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Archives of Biochemistry and Biophysics 531 (2013) 4–13

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Archives of Biochemistry and Biophysics

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Review The stability of 2-state, 3-state and more-state proteins from simple spectroscopic techniques... plus the structure of the equilibrium intermediates at the same time ⇑ Javier Sancho

Departamento de Bioquímica y Biología Molecular y Celular, Facultad de Ciencias, Universidad de Zaragoza. Pedro Cerbuna 12, 50009 Zaragoza, Spain Biocomputation and Complex Systems Physics Institute (BIFI), Joint Unit BIFI-IQFR, CSIC, Universidad de Zaragoza. Mariano Esquillor, Ediﬁcio I+D, 50018 Zaragoza, Spain article info abstract

Article history: Protein stability is not just an academic matter. Biotechnology, Cell Biology and Drug Design are some of Available online 8 November 2012 the fields where both theoretical and practical knowledge of protein stability is required. Simple equipment and chemicals, such as a thermostated fluorimeter and common denaturants, suffice to determine the conformational stability of a protein. To this end, the most important experiments are the preliminary ones done to establish the minimum number of species (conformations) accumulating in the equilibrium. For proteins with non-functional equilibrium intermediates, determining the relevant stability of the protein (the free energy difference between the native conformation and the intermediate) is most important, and it allows very valuable structural information on the intermediate to be derived when protein variants are compared to wild type using equilibrium /-analysis. The principles, tricks and equations involved in the analysis of denaturant induced or temperature induced equilibrium unfolding curves by the linear extrapolation method or using the integrated Gibbs–Helmholtz equation, respectively, will be discussed, and a brief outline of challenges and frontiers in the protein stability field will be presented. Ó 2012 Elsevier Inc. All rights reserved.

The different types of protein stability a low chemical or biochemical stability is that the population of active protein molecules will be progressively reduced in an irrevers- Proteins are the molecules that do most things in living beings, ible manner because the reactions involved tend to be irreversible and the wonders they do are almost always related to their molec- and tend to compromise function. Increasing their chemical stabil- ular surfaces and intrinsic dynamics. These, in turn, are shaped by ity is an issue for proteins that are used in biotechnological pro- folding reactions that lead, for each protein, to stabilization of one cesses, which sometimes require extreme conditions such as high specific tridimensional structure among the inconceivably large temperature, low pH, presence of cosolvents, etc. [2]. In contrast, number of possible alternative conformations. In apparent con- the biochemical stability of any given protein, whether high or trast, there are proteins that display unfolded conformations under low, is in principle a functional property that might be thought of native solution conditions [1]. Yet, some of these proteins have as being best left unmodified. However, the increasing availability been observed to become folded when they bind to appropriate of biologics as therapeutic agents [3] makes the rational tailoring molecular targets, which indicates the stabilization of those pro- of biological stability an important goal. teins into defined structures is coupled to binding events. Being The conformational stability of a protein is something different. conformationally stable at some time seems to be a general requi- A protein molecule that leaves the ribosome and becomes folded site of functional proteins. can still experience the inverse process of becoming unfolded It should be noticed that ‘‘protein stability’’ is an ambiguous term and then folded again for as long as its chemical integrity is main- that may refer to several different things (Fig. 1). The chemical or tained. Therefore, for any population of identical protein molecules biochemical stability of a protein is related to its resistance to expe- there is an equilibrium constant (Kf) that governs the fraction of rience changes in its covalent structure, i.e., have some covalent molecules that are folded (vf) or unfolded (vu). bonds cleaved or some atoms replaced. The consequence of having

Kf ¼ vf =vu ð1Þ Such an equilibrium constant can be determined using many ⇑ Address: Departamento de Bioquímica y Biología Molecular y Celular, Facultad de Ciencias, Universidad de Zaragoza. Pedro Cerbuna 12, 50009 Zaragoza, Spain. different techniques and it can be mathematically transformed into Fax: +34 976762123. a free energy difference of folding (DGf) which is usually referred to E-mail address: [email protected] as the conformational stability of the protein.

