective codons in its protein genes: a

proposal for a synonymous codon choice that is optimal for the E. coli translational

system. J Mol Biol 151(3): 389-409

34. Ikemura, T. (1985). Codon usage and tRNA content in unicellular and

multicellular organisms. Mol Biol Evol 2(1): 13-34

35. Kurland, C. G. (1993). Major codon preference: theme and variations. Biochem

Soc Trans 21(4): 841-6

36. Sun, L., Campbell, F. E., Yandek, L. E., and Harris, M. E. (2010) Binding of C5

protein to P RNA enhances the rate constant for catalysis for P RNA processing of pre-

tRNAs lacking a consensus (+ 1)/C(+ 72) pair. J Mol Biol 395, 1019-1037

37. Tallsjo, A., and L.A. Kirsebom (1993). Product release is a rate-limiting step during cleavage by the catalytic RNA subunit of Escherichia coli RNase P. Nucleic Acids

Res 21(1):51-57

38. Koutmou, K.S., Hsieh J., and C. A. Fierke (2010) Kinetic mechanism of Bacterial

RNase P. Protein Reviews Volume 10: Ribonuclease P, Vol. 25 (eds. Altman, R.B. and F.

Liu) 93-111 (Springer, New York)

39. Hsieh, J., and Fierke, C. A. (2009) Conformational change in the Bacillus subtilis

RNase P holoenzyme--pre-tRNA complex enhances substrate affinity and limits cleavage

rate. RNA 15, 1565-1577

40. Zahler, N. H., Sun, L., Christian, E. L., and Harris, M. E. (2005) The pre-tRNA nucleotide base and 2'-hydroxyl at N(-1) contribute to fidelity in tRNA processing by

RNase P. J Mol Biol 345, 969-985

116

41. Karbstein, K., Tang, K. H., and Herschlag, D. (2004) A base triple in the

Tetrahymena group I core affects the reaction equilibrium via a threshold effect. RNA 10,

1730-1739

42. Kikovska, E., Brannvall, M., Kufel, J. & Kirsebom, L.A. (2005) Substrate discrimination in RNase P RNA‐mediated cleavage: importance of the structural environment of the RNase P cleavage site. Nucleic Acids Res 33:2012‐2021

43. Brannvall, M., Kikovska, E., and L.A. Kirsebom. (2004) Cross talk between the

+73/294 interaction and the cleavage site in RNase P RNA mediated cleavage. Nucleic

Acic Res 32(18): 5418-5429

44. Kikovska, E., Brannvall, M. and Kirsebom, L.A. (2006) The exocyclic amine at the RNase P cleavage site contributes to substrate binding and catalysis. J Mol Biol

359:572‐584

45. Yandek, L.E., Lin, H., and Harris M.E. (2013) Alternative Substrate Kinetics of

Escherichia coli Ribonuclease P: Determination of relative rate constants by internal competition. J Biol Chem. 288(12):8342-54.

46. Harris, M.E. & Yandek, L.E. (2010) Challenges in substrate recognition by

RNase P: Facing up to the biological context. Protein Reviews Volume 10: Ribonuclease

P, Vol. 25 (eds. Altman, R.B. & Liu, F.) 135‐152 (Springer, New York)

47. Koutmou, K. S., Zahler, N. H., Kurz, J. C., Campbell, F. E., Harris, M. E., and

Fierke, C. A. (2010) Protein-precursor tRNA contact leads to sequence-specific recognition of 5' leaders by bacterial ribonuclease P. J Mol Biol 396, 195-208

117

48. Loria, A., Niranjanakumari, S., Fierke, C. A., and Pan, T. (1998) Recognition of a

pre-tRNA substrate by the Bacillus subtilis RNase P holoenzyme. Biochemistry 37,

15466-15473

49. Zahler, N. H., Christian, E.L., and Harris M.E. (2003) Recognition of the 5' leader

of pre-tRNA substrates by the active site of ribonuclease P. RNA 9(6): 734-45

50. Christian, E. L., McPheeters, D.S., and Harris M.E. (1998) Identification of individual nucleotides in the bacterial ribonuclease P ribozyme adjacent to the pre-tRNA cleavage site by short-range photo-cross-linking. Biochemistry 37(50): 17618-28

51. Loria, A. and T. Pan (1999) The cleavage step of ribonuclease P catalysis is determined by ribozyme-substrate interactions both distal and proximal to the cleavage site. Biochemistry 38(27): 8612-20

52. Lai, L. B., Vioque, A., Kirsebom, L. A., and Gopalan, V. (2010) Unexpected diversity of RNase P, an ancient tRNA processing enzyme: challenges and prospects.

