Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1484
Extending the Reach of Computational Approaches to Model Enzyme Catalysis
BEAT ANTON AMREIN
ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-554-9816-0 UPPSALA urn:nbn:se:uu:diva-314686 2017 Dissertation presented at Uppsala University to be publicly examined in A1:111a, BMC, Husargatan 3, Uppsala, Friday, 24 March 2017 at 09:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Prof. Adrian Mulholland (University of Bristol).
Abstract Amrein, B. A. 2017. Extending the Reach of Computational Approaches to Model Enzyme Catalysis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1484. 67 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-554-9816-0.
Recent years have seen tremendous developments in methods for computational modeling of (bio-) molecular systems. Ever larger reactive systems are being studied with high accuracy approaches, and high-level QM/MM calculations are being routinely performed. However, applying high-accuracy methods to large biological systems is computationally expensive and becomes problematic when conformational sampling is needed. To address this challenge, classical force field based approaches such as free energy perturbation (FEP) and empirical valence bond calculations (EVB) have been employed in this work. Specifically:
1. Force-field independent metal parameters have been developed for a range of alkaline earth and transition metal ions, which successfully reproduce experimental solvation free energies, metal- oxygen distances, and coordination numbers. These are valuable for the computational study of biological systems. 2. Experimental studies have shown that the epoxide hydrolase from Solanum tuberosum (StEH1) is not only an enantioselective enzyme, but for smaller substrates, displays enantioconvergent behavior. For StEH1, two detailed studies, involving combined experimental and computational efforts have been performed: We first used trans-stilbene oxide to establish the basic reaction mechanism of this enzyme. Importantly, a highly conserved and earlier ignored histidine was identified to be important for catalysis. Following from this, EVB and experiment have been used to investigate the enantioconvergence of the StEH1-catalyzed hydrolysis of styrene oxide. This combined approach involved wildtype StEH1 and an engineered enzyme variant, and established a molecular understanding of enantioconvergent behavior of StEH1. 3. A novel framework was developed for the Computer-Aided Directed Evolution of Enzymes (CADEE), in order to be able to quickly prepare, simulate, and analyze hundreds of enzyme variants. CADEE’s easy applicability is demonstrated in the form of an educational example.
In conclusion, classical approaches are a computationally economical means to achieve extensive conformational sampling. Using the EVB approach has enabled me to obtain a molecular understanding of complex enzymatic systems. I have also increased the reach of the EVB approach, through the implementation of CADEE, which enables efficient and highly parallel in silico testing of hundreds-to-thousands of individual enzyme variants.
Keywords: epoxide hydrolase, enantioselectivity, regioselectivity, enantioconvergence, biocatalysis, empirical valence bond, computational directed evolution
Beat Anton Amrein, Department of Cell and Molecular Biology, Box 596, Uppsala University, SE-75124 Uppsala, Sweden.
© Beat Anton Amrein 2017
ISSN 1651-6214 ISBN 978-91-554-9816-0 urn:nbn:se:uu:diva-314686 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-314686) /LVW RI SDSHUV
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[17] or intrinsically unstructured proteins [18]). Also, the experimental tools needed to obtain information may not exist (e.g., as when a substrate has many possible but experimentally indistinguishable conformations [19]. As we will see later in this thesis, thanks to the computing power of hardware and software that is available today (and which is undergoing continuous development), it is possible to simulate reactions in silico to provide additional insight [20, 21]. For some specialized problems, computational approaches have even shown potential for the design of new catalysts [22, 23]).
1.2 Biochemistry, Biocatalysis and Enzymes Biological processes adapt to their native environments, namely the tempera- ture, pressure, and solvent of the biological cell. Proteins that are biocatalyti- cally active (i.e., enzymes) that can handle reactions proficiently under the con- ditions in living cells, even at the diffusion limit, have evolved [24–26]. At the same time, although highly specific and efficient enzymes are needed for some reactions, biological organisms need to adapt new functions (e.g., to respond to new molecules in their environments). As early as 1976, Jensen suggested that catalytic promiscuity (i.e., the ability of some enzymes to turnover multi- ple substrates) is important to evolve new functions [27]. Today, this natural process is mimicked by protein engineers and facilitates a better understanding of the evolution of new functions [28]. In this context, various computational tools have been developed to predict enzyme promiscuity and also to recon- struct ancestral proteins [29, 30]. (For more details refer to our perspective on the catalytic promiscuity of the alkaline phosphatase superfamily [31]). Biocatalysts are catalysts that work in aqueous solutions, usually in the cell cytoplasm, with high concentrations of protein and other biological molecules present [32, 33]. For many reactions it is therefore crucial for an organism to have very selective catalysts. This, together with their high efficiency and the ability to function without precious metals, makes biocatalysts potent con- tributors to greener chemistry. Also, enzymes can be very selective in terms of chemo-, regio- and enantioselectivity. This can allow for greater atom- efficiency in chemistry because cleaning a product mixture both wastes mole- cules and is tedious. This, together with high efficiency, allows some enzymes to be used in industrial applications (see Table 1.1), and the number of enzymes applicable to industrial processes is increasing [34, 35]. Important factors of this development are that enzymes work under mild conditions and that they can be very selective. The application of enzymes can, however, be limited by the properties of their environment, namely phys- iological conditions with low substrate and enzyme loads. Enzymes are hence increasingly tuned toward process requirements [43, 44], but many challeng- ing problems remain unsolved [44]. Various computational approaches have been put forward to address those challenges [23, 45–48].