J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13 5

DGf ¼RT ln Kf ð2Þ etc. Mechanical stability refers to the resistance of native proteins to be unfolded by external forces, and it is studied with atomic It is easy to get confused with the sign of this magnitude be- force microscopes or optical tweezers [8]. Mechanical unfolding cause there is a tendency in the literature to state that if the free is usually reversible and the magnitude of the force needed to un- energy of folding of a protein is, say, 10 kcal/mol, then its confor- fold a particular protein changes with the orientation of the force. mational stability is 10 kcal/mol. This is in part explained by the This indicates that different transition states may be sampled fact that what is determined and reported in most cases is the free when the force is applied at different points. Thus the mechanical energy of unfolding, which for a stable protein bears, of course, a stability of a protein will be related to the specific energy barrier positive sign. that has to be crossed, given the force applied, to convert native Equilibrium constants are ratios of kinetic constants, and two molecules into unfolded ones. It seems that b proteins tend to dis- proteins with the same value for their folding equilibrium constants play higher mechanical stabilities than a proteins. may differ much in their folding and unfolding rate constants. This It is common that in the folding/unfolding equilibrium of small is not without practical consequences because the reactivity of proteins the only conformations that populate to measurable molar folded and unfolded states [4] may not be the same. A protein rap- fractions are the native, folded state and the unfolded state (U M F) idly sampling the folded and unfolded states may often get a chance [9,10]. In contrast, for most proteins, additional intermediate con- to engage in reactions only possible for or just much faster in the formations (less folded than the native state but more folded than unfolded conformation. If these are irreversible reactions leading the denatured state) accumulate as the solution conditions become to loss of function, a much greater fraction of such a protein may be- more destabilizing of the native conformation, yet not fully stabiliz- come inactive in a given time period than in a protein with the same ing of the denatured state [11]. The number of species that will ap- conformational stability but with slow unfolding kinetics. Proteins pear as the solution conditions are shifted from native to denaturing whose native conformation is preserved from experiencing inacti- will depend on the specific shape of the folding landscape in native vation related to reactions of its unfolded conformation due to their conditions and on the changes that the specific denaturing agent slow unfolding kinetics are considered to display a high kinetic sta- used to probe the equilibrium will induce in that shape. The more bility [5]. It seems now that aggregates rich in b-strands may be for complex the landscape, the more likely a higher number of interme- many, perhaps most, proteins more stable than their corresponding diates will be observed. On the other hand, a particular denaturing native conformations [6]. It is thus possible that proteins have agent (say, urea) may not reveal the presence of a potential interme- evolved to protect their native conformations from transformation diate while other (say, temperature) may do so [12]. For proteins into more stable aggregated conformations such as those mani- displaying equilibrium intermediates, the global equilibrium be- fested in aggregative diseases [7]. A high energy barrier between tween the native and the unfolded states can be divided into partial those native conformations and the more stable aggregated states equilibria between the different species, each one governed by an would originate a high kinetic stability, which would minimize pro- equilibrium constant and, therefore, by a free energy difference. tein aggregation in vivo. For the simplest, non two-state equilibrium scenario with a single A particular type of kinetic stability is mechanical stability, intermediate accumulating at moderate denaturing conditions which plays important roles in essential cellular processes such (U M I M F), the global conformational stability can be partitioned as cell division, cell adhesion, protein translocation, locomotion, into the relevant conformational stability (the free energy difference

between the native and intermediate conformation, DGif) and the residual conformational stability of the intermediate (its free energy

difference with the denatured state, DGui) [13,14]. The words (relevant and residual) chosen to qualify these stability fractions adding up to the global conformational stability is prejudging that the intermediate will be devoid of biological activity. In what follows, I will review practical methods to determine equilibrium constants between protein conformations using either chemicals or heat as denaturants. Only spectroscopic methods will be discussed because calorimetric approaches are reviewed in another article in this issue [15]. I will then illustrate, for proteins with an equilibrium intermediate, how stability data can be used to obtain an approximate structure of the equilibrium intermediate using equilibrium /-analysis [16,17], an adaptation of classical kinetic /-analysis, originally devised to investigate transition states of protein folding [18]. Finally, some current challenges in the protein stability ﬁeld will be outlined. For the sake of simplicity, no at- tempt will be done in this article to distinguish between native and folded, denatured and unfolded or state and ensemble.

Fig. 1. Different types of protein stabilities illustrated in a free energy diagram. The conformational stability of the protein (DGuf) is the free energy difference between the fully folded (F) and fully unfolded (U) protein conformations. For proteins Counting molecules using light allows determining protein displaying a non-functional intermediate (I) that accumulates in equilibrium conformational stability conditions, the conformational stability is composed of the relevant stability

(DGif) plus the residual stability of the intermediate (DGui). The kinetic stability of a protein is related to the height of the energy barrier between the folded (native) Determining the conformational stability of a protein only state and the (partly or fully) unfolded state, which for a two-state protein is requires measuring the equilibrium constant of the folding reac- measured by DG à. It is possible that proteins are protected by high energy barriers tion. Therefore, one only needs to count, in equilibrium conditions, against forming b-aggregates more stable than the native conformation. The the molecules that are folded and those that are unfolded, and to (bio)chemical stability of a protein in a given solution condition will be large when calculate the ratio. The task would be, in theory, simple if: (i) the modiﬁed alternatives are of much higher energy than the native state or when large energy barriers separate the native basin from that of the irreversibly folded and unfolded molecules were of an entirely different ‘‘color’’ denatured one. so that the signal arising from the folded molecules did not Author's personal copy

6 J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13 interfere with that arising from the unfolded ones and vice versa, where one of the conformations is populated at a very high molar and (ii) the actual number of both folded and unfolded molecules fraction (usually some native condition where vf > 0.99). For many were high enough so as to give rise to significant signals from both proteins, the native conformation is dominant at a close to neutral conformations. In practice, this is not the case. Both folded and un- pH, a moderate temperature (25.0 °C has been a favorite for protein folded proteins absorb light, emit light, etc. Even if a signal can be stability studies) and a moderate ionic strength (e.g., 0.05–0.2 M). monitored that is specific to one of the two conformations and al- Having chosen the property and the solution conditions, the signal lows to quantify the number of molecules in that conformation of the solution essentially containing native protein molecules is (e.g., a high field methyl resonance of a native protein in a 1H recorded and then the solution conditions are modified step-wise NMR experiment), the problem remains that in native conditions to progressively make them more destabilizing of the native con- there is no easy way to determine precisely the number of mole- formation so that the molar fraction of the native state begins to cules in the unfolded conformation (in the fortunate case that we decrease and that of the unfolded state begins to increase had a signal specific of the unfolded state) because unfolded mol- (Fig. 2a). For a while (meanwhile solution conditions are being ana- ecules tend to be a tiny percentage of the total proteins molecules. lyzed where the molar fraction of the denatured state remains very Sometimes, even relating the signal intensity of the more popu- small) we will notice little because even very small experimental lated species with the actual number of molecules is difficult. So, errors will offset the very small changes taking place in total signal what do we do? (see Eq. (3), below). However, at some point, as the solution condi- In most cases we begin by choosing a property for which the tions allow unfolded molecules to accumulate to a significant mo- folded and unfolded molecules display a different value. It can be lar fraction, the signal will depart from its initial native value and the absorbance at a wavelength where the two conformations dis- will begin to progressively approach whatever value is characteris- play a different extinction coefficient, the emission fluorescence tic of the unfolded molecules. In some cases the signal will increase intensity at a wavelength where the quantum yield of the two con- and in others it will decrease. As soon as the molar fraction of the formations is different, etc. Then, we select a solution condition unfolded state becomes very large (vu > 0.99) little change in the signal will take place, regardless of a further increase of vu.