FEBS Lett 584: 287-296.

53. Esakova, O., and Krasilnikov, A. S. (2010) Of proteins and RNA: the RNase

P/MRP family. RNA 16: 1725-1747

54. Ellis, J. C., and Brown, J. W. (2009) The RNase P family. RNA Biol 6: 362-369

55. Guerrier-Takada, C., and Altman, S. (1984) Catalytic activity of an RNA molecule prepared by transcription in vitro. Science 223: 285-286

56. Gardiner, K. J., Marsh, T. L., and Pace, N. R. (1985) Ion dependence of the

Bacillus subtilis RNase P reaction. J Biol Chem 260: 5415-5419

118

57. Buck, A. H., Kazantsev, A. V., Dalby, A. B., and Pace, N. R. (2005) Structural

perspective on the activation of RNAse P RNA by protein. Nat Struct Mol Biol 12: 958-

964

58. Niranjanakumari, S., Stams, T., Crary, S. M., Christianson, D. W., and Fierke, C.

A. (1998) Protein component of the ribozyme ribonuclease P alters substrate recognition by directly contacting precursor tRNA. Proc Natl Acad Sci USA 95: 15212-15217

59. Reiter, N. J., Osterman, A. K., and Mondragon, A. (2012) The bacterial ribonuclease P holoenzyme requires specific, conserved residues for efficient catalysis and substrate positioning. Nucleic Acids Res 40: 10384-10393

60. Hiller, D. A., and Strobel, S. A. (2011) Philosophical transactions of the Royal

Society of London. Series B, Biological sciences 366: 2929-2935

61. Hougland, J., Piccirilli, J., Forconi, M., Lee, J., and Herschlag, D. (2006) The

RNA World, 3rd ed. Cold Spring Harbor Laboratory Press, Cold Spring Harbor, NY.

62. Pyle, A. M. (2010) The tertiary structure of group II introns: implications for biological function and evolution. Crit Rev Biochem Mol Biol. 45: 215-232

63. Hartmann, R. K., Gossringer, M., Spath, B., Fischer, S., and Marchfelder, A.

(2009) The making of tRNAs and more - RNase P and tRNase Z. Prog Mol Biol Transl

Sci 85: 319-368

64. Chan, P. P., and Lowe, T. M. (2009) GtRNAdb: a database of transfer RNA genes

detected in genomic sequence. Nucleic Acids Res 37: 93-97

65. Treiber, T., Treiber, N., and Meister, G. (2012) Regulation of microRNA biogenesis and function. Thromb Haemost 107: 605-610

119

66. Okamura, K. (2012) Diversity of animal small RNA pathways and their biological

utility. Wiley Interdiscip Rev RNA 3: 351-368

67. Singh, R. K., and Cooper, T. A. (2012) Pre-mRNA splicing in disease and therapeutics. Trends in molecular medicine 18: 472-482

68. Steimer, L., and Klostermeier, D. (2012) RNA helicases in infection and disease.

RNA Biol 9: 751-71

69. Kirsebom, L. A., and Trobro, S. (2009) RNase P RNA-mediated cleavage.

IUBMB Life 61: 189-200

70. Pan, T., Loria, A., and Zhong, K. (1995) Probing of tertiary interactions in RNA:

2'-hydroxyl-base contacts between the RNase P RNA and pre-tRNA. Proc Natl Acad Sci

USA 92: 12510-12514

71. Gaur, R. K., and Krupp, G. (1993) Modification interference approach to detect ribose moieties important for the optimal activity of a ribozyme. Nucleic Acids Res 21:

21-26

72. Suwa, S., Nagai, Y., Fujimoto, A., Kikuchi, Y., and Tanaka, T. (2009) Analysis

on substrate specificity of Escherichia coli ribonuclease P using shape variants of pre- tRNA: proposal of subsites model for substrate shape recognition. J Biochem 145: 151-

160

73. Loria, A., and Pan, T. (2000) The 3' substrate determinants for the catalytic efficiency of the Bacillus subtilis RNase P holoenzyme suggest autolytic processing of the RNase P RNA in vivo. RNA 6: 1413-1422

120

74. Wu, S., Chen, Y., Lindell, M., Mao, G., and Kirsebom, L. A. (2011) Functional

coupling between a distal interaction and the cleavage site in bacterial RNase-P-RNA-

mediated cleavage. J Mol Biol 411: 384-396

75. Reiter, N. J., Osterman, A., Torres-Larios, A., Swinger, K. K., Pan, T., and

Mondragon, A. (2010) Structure of a bacterial ribonuclease P holoenzyme in complex

with tRNA. Nature 468: 784-789

76. Crooks, G.E., Hon, G., Chandonia, J.M., and Brenner, S. E. (2004) Weblogo:a sequence logo generator. Genome Res. 14:1188-1190