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Figure 1.3. The potato (Solanum tuberosum) epoxide hydrolase 1 (StEH1), PDB- ID: 2CJP. (A) The wild-type StEH1 displayed as surface view with part of the active site visible in the center of the image. (B) The substrate-free active site of wild-type StEH1 featuring the catalytically relevant residues: For the first step, these are the nucleophile D105, the oxyanion-hole tyrosines Y154 an Y235, and histidine H300 and the nucleophilic water. activated by H300. Finally, the tetrahedral intermediate is converted to product and then released to close the catalytic cycle (see Figure 1.4). The mechanistic cycle is unable to explain the origin of the regio- and enan- tioselectivity of StEH1. This is exactly where computational modeling unfolds its potential. A variety of substrates that were subjected to kinetic measure- ments with different protein variants and crystal structures of some protein variants allowed us to build a computational model that could reproduce the experimental data. With the help of this computational model, we were able to establish the mechanism in even more detail and identified a previously ne- glected catalytically important residue – H104 – in the active site, see Paper II. We have then, thanks to the established details of the reaction mechanism, obtained insight to detailed regio- and enantioselectivity, see Paper III. As the trans-stilbene oxide (TSO) substrate, styrene oxide (SO) can be open- ed at both epoxide carbons (C1 and C2). In contrast to TSO, however, the product is not always the meso-diol, but it is experimentally distinguishable. It was found in earlier work that the wild-type enzyme is enantioconvergent and converts both (R)-SO and (S)-SO preferably to the (R)-product (see also Figure 1.5) [53, 69]. StEH1 was investigated using a combined experimental and computational approach and different enzyme variants have been tested with all stereoiso- mers of the substrate. In Paper II and Paper III EVB calculations have been performed on StEH1 with different mutant structures and two substrates, trans- stilbene oxide (TSO, Paper II) and styrene oxide (SO, Paper III), see also Fig-
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more and more processor-cores and so code has to be optimized to run on multiple processors, see Figure 1.8). Two major computational modeling approaches are in use today. Approach- es based on molecular mechanics (MM) rely on force fields to simulate a molecule with Newtonian limitations and scale, depending on the implemen- tation details between O(n log(n)) to O(n2), see also Figure 1.7. While the O(n· log(n)) algorithm involves a computationally expensive reverse Fourier transformation, it scales much better with larger problem sizes.
Figure 1.7. It is important to estimate the computational costs of algorithms. The big O notation describes the worst-case performance of an algorithm, when the argument n tends to infinity, and it provides a worst-case estimate of how many operations an algorithm will need to arrive at a result given a problem of size n. For example, O(n) means that the computational cost will increase linearly with the problem size, and O(n2) that it will increase to the square, as the problem size is increased. The big O notation estimates only how many iterations the algorithm needs. In practice, a higher- order algorithm may be faster for a range of problem sizes if the costs per iteration are lower.
One limitation of classical force fields is that they are unable to describe ex- cited states and thus usually limited to nonreactive simulations (i.e., no bonds can be formed or broken). To describe excited states numerical approxima- tions to solve the Schrödinger equation are employed. These approaches are referred as quantum mechanical (QM) approaches and scale, depending on the implementation details, usually between O(n3) (DFT) to O(n7) (CCSD(T)), O(n8) (CCSDT) [71, 72]. Many of the QM approaches used today are hence limited to system sizes ranging from between a few dozens to about 1,000 atoms, depending on the available resources and approach used. Efforts are ongoing to reduce the or- der of quantum mechanical approaches required and to achieve linear scal-
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hardware (ANTON) milliseconds (ms) [94], to obtain information of the con- formational landscape of a molecule. Often, molecules have many degrees of freedom, making it very hard or impossible to find the global minimum energy conformation and simulations can get trapped in local minima. Additionally, large molecules have many energetically similar configurations that are all ac- cessible with temperatures around 300K. It is therefore of central importance to sample a molecule’s energetic landscape long enough and with different ini- tial conditions, to obtain sufficient sampling and collect an understanding for the states a molecule visits over time. This approach is routinely used to per- form simulations of protein in solvent and is implemented in many simulation packages (e.g. GROMACS [115, 116], AMBER [117], CHARMM [118] and Q [119]). Depending on the simulated system, code, and hardware used, 1 second compute time translates to 10−14 (single core [120]) to 10−9 seconds (ANTON 2 [94]).