Chemical and thermal denaturation: general considerations

Typically, to obtain solution conditions more destabilizing of the native state, chemicals such as urea, guanidinium chloride and others are added or, alternatively, the temperature is increased. There are more possibilities, such as changing pH [19], ionic strength, li- gands concentration, etc., and each approach requires speciﬁc experimental setups and different ﬁtting equations. For chemical denaturation, a number of protein aliquots at ex- actly the same concentration and in the same buffer are prepared that differ in the concentration of denaturant. The spectroscopic signal of each of these solutions is determined and a representation of signal versus denaturant concentration is built, which typically resembles a sigmoidal curve (Fig. 2a). It should be noticed that the presence of denaturant can modify the optical properties of the native and/or of the unfolded protein molecules, and that those changes will contribute to modify the observed signal even in denaturant concentration ranges where one of the two species is clearly dominant and no conformational transition is taking place

(i.e., vf or vu > 0.99, at low or high denaturant concentration, respectively). These changes in signal, unrelated to significant changes in molar fractions, must also be contemplated in the fitting equation. For this reason, one needs to assess whether the denaturant actually modifies the signal of the native and/or the unfolded molecules or not. This fact becomes clear observing the evo- lution of the signal at very low and at very high denaturant concentrations where the unfolding transition has not begun or has come to completion (Fig. 2b). In other words, we want to have the conformational transition preceded by a number of measure-

ments in a denaturant range where vf is very high (where all changes in signal can be attributed to the inﬂuence of denaturant in the optical properties of the native state) and followed by a

number of measurements in a denaturant range where vu is very high (the denaturation is completed and any changes in signal Fig. 2. Spectroscopic protein unfolding curves. A spectroscopic signal is represented as a function of either denaturant concentration (in chemical denaturation) or have to be attributed to inﬂuence of denaturant in the optical prop- temperature (in heat denaturation). (a) In this curve, the signals of folded and erties of the denatured molecules). If guanidinium chloride is used unfolded protein molecules do not change with denaturant concentration or as denaturant, bear in mind that it is a salt and therefore it inﬂu- temperature. (b) In this curve, the signals of folded and unfolded protein molecules ences the ionic strength of the protein solutions. If urea is used, are not independent of denaturant concentration or temperature, on which they fresh solutions are needed because aqueous urea forms cyanate, depend in a linear manner. The equations shown (corresponding to Eqs. (5) and (6) in the text) model the denaturant or temperature dependence of the signal of folded which can react with protein molecules. In either case, always and unfolded protein molecules. use a high grade denaturant. Author's personal copy