77. Leung, E. K., Suslov, N., Tuttle, N., Sengupta, R., and Piccirilli, J. A. (2011) The mechanism of peptidyl transfer catalysis by the ribosome. Ann Rev Biochem 80:527-555

78. Moor, N., Lavrik, O., Favre, A., and Safro, M. (2003) Prokaryotic and eukaryotic

tetrameric phenylalanyl-tRNA synthetases display conservation of the binding mode of

the tRNA(Phe) CCA end. Biochemistry 42:10697-10708

79. Tamura, K., and Hasegawa, T. (1997) Role of the CCA end of tRNA and its

vicinity in aminoacylation. Nucleic Acids Symp Ser 37:133-134

80. Liu, J. C., Liu, M., and Horowitz, J. (1998) Recognition of the universally

conserved 3'-CCA end of tRNA by elongation factor EF-Tu. RNA 4:639-646

81. Karbstein, K., Tang, K. H., and Herschlag, D. (2004) A base triple in the

Tetrahymena group I core affects the reaction equilibrium via a threshold effect. RNA

10:1730-1739

82. Guo, X., Campbell, F.E., Sun, L., Christian, E.L., Anderson, V.E., and Harris,

M.E. (2006) RNA-dependent folding and stabilization of C5 protein during assembly of

the E. coli RNase P holoenzyme. J. Mol. Biol. 360:190-203

121

83. Siew, D., Zahler, N. H., Cassano, A. G., Strobel, S. A., and Harris, M. E. (1999)

Identification of adenosine functional groups involved in substrate binding by the

ribonuclease P ribozyme. Biochemistry 38: 1873-1883

84. Rpse, I.A., O’Connell, E.L., and Litwin, S. (1974) Determination of the rate of

hexokinase-glucose dissociation by the isotope-trapping method. J. Biol. Chem.

249:5163-5168

85. Cornish-Bowden, A. (1984) Enzyme specificity: its meaning in the general case. J

Theor Biol 108:451-457

86. Fersht, A. (1985) Enzyme structure and mechanism, 2nd ed., Freeman and Co.,

New York, NY.

87. Herschlag, D. (1988) The role of induced fit and conformationla changes of enzymes in specificity and catalysis. Bioorganic chemistry 16:62-96

88. Northrop, D. B. (1998) On the meaning of Km and V/K in enzyme kinetics. J

Chem Ed 75:1153-1157

89. Northrop, D. B. (1999) Rethinking fundamentals of enzyme action. Adv Enzymol

Relat Areas Mol Biol 73:25-55

90. Cleland, W. W. (2006) Isotope Effects in Chemistry and Biology (Kohnen, A. ed.), Taylor & Francis. Boca Raton, FL.

91. Cleland, W. W., and Cook, P. F. (2007) Enzyme Kinetics and Mechanism,

Garland Publishers, London and New York, NY.

92. Fersht, A. (1998) Structure and Mechanism in Protein Science, W.H. Freemand &

Co., New York, NY.

122

93. Slyke, D. D. V., and Cullen, G. E. (1914) The mode of action of urease and of

enzymes in general. J Biol Chem 19:141-180

94. Cha, S. (1968) Kinetics of enzyme reactions with competing alternative

substrates. Mol Pharmacol 4:621-629

95. Schellenberger, V., Siegel, R. A., and Rutter, W. J. (1993) Analysis of enzyme

specificity by multiple substrate kinetics. Biochemistry 32:4344-4348

96. Kirsebom, L.A. (2007) RNase P RNA mediated cleavage: Substrate recognition

and catalysis. Biochemie 89:1183-1194

97. Cook, P. F., and Cleland, W. W. (2007) Enzyme Kinetics and Mechanism.

Garland Science, New York, NY.