2.5.3 Quantum Mechanical Simulations Quantum mechanical approaches (QM) simulate a molecule entirely, including electrons. Since electrons have much less mass than the nuclei they are almost instantaneously adapting to the movement of the nuclei and this can be used to separate the nuclei from the electrons. This fundamental approximation is called Born-Oppenheimer approximation. The goal of the QM approaches is to calculate the wave function of a mo- lecule, as can be done by solving the Schrödinger equation. The Schrödinger equation has however only an analytical solution for the simplest atoms (e.g. hydrogen atom) and it needs to be solved numerically for other atoms and molecules. Using the Born-Oppenheimer approximation, the Schrödinger equa- tion can be solved for the electrons separately. The Hartree-Fock method ap- proximates further, by calculating the electron interaction with the meanfield of the other electrons, thus neglecting electron-electron correlations. To in- clude electron correlation QM methods based on Møller–Plesset perturbation theory (e.g. MP2), configuration interaction (CI) or coupled cluster (CC) can be employed. These methods are, however, computationally expensive (N4 to N8), growing with the number of electrons in the system. Hence they are un- practical for large systems. Density function theory (DFT) is an approach that can be used for larger systems, which does not aim to approximate the wave- function, but instead the electron density. A shortfall of DFT is the description of exchange-correlation and different functionals should be tested for a system to avoid non-physical DFT artefacts.
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3. Methodology Advances
3.1 Paper I Force Field Independent Metal Parameters Using a Nonbonded Dummy Model Metals play ubiquitous roles in proteins and enzymes: Nearly 1/3 of the protein structures stored on the PDB contain metal ions [135]. Also, metals are found in all classes of enzymes and for example 44% of all known oxidoreductases contain a metal-center [136]. Clearly accurate metal models are important to model metallo proteins.
Modeling metal ions is challenging because metals are easily ionized and highly reactive. Hence, one would preferably model metals with QM ap- proaches which is increasingly done in QM/MM studies [137–139]. It is how- ever often still problematic to reproduce physical properties accurately with QM methods [140, 141]. Additionally, QM approaches are computationally expensive. This is accented, especially if one wishes to perform free energy calculations, which require significant conformational sampling. Different strategies to model metal ions with classical simulations have been published previously. In Paper I, we have described them broadly as three classes; the non-bonded soft-sphere model, the covalently bonded approach and the non-bonded dummy model approach. The simple non-bonded soft- sphere models are describing metal-ligand interactions trough electrostatic and van der Waals potentials. While both earth-alkali and alkali metals have been modeled successfully with this approach, the model appeared to be inadequate for modeling multinuclear metal centers [142]. An additional challenge was the simultaneous reproduction of both metal - water distances and free ener- gies of solvation. The second approach using covalently bonded approaches is not allowing ligand exchange and/or interconversion between different co- ordination geometries [143] and generally suffers from predefined bonds and challenges with a large number of parameters and additionally it needs repara- metrization for new systems [135]. The final approach is using a dummy model, originally developed by Åqvist and Warshel for the octahedral dummy model of Mn2+ ions [144]. The dummy model approach aims to provide an alternative metal model to deal with short- comings of the other approaches and reproduce experimental data. For the oc- tahedral dummy model a metal ion consists of six δ+ charged dummy-particles
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6. Populärvetenskaplig Sammanfattning
Modellering av Enzymkatalys och Nya Möjligheter för Datorberäkningar I min avhandling har jag använt datorer för att studera och förklara kemiska fenomen på molekylär nivå. De senaste åren har datorer lett till en våldsam teknisk utveckling såväl i privatlivet som inom vetenskapen, vilken jag dragit nytta av inom min forskning.
Jag har använt en metod för att utnyttja de tillgängliga beräkningsresurserna på det mest effektiva sättet. Detta är möjligt främst då vår metod förenklar det studerade systemet.
”Så enkelt som möjligt, men inte enklare!” - Albert Einstein
Vi använder en klassisk beskrivning av de atomära systemen. Vi simulerar molekyler bestående av atomer och bindingar som kulor och fjädrar, vilken i motsats till kvantmekaniska beskrivningar innebär att elektronkonfiguration- erna inte beräknas exakt. Detta behövs för att beräkna molekyler och reak- tioner så noggrant som möjligt. Kvantmekaniska modeller är dock mycket beräkningsintensiva och därför kan vissa egenskaper hos stora molekyler inte beräknas tillräckligt noggrant eller med tillräckligt många upprepningar (för biologiska system måste olika startkonfigurationer provas och systemet måste ges en viss tid att komma jämvikt). Med den förenklade klassiska beskrivnin- gen har jag forskat på atomer, molekyler och reaktioner. Jag har publicerat fyra arbeten inom följande tre områden:
För det första har jag tillsammans med ett antal kollegor arbetat med simu- lering av metalljoner med klassiska molekylära simuleringar. Vi har tagit fram parametrar med den så kallade Octahedral Dummy Model. Det finns redan sedan tidigare modeller för metalljoner som dock inte varit lämpade att beskriva jonernas egenskaper