J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13 7

For thermal denaturation, a single protein sample is needed, the S ¼ Sf vf þ Suvu ð3Þ signal of which is recorded as the temperature is raised. Evapora- where S and S correspond, respectively, to the signal arising from a tion should be avoided. A sigmoidal shape of signal versus temper- f u protein solution of the same concentration that would contain only ature is also expected, and the same considerations on the possible folded or only unfolded molecules. influence of denaturant on the intrinsic optical properties of the na- Eqs. (1)–(3) combine into: tive and unfolded molecules apply to temperature in thermal dena- ÀÁÀÁ turation. One, therefore, would like to have the conformational DGf =RT DGf =RT S ¼ Su þ Sf e = 1 þ e ð4Þ transition ‘‘centered’’ between a low temperature region where almost all protein molecules are native and a high temperature region which is valid for both chemical and thermal denaturation. If a where practically all protein molecules are unfolded. Neither for ‘‘centered’’ transition flanked by pre and post transition signal base- chemical nor for thermal denaturation are theoretical models used lines can be recorded, and those baselines look like straight lines, to describe the dependency of the optical properties of native and then Sf and Su in Eq. (4) can be modeled as: denatured molecules on denaturant concentration or temperature. 0 Instead, since quite often the pre and post transition regions of the Sf ¼ Sf þ mf ½Dð5Þ 0 signal look like straight lines (sometimes very flat and sometimes Su ¼ Su þ mu½Dð6Þ very steep) it is customary to approximate those dependencies as 0 0 linear (Fig. 2b) with denaturant concentration or with temperature where Sf and Su correspond, respectively, to the signal of the solu- [20]. In cases where the transition is not centered between pre and tion of native or unfolded molecules at a denaturant concentration post transition regions it is better not to include those dependencies of 0 M (no denaturant present), while mf and mu are the slopes of in the fitting equation. In cases where cold denaturation is observed the linear dependency attributed to the spectroscopic signals with [21], it may also be appropriate not to include a denaturant depen- denaturant concentration. You may not be very interested in the ac- 0 0 dency of the optical property of the native state, which would make tual values of Sf , mf, Su and mu but you will have to calculate them 0 very difficult deriving good values for other more important param- in the fitting. In many cases, the value of Sf can be accurately antic- eters that will be present in the fitting equation. Similarly, in the fit- ipated by visual inspection of the chemical unfolding curve. Change ting of curves corresponding to unfolding equilibria where three or [D] by temperature in Eqs. (5) and (6) for thermal denaturation. more-states populate (equilibrium intermediates are present) it To obtain specific equations for chemical or temperature dena- may also be convenient not to include a dependency of the optical turation, we just need to replace DGf in Eqs. (4) by an expression property of the intermediate, unless the two transitions (F M I and relating the folding free energy difference to either denaturant I M U) are very well separated. concentration or to temperature. For chemical denaturation, it Implicit in all above discussion is the fact that one wants to has been known for a long time that DGf is roughly proportional determine equilibrium constants, i.e., properties of an equilibrium. to denaturant concentration [23]. There are theoretical models try- This means that when the signal of a protein solution is measured, ing to explain this observation, such as the binding model or the the protein molecules in that solution must have reached the equi- solvent exchange model [24,25]. Whatever the physical reason librium between the different conformations available. If that is the why denaturants destabilize the native conformations of proteins, case, longer incubation in denaturant or different heating rates will it seems that DGf can be approximated by very simple functions not show as differences in the unfolding curve. It is also very impor- such as: tant to bear in mind that sometimes denaturants and often heat w DGf ¼ DG m½Dð7Þ may favor irreversible reactions of the protein which may be f w incompatible with refolding and therefore with a proper measure- where DGf is the folding free energy difference, or protein confor- ment of equilibrium properties. Thus, before the stability of a pro- mational stability, ‘‘in water’’ (more precisely in buffer with no tein is calculated, the unfolded protein solution has to be shown denaturant), which constitutes the goal of our experiment, and m to be refolding competent. In chemical denaturation, one can dilute is the slope of the linear dependency observed between folding free aliquots of a concentrated protein solution, previously denatured in energy and denaturant concentration. This way of modeling the high denaturant concentration, to obtain a set of protein solutions folding free energy difference as a linear function of denaturant of the same protein concentration but with different final denatur- concentration is known as the linear extrapolation method (LEM)1. w ant concentrations. The refolding curve that can be determined In precomputer times, DGf was determined using a graphical with those solutions should be identical to the forward unfolding method. First, from the denaturation curve, a set of Kf values were curve of the protein at the same concentration [22]. For thermal calculated at different denaturant concentrations laying in the re- denaturation one can record a cooling curve and, after that, a gion where the conformational transition took place (Fig. 3a). Then, reheating curve. If analysis of the reheating curve yields the same those Kf values were transformed into DGf values and a represen- thermodynamic parameters as for the initial unfolding curve (albeit tation of DGf versus denaturant concentration was fitted to Eq. with perhaps a somewhat smaller signal change reflecting that a (7) to determine, by extrapolation at 0 M denaturant concentra- w part of the protein did not recover from the denaturation), the ther- tion, the intercept, which corresponds to DGf (Fig. 3b). This meth- mal unfolding is considered to be reversible and the thermal od (LEM), whether graphically or computationally implemented, is unfolding curves can be used to determine protein stability. still the basis of virtually all protein stability determinations based in chemical denaturation. The experimental trick becomes now

The ﬁtting equations for two-state equilibria evident. We add denaturant to increase vu so that we can obtain, at certain denaturant concentrations in the transition region, reli-

Let us consider an homogeneous protein solution where any able values of Kf, hence of DGf, which would not be possible in na- given protein molecule can only be either fully folded or fully un- tive conditions where vu is too small to be measured. On the other folded, and there is an equilibrium between the two conformations hand, the fact that the two conformations are of a similar ‘‘color’’ (U M F). This may be an oversimpliﬁcation but many small proteins (both contribute to the global signal) is not a problem if pre and appear to comply with this simple two-state model. post transition signal baselines have been determined (Fig. 3a). The folding equilibrium constant (and the corresponding folding free energy) are given by Eqs. (1) and (2). The observed signal 1 Abbreviations used: LEM, linear extrapolation method; DSC, differential scanning (S) of the protein solution is given by: calorimetry. Author's personal copy

8 J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13

protein in the absence of denaturant, a negative number for a stable protein. Second: m, which is often referred to as ‘‘the slope’’ and that is known to be proportional to the change in solvent exposed sur- w face associated to the unfolding of the protein [26]. Because DGf is obtained by extrapolation, it is usually less accurate than any of

the DGf determined at a given denaturant concentrations in the transition region. Practitioners of chemical denaturation some-

times chose to report the concentration of denaturant where vn =- w vu = 0.5 (known as D1/2 and calculated as DGf /m) as a measure of protein stability. This is common when the stability of point mutants is compared to that of the wild type protein. One advantage

of D1/2 values is that they are more reproducible that the extrapo- w lated, and more interesting!, DGf values. The best practice is to ob- w tain as accurate as possible DGf values by recording unfolding curves with many data points, especially in the transition region, and averaging the results of the ﬁtting of several unfolding curves.