98. Hansen, A., Pfeiffer, T., Zuleeg, T., Limmer, S., Ciesiolka, J., Feltens, R., and

Hartmann, R. K. (2001) Exploring the minimal substrate requirements for trans-cleavage by RNase P holoenzymes from Escherichia coli and Bacillus subtilis. Mol Microbiol

41:131-143

99. Ando, T., Tanaka, T., Hori, Y., and Kikuchi, Y. (2002) Kinetics of hyper-

processing reaction of human tyrosinetRNA by ribonuclease P ribozyme from

Escherichia coli. Biosci. Biotechnol. Biochem. 66: 1967-1971

100. Hori, Y., Baba, H., Ueda, R., Tanaka, T., and Kikuchi, Y. (2000) In vitro

hyperprocessing of Drosophila tRNAs by the catalytic RNA of RNase P the cloverleaf

structure of tRNA is not always stable? Eur. J. Biochem. 267:4781-4788

101. Gupta, A., and M. Gribskov (2011) The role of RNA sequence and structure in

RNA-protein interactions. J. Mol. Biol. 409:574-97

123

102. Singh R. and Valcarcel J. (2005) Building specificity with nonspecific RNA- binding proteins. Nat. Struct. Mol. Biol. 12:645-53

103. Rajkowitsch L., Chen, D., Stampfl, S., Semrad, K., Waldsich, C., Mayer, O.,

Jantsch, M.F., Konrat, R., Blasi, U., and Schroeder R. (2007) RNA chaperones, RNA annealers and RNA helicases. RNA Biol. 4:118-30

104. Linder P. and E. Jankowsky (2011) From unwinding to clamping – the DEAD box RNA helicase family. Nat Rev Mol Cell Biol 12:505-16

105. Zhuang, F., Fuchs, R.T., Sun, Z., Zheng, Y., and Robb G.B. (2012) Structural bias in T4 RNA ligase-mediated 3’-adapter ligation. Nucleic Acids Res. 40, e54

106. Kaymak, E., Wee, L.M., and Ryder S.P. (2010) Structure and function of nematode RNA-binding proteins. Curr. Opin. Struct. Biol. 20, 305-12

107. Ray, D., Kazan, H., Chan, E.T., Pena, Castillo, L., Chaudhry, S., Talukder, S.,

Blencowe, B.J., Morris, Q., and T.R. Hughes (2009) Rapid and systematic analysis of the

RNA recognition specificities of RNA-binding proteins. Nat. Biotechnol. 27:667-70

108. Campbell, Z.T., Bhimsaria, D., Valley, C.T., Rodriguez-Martinez, J.A.,

Menichelli, E., Williamson, J.R., Ansari, A.Z. and Wickens M. (2012) Cooperativity in

RNA-protein interactions: global analysis of RNA binding specificity. Cell Rep. 1:570-

109. Pitt, J.N. & Ferre-D’Amare, A.R. (2010) Rapid construction of empirical RNA

fitness landscapes. Science 330: 376-9.

110. Li, Z., and Deutscher, M. P. (2002) RNase E plays an essential role in the

maturation of Escherichia coli tRNA precursors. RNA 8:97-109

124

111. Ow, M. C., and Kushner, S. R. (2002) Initiation of tRNA maturation by RNase E

is essential for cell viability in E. coli. Genes Dev 16:1102-1115

112. Nagalakshmi, U. et al. (2008) The transcriptional landscape of the yeast genome

defined by RNA sequencing. Science 320: 1344-9

113. Mortazavi, A., Williams, B.A., McCue, K., Shaeffer, L. & Wold, B. (2008)

Mapping and quantifying mammalian trascriptomes by RNA-Seq. Nat. Methods 5: 621-8

114. Badis, G., Berger, M.F., Philippakis, A.A., Talukder, S., Gehrke, A.R., Jaeger,

S.A., Chan, E.T., Metzler, G., Vedenko, A., Chen, X., Kuznetsov, H., Wang, C.F.,

Coburn, D., Newburger, D.E., Morris, Q., Hughes, T.R., and M.K. Bulyk (2009)

Diversity and complexity in DNA recognition by transcription factors. Science 324, 1720

115. Rowe W., Platt, M., Wedge, D.C., Day, P.J., Kell, D.B., and J. Knowles (2009)

Analysis of a complete DNA-protein affinity landscape. J. R. Soc. Interface 7:397

116. Kurland, C. G. (1991) Codon bias and gene expression. FEBS Lett 285, 165-169

117. Deutscher, M. P. (2009) Maturation and degradation of ribosomal RNA in

bacteria. Prog Mol Biol Transl Sci 85:369-391

118. Seif, E., and Altman, S. (2008) RNase P cleaves the adenine riboswitch and

stabilizes pbuE mRNA in Bacillus subtilis. RNA 14:1237-1243

119. Ko, J. H., and Altman, S. (2007) OLE RNA, an RNA motif that is highly conserved in several extremophilic bacteria, is a substrate for and can be regulated by