For thermal denaturation, DGf is approximated by the integrated Gibbs–Helmholtz equation:

Tm DGf ¼ DHf ðÞ1 T=Tm DCp;f ½ðTm T þ TlnðT=TmÞ 8Þ

where Tm is the temperature where Kf = 1 (temperature of mid dena- Tm turation), DHf is the folding enthalpy change at that temperature, and DCp,f is the folding heat capacity change (at constant pressure) at that temperature. Combining Eqs. (4) and (8) to ﬁt the thermal unfolding transition of a protein known to display a two-state equi- Tm librium allows to obtain values of DHf and Tm in excellent agree- ment with those derived from differential scanning calorimetry

(DSC) analysis, while the ﬁtted value of DCp,f is essentially unreliable w [9]. For this reason, determination of DGf using Eq. (8) and the ﬁt- Tm ted values of DHf , Tm and DCp,f is not usually possible unless DCp,f is determined in some other way. One possibility, leaving aside di-

rect DCp,f determination by DSC, is to record several unfolding curves in different solution conditions (different pH or ionic strength values) where the stability of the protein is significantly different. Fig. 3. Illustration of the linear extrapolation method (LEM) used to calculate the The fitting of each of those unfolding curves to Eq. (8) will provide stability of proteins using chemical denaturation. (a) Calculation, from a chemical Tm a particular pair of DHf and Tm values. Then, the slope of a plot denaturation curve, of unfolding equilibrium constants (Ku1, Ku2, Ku3) at three Tm denaturant concentrations (u1,u2 and u3) in the transition region. Many more of DHf values versus their corresponding Tm values is usually a w should be calculated to obtain reliable values of DG . The lengths of the blue and good approximation of DCp,f. Analogously to D1/2 values, Tm values red arrows are proportional, respectively, to the molar fractions of unfolded and are often used to rank the stability of wild type and mutant variants folded molecules. Folding equilibrium constants are easily calculated as the inverse of a protein without having to report the actual stability of the native of the unfolding ones. Folding or unfolding equilibrium constants are transformed into free energy differences for subsequent linear extrapolation. (b) Calculation of protein conformation at lower temperature or lacking denaturant. protein conformational stability in the absence of denaturant by the linear extrapolation method. Data in blue correspond to unfolding free energies, while data in red correspond to folding free energies. Only the data corresponding to the Useful spectroscopic techniques to measure protein stability transition region where the folded and unfolded molar fractions can be accurately determined is used in the linear fit. The useless data corresponding to the pre and In most cases, chemical or thermal denaturation curves are ob- post transition regions is also plotted to emphasize the practical impossibility to tained using either fluorescence or circular dichroism. However, determine these free energy differences in solution conditions where the molar fraction of one of the conformations is close to 1, hence the need to perturb the the only requisite to use a particular spectroscopic technique is equilibrium by adding denaturants. that equimolecular solutions of native and unfolded protein differ in the value of their signals. It is thus advisable to begin exploring the suitability of a given spectroscopic technique by recording a This being the case, the total signal change can be calculated at any spectrum of the native solution and comparing it to that of the denaturant concentration as the difference between the native and equimolar unfolded solution (with either a high denaturant con- unfolded signal baselines. In the transition region, vu is simply pro- centration or at a high temperature). This is also of help to identify portional to the fractional loss of total signal change associated to the particular wavelength giving the largest signal change, or the the denaturation transition, and vf is proportional to the fraction of lowest interference from the solvent. When doing this preliminary signal change that has not occurred yet. Therefore, the equilibrium analysis, one should bear in mind that the existence of spectro- constant is the ratio of those fractional changes. This is why it is scopic changes not related to the conformational transition, such important to have obtained good pre and post transition baselines as denaturant or temperature-related fluorescence emission in the denaturation curve. quenching, may mislead us if only two spectra (native and fully un- When using computers, DGf in Eq. (4) is replaced by its expres- folded) are compared. If one can afford it, one should record several sion given by Eq. (7), and the experimental data (signal versus dena- spectra at different denaturant concentrations or at different tem- turant concentration) is fitted with the modified Eq. (4). The fitting peratures to clearly observe a transition before selecting the single provides the best values of a number of uninteresting parameters wavelength of observation for further experiments. 0 0 (such as Sf , mf, Su and mu) and the values of two interesting ones. It is very important that the observed signal reflects the pro- w Most important: DGf , the folding free energy difference of the gress of the unfolding reaction. Only extensive properties are Author's personal copy

J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13 9 appropriate (see appendix in [17]). Let us illustrate this seemingly two-state unfolding equilibrium, most proteins are not small and trivial point with the example of an unfolded curve recorded using a two-state mechanisms should not be taken for granted. Instead, a fluorimeter. For proteins containing tryptophan residues (most a more complex unfolding equilibrium populated by one or several proteins) and lacking cofactors, the fluorescence emission spec- partly unfolded conformations is more likely. trum reflects tryptophan optical properties, which are sensitive In a three-state equilibrium there is just one such partly un- to solvent. Thus, the fluorescence emission spectra of most pro- folded conformation, which accumulates as the denaturant con- teins display maxima around 320–340 nm in the native state, centration or the temperature is raised, and then becomes fully which are shifted to 355 nm as the protein unfolds and the trypto- unfolded in more denaturing solution conditions (U M I M F). In a phan residues (to some extent buried in the native conformation) very favorable case where (i) the intermediate is the most stable become fully exposed to solvent. Protein unfolding is thus very fre- species in a wide range of denaturant concentrations or tempera- quently accompanied by a tempting concomitant red-shift in emis- ture and (ii) the value in the intermediate of the spectroscopic sion fluorescence that one would like to use to follow the unfolding property used to follow the progress of the unfolding is clearly dif- transition. This seems to be especially convenient since the wave- ferent from those of the native and denatured conformations (say, length of maximal fluorescence emission is, in principle, concen- the mean of those values), detection of the intermediate will be tration independent thus small aliquoting errors (not infrequent easy because the unfolding curve will be a double sigmoidal curve in chemical denaturation experiments) would not affect the re- (Fig. 4b). However, if the molar fraction of the intermediate is sults. However, the fitting to Eq. (4) of a representation of the never high, the unfolding curve will look like a single broader sig- wavelength of maximal emission (an intensive property) as a func- moidal curve, while if the value for the spectroscopic property of tion of denaturant concentration may or may not provide correct the intermediate is similar to that of the native or of the unfolded w values of DGf . Just think of a protein with an intense native emis- conformation, the double sigmoidal will pass unnoticed, hidden in sion spectrum and a weak denatured emission spectrum. For one the experimental noise of the pre or post transition baselines. such protein, no change in the wavelength of maximal emission In many cases, the occurrence of an equilibrium intermediate is will be observed until most of the protein molecules are unfolded. noticed when several single sigmoidal-looking unfolding curves re- Therefore, Eq. (3) will not hold, neither Eq. (4) will. The same can corded following different spectroscopic properties (e.g., fluores- be said of the widely used center of spectral mass. Another com- cence and circular dichroism, (Fig. 4a)) cannot be superimposed mon example of a suboptimal use of fluorescence properties is [12,29], in other words: when their separate fitting to a two-state working with intensity ratios. For recording a chemical unfolding equation yields different values for the conformational stability of curve many different solutions need be measured, and one may the protein. When this occurs, a three-state model should be used want to minimize aliquoting errors. On the other hand, for record- to simultaneously fit the two or more curves recorded. Obviously, ing a thermal unfolding curve, one may want to counteract the it is very important to record unfolding curves with as many spec- very strong quenching of fluorescence due to increased tempera- troscopic techniques as possible to see whether they all can be ture that is manifested in very step pre and post transition base- superimposed or not. When your protein is two-state, all the lines. Both problems are alleviated if a ratio of emission curves will superimpose (Fig 4c). If a fluorimeter and a circular fluorescence at two different wavelengths is plotted as a function dichrograph are available, one should try to record at least a tryp- of temperature. However, such a ratio of intensities is not an exten- tophan fluorescence emission unfolding curve, a CD unfolding sive property and does not need to satisfy Eq. (3). Although plotting curve in the far UV and a CD curve in the near UV. Since CD is based the fluorescence intensity at a single wavelength may require a in absorbance, recording a CD curve means that an absorbance more careful experimentation, it is the right way. curve has also been recorded, whether the instrument indicates The same ideas apply to other techniques. Circular dichroism is it or not. Such an absorbance curve should be found and used in very useful for following protein unfolding transitions. In the far- the global fitting because sometimes it cannot be superimposed UV region, the characteristic minima of beta and alpha secondary to the associated CD curve, which serves to reveal the presence structure conformations are widely used because they fade as the of an intermediate [12,29]. secondary structure is disrupted due to unfolding. In the near-UV, The equation needed to fit the unfolding curve of a three-state the signal arising from aromatic residues in native, asymmetry- unfolding equilibrium, Eq. (9), can be derived similarly to that for inducing environments is also very useful because it disappears a two-state equilibrium by combining equations equivalent to when the protein unfolds. Compared to monitoring in the near- Eqs. (1)–(3), considering that there are three species and two equi- UV region, the stronger signal in the far-UV region allows saving librium constants. protein but restricts the buffers and additives that can be present ÀÁÀÁ in the protein solution. The absorbance, in the near-UV of the aro- DGui=RT ðDGuiþDGif Þ=RT DGui=RT ðDGuiþDGif Þ=RT S ¼ Su þ Sie þ Sf e = 1 þ e þ e matic residues present in most proteins can also be used to moni- ð9Þ tor unfolding, but changes related to unfolding tend to be small

(usually a blue-shift of the absorbance spectrum) [27] and a careful In Eq. (9), Su and Sf are usually substituted by linear functions of choice of wavelength will be needed if absorbance is to be used. denaturant concentration or temperature: Eqs. (5) and (6), plus an

NMR, FT-IR and many other techniques such as SAXS [28] can be equivalent equation for Si. For chemical denaturation, the two free similarly used if available. energy differences in Eq. (9) are modeled by the LEM using two equations equivalent to Eq. (7). For temperature denaturation, the two free energy differences are modeled by two equations Revealing and analyzing three-state and more-state proteins equivalent to Eq. (8). When one unfolding curve is clearly a double sigmoidal, ﬁtting the curve to Eq. (9) provides the relevant infor-

The equations and experiments described above allow to calcu- mation of the two equilibria. In chemical unfolding: DGui (the sta- late the conformational stability of two-state proteins but, how can bility of the intermediate conformation relative to the unfolded one know whether the protein being analyzed follows a two-state state, sometimes known as the residual stability of the protein mechanism? The answer is that one should actively look for devi- [13,14]) and DGin (the stability of the native conformation relative ations from a two-state behavior and, if none is found, the two- to the intermediate state, known as the relevant stability of the state mechanism is then considered an appropriate description of protein). In thermal unfolding: the enthalpy change and tempera- the protein equilibrium. While small proteins often follow a ture of mid denaturation of each of the two equilibria. Author's personal copy

10 J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13

Fig. 4. Unfolding curves of three-state proteins compared to a two-state one. (a) Global fitting (continuous lines) of experimental thermal denaturation curves of wild-type apoflavodoxin followed by far-UV CD (black), near-UV CD (red), fluorescence (blue) and absorbance (green). Each curve was normalized to values from roughly 1 to 0 before performing the global fitting [16]. Neither of the individual curves looks like a double-sigmoidal but their mid-points are clearly at different temperatures indicating a three- state mechanism. (b) Same analysis for a point mutant of the same protein (E20 K apoflavodoxin) where two of the curves (red and blue) look like double-sigmoidals [11]. Although any of them alone could have been used to perform a three-state fit, the global fit of the four curves shown is preferred. The different curves have been roughly normalized to signal spans or around 1 before performing the global fitting. (c) A two-state protein (wild type apoflavodoxin saturated with its natural, colored, FMN cofactor) [32]. Seven different curves are superimposed. They have been transformed, after global fitting to a two-state model, to represent fraction of folded protein. Far-UV CD at 222 nm (orange circles), near-UV CD at 288 nm (green circles), visible–UV CD at 367 nm (red triangles), absorbance at 288 nm (inverted red triangles), at 440 nm (green triangles), at 500 nm (blue triangles), and fluorescence at 320 nm (pink stars). The yellow solid line represents the global fit of the seven curves to a two-state model.

If the unfolding curves are not double sigmoidals but a three- The unfolding equilibrium of some proteins involves more than state equilibrium has been nevertheless revealed, all the single sig- one equilibrium intermediate and they are therefore four-state moidal-looking unfolding curves obtained have to be simulta- [29,30] or even more state proteins. Four-state equilibria are re- neously fitted to Eq. (9). This fitting cannot be done with very vealed when a three-state model is unable to simultaneously fit simple fitting software but there are many commercial programs all the unfolding curves obtained for a given protein. The equations (such as ORIGIN, from OriginLab or MLAB from Civilized Software used to derive the stability of four-state of more-state proteins can Inc) that can be used. Using such programs, the different unfolding be deduced similarly to those of three-state proteins. curves are fitted simultaneously to Eq. (9) forcing all relevant ther- Unlike the stability of monomeric proteins not carrying bound modynamic parameters (DG and m,orDH, DCp and Tm) of the two cofactors, which we have analyzed here, that of oligomeric proteins equilibria to be the same for all curves, while the spectroscopic and that of proteins containing tightly bound ions or prosthetic groups parameters (Sf, Si, Su, plus those defining their linear dependencies are concentration dependent and should be analyzed using specific with denaturant concentration or temperature if used) are allowed equations. Examples of such analyses can be found in [31–34]. to vary from curve to curve [16]. In spite of the many parameters involved, robust fittings can usually be obtained if several, good quality unfolding curves monitored following different spectro- Comparing the stability of mutant proteins scopic signals are available for simultaneous fitting. As previously discussed, the two DCp values obtained will not be reliable. Due The stability of proteins is sometimes determined to allow com- to the many parameters involved, providing reasonable initial esti- parison with that of mutants thereof. These may be engineered mates is required for the fit to converge. So, before triggering the variants designed to achieve a higher thermostability [2], but can fitting, think a bit about reasonable values for the initial estimates also be disease-involved mutant proteins. Indeed, many human of each fitting parameter present in the specific form of Eq. (9) you mutations associated to disease give rise to defective proteins by may be using. a very trivial reason: they decrease the stability of the native Author's personal copy

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protein to the point of significantly lowering vf [35]. For a two- information on the intermediate. The method is known as equilib- state protein, the best way to compare the stability of a mutant rium /-analysis [16,17] because it is an extension of the kinetic to that of the wild type form is to compare their DGf values in /-analysis method used to obtain structural information of transi- the appropriate solution conditions or, if the main concern is ther- tion states of protein folding [18]. Equilibrium /-analysis has been mal denaturation, to compare their Tm values. For three-state pro- used to obtain a low-resolution structural model of the intermedi- teins, one can compare the global stability (DGf = DGuf) of wild type ate of a three-state protein [16], in which two regions could be and mutant or the stabilities of their native conformations relative identified: one larger region that remained natively folded, and to the intermediate (DGif), or those of their intermediates relative one smaller one that was unfolded in the intermediate. Based in to the fully denatured conformation (DGui). When the region of this low resolution structure, a mutant protein was designed and the protein that is unfolded in the intermediate is known, it is even expressed that adopted the conformation of the intermediate, with possible to specifically modify DGif or DGui by a rational choice of vi 1, and whose structure could be solved by NMR [37]. The mutation [14]. Obviously, one will in most cases want to increase correspondence between the low-resolution structure previously

DGif so that the native conformation becomes more resistant to obtained by equilibrium /-analysis and the NMR solution structure transformation into the intermediate, partly unfolded conforma- was excellent, proving the usefulness of the approach. tion. As discussed, deriving DG values from thermal denaturation Equilibrium /-analysis is based in probing the structure of a experiments requires some extra work to independently determin- protein by making single point mutants, the less disruptive the ing DCp values. However, even when accurate DCp values are not better, and each significantly modifying the global stability of the available, reasonable stability differences between mutant and protein (Fig. 5). The stability of the mutants is then analyzed, by wild type can be estimated as: the spectroscopically-based curve fitting procedures we have ÀÁ described above, in order to determine how the global stability mutwt mut wt mut DDGf ¼ DHf 1 Tm =Tm ð10Þ change introduced by the mutation has modified the relevant and residual stabilities of the protein. From the stability of the wild or using equivalent equations [36]. This approximate stability dif- type protein and that of each of the mutants, /-values are defined ference calculation can be similarly done [16] for obtaining DDG ui [16] as: and DDGif. / ¼ DDG =ðÞDDG þ DDG ð11Þ Combining stability data and protein engineering to determine ui ui if the structure of protein intermediates Equilibrium /-values take the value of 1 when the interaction modified in the mutant is as formed in the native state as it is in Obtaining the structure of conformational intermediates by the intermediate, and a value of 0 when the interaction modified conventional methods is difficult when they do not accumulate in the mutant is as disrupted in the intermediate as it is in the dena- to a high molar fraction because they appear mixed with large frac- tured state. /-values lower than 0 or higher than 1 indicate the pres- tions of either native or unfolded protein molecules. Fortunately, ence of non native interactions in the intermediate. You will need to for a protein displaying a three-state equilibrium unfolding, the analyze a few dozen mutants (Fig 5b) to obtain enough /-values so relative effects of mutations on the relevant and residual stabilities as to get a low resolution structure of your intermediate. In addition,

(DDGif, DDGui) can be used to obtain important structural the spectroscopic properties of each of those mutants (at least far

Fig. 5. Equilibrium /-analysis to derive low resolution, highly useful structures of protein intermediates. (a) The global (DGuf), relevant (DGif) and residual (DGui) stabilities of the wild type protein are determined from analysis of its three-state unfolding equilibrium, and the corresponding differences with point mutant proteins are computed. A /- value, defined as in the figure, is then calculated for each mutant, which quantitates the extent to which the native interaction broken in the particular mutant is formed in the equilibrium intermediate of the wild type protein. /-values of 1 are obtained when the interaction is fully formed in the intermediate and of 0 when it is as broken as in the unfolded state. (b) Analysis of several dozen mutants probing the protein structure allows to derive enough / -values so as to obtain a low-resolution structure of the intermediate [16]. These /-structures allow to rationally design mutations to specifically increase the relevant stability of the protein [14]. They also allow to design mutants where the molar fraction of the intermediate is 1 in solution conditions appropriate for determining the solution structure by NMR [37]. Author's personal copy

12 J. Sancho / Archives of Biochemistry and Biophysics 531 (2013) 4–13 and near-UV CD, and fluorescence) should be compared to those of Miniaturized protein stability assays [58] have proved very useful the wild type protein in order to identify and discard mutants show- for the discover of both pharmacological chaperones [59] and clas- ing signs of non-native structure. Be also careful with non canonical sical enzyme inhibitors [60]. /-values, lower than 0 of higher than 1. Although they can indicate Finally it should be mentioned that the much sought goal of stabi- the presence of non-native interactions in the intermediate, in our lizing proteins at will using Protein Engineering techniques is only experience they are sometimes associated to poor experiments or partly realized and that protein stabilization remains something in to mutations giving rise to small stability changes. The error associ- between rational design and trial and error. Renewed investigation ated to each /-value has to be always calculated and taken into ac- into the quantitation of basic interactions influencing protein stability count, which means some of the mutants that you have painfully is needed. In addition, development of simple bioinformatics tools to analyzed may not be useful after all. The good news is that the struc- guide protein stabilization design would greatly benefit industry. tural information that can be obtained by equilibrium /-analysis is far more detailed than the information that can be derived from Conclusions common approaches used to characterize protein intermediates never accumulating to high v , such as spectral deconvolution, i In conclusion, simple equipment and chemicals, such as a thermo- ANS binding or 1D 1H NMR. Specifically, a /-structure will already stated fluorimeter and common denaturants, suffice to determine the allow you to stabilize the locally unstable region of your three-state conformations stability of a protein. To this end, the most important protein by designing appropriate mutants right in the unstable spot experiments are the preliminary ones done to establish the minimum [14]. In addition, if you want to know more about your intermediate, number of species (conformations) accumulating in the equilibrium. the /-structure will allow you to design mutant models of the inter- For proteins with non-functional equilibrium intermediates, deter- mediate, which you will be hopefully able to express to obtain a pro- mining the relevant stability of the protein (the free energy difference tein solution with v = 1 that will allow you solving the structure of i between the native conformation and the intermediate) is most the intermediate by NMR [37]. important, and it allows deriving very valuable structural information of the intermediate when proteins variants are compared to wild Some challenges in the protein stability field type. Understanding protein folding and stability is no longer just a highly exciting physicochemical challenge but holds the key to Although the stability and folding of two-state proteins are understand essential cellular mechanisms and to obtain novel drugs understood far better than those of more complex ones, a consensus to treat conformational diseases. view is still lacking [38]. Understanding the structure and energetics of protein folding intermediates (either transient or at equilibrium) is most important to illuminate the folding reaction and the rela- Acknowledgments tionships between protein dynamics, function and misfolding [39–41]. In this respect, identification of the highly dynamic regions This work was supported by grants BFU2010-16297 (Ministerio present in native structures using simple bioinformatics tools is an de Ciencia e Innovación: MICINN, Spain) and Grupo Protein Targets active field [39,40]. B89 (Diputación General de Aragón, Spain). The author would like Experimental approaches such as equilibrium /-analysis [16], to thank his past and present young and otherwise collaborators in NMR [37], SAXS [28] and others can be combined with MD simula- protein stability studies at Cambridge and Zaragoza Universities tions [42] to derive detailed information on partly unfolded confor- and others. mations of proteins. Advances in NMR analysis promise a wealth of new data [43]. The compilation of a curated database gathering the References available structural information of folding intermediates, not lim- ited to NMR data, would be very useful. [1] H.J. Dyson, P.E. Wright, Nat. Rev. Mol. Cell Biol. 6 (2005) 197–208. Aside from the native state, the unfolded ensemble remains the [2] V.G. Eijsink, A. Bjørk, S. Gåseidnes, R. Sirevåg, B. Synstad, B. van den Burg, G. Vriend, J. Biotechnol. 113 (2004) 105–120. most distinct and less characterized protein conformation [44–46]. [3] Biologic drugs set to top 2012 sales. (2012). 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