RNase P RNA. Proc Natl Acad Sci USA 104:7815-7820

120. Altman, S., Wesolowski, D., Guerrier-Takada, C., and Li, Y. (2005) RNase P cleaves transient structures in some riboswitches. Proc Natl Acad Sci USA 102:11284-

11289

125

121. Fredrik Pettersson, B. M., Ardell, D. H., and Kirsebom, L. A. (2005) The Length

of the 5' Leader of Escherichia coli tRNA Precursors Influences Bacterial Growth. J Mol

Biol 351:9-15

122. Mohanty, B. K., and Kushner, S. R. (2008) Rho-independent transcription

terminators inhibit RNase P processing of the secG leuU and metT tRNA polycistronic

transcripts in Escherichia coli. Nucleic Acids Res 36:364-375

123. Mohanty, B. K., and Kushner, S. R. (2007) Ribonuclease P processes

polycistronic tRNA transcripts in Escherichia coli-independent of ribonuclease E.

Nucleic Acids Res 35:7614-7625

124. Mohanty, B. K., and Kushner, S. R. (2010) Processing of the Escherichia coli

leuX tRNA transcript, encoding tRNA(Leu5), requires either the 3'-->5' exoribonuclease

polynucleotide phosphorylase or RNase P to remove the Rho-independent transcription

terminator. Nucleic Acids Res 38:597-607

125. Marvin, M. C., Walker, S. C., Fierke, C. A., and Engelke, D. R. (2011) Binding

and cleavage of unstructured RNA by nuclear RNase P. RNA 17:1429-1440

126. Marvin, M. C., Clauder-Munster, S., Walker, S. C., Sarkeshik, A., Yates, J. R.,

3rd, Steinmetz, L. M., and Engelke, D. R. (2011) Accumulation of noncoding RNA due

to an RNase P defect in Saccharomyces cerevisiae. RNA 17:1441-1450

127. Dale, T., Sanderson, L. E., and Uhlenbeck, O. C. (2004) The affinity of

elongation factor Tu for an aminoacyl-tRNA is modulated by the esterified amino acid.

Biochemistry 43:6159-6166

126

128. LaRiviere, F. J., Wolfson, A. D., and Uhlenbeck, O. C. (2001) Uniform binding of

aminoacyl-tRNAs to elongation factor Tu by thermodynamic compensation. Science

294:165-168

129. Dale, T., and Uhlenbeck, O. C. (2005) Amino acid specificity in translation.

Trends Biochem Sci 30:659-665

130. Dale, T., and Uhlenbeck, O. C. (2005) Binding of misacylated tRNAs to the

ribosomal A site. RNA 11:1610-1615

131. Olejniczak, M., Dale, T., Fahlman, R. P., and Uhlenbeck, O. C. (2005)

Idiosyncratic tuning of tRNAs to achieve uniform ribosome binding. Nat Struct Mol Biol

12:788-793

132. Hseih, J., Koutmou, K.S., Rueda, D., Koutmos, M., Walter, N.G., and Fierke,

C.A. (2010) A divalent cation stabilizes the active conformation of the B. subtilis RNase

P x pre-tRNA complex: a role for an inner sphere metal ion in RNase P. J. Mol. Biol.

400:38-51

133. Koutmou, K.S., Day-Storms, J.J., and Fierke, C.A. (2011) The RNR motif of B.

subtilis RNase P protein interacts with both P RNA and pre-tRNA to stabilize an active

conformer. RNA. 17(7):1225-1235

134. Saks, M.E., Sampson, J.R., and Abelson, J. (1998) Evolution of a transfer RNA

gene through a point mutation in the anticodon. Science. 279: 1665-1670.

135. Briggs, G.E., and Haldane, J.B.S. (1925) A note on the kinetics of enzyme action.

Biochem J. 19: 338-340

136. Michaelis, L. and Menten, M.L. (1913) Biochem Z. 49:333

127

137. W.W. Cleland. (1975) Partition analysis and the concept of net rate constants as

toold in enzyme kinetics. Biochemistry. 14:3220-3224.

138. A. Fersht (1985) Enzyme structure and mechanism, Freeman and Co., New York,

139. W.J. Ray, Jr., (1983) Rate-limiting step: a quantitative definition. Application to

steady-state enzymic reactions. Biochemistry. 22:4625-37.

140. T. Pocklington, and Jeffery, J. (1969) Competition of two substrates for a single enzyme. A simple kinetic theorem exemplified by a hydroxy steroid dehydrogenase reaction. Biochem J. 112:331-334.

141. S.G. Waley. (1983) Kinetic parameters from progress curves of competing substrates. Application to beta-lactamases. Biochem J. 211:511-3.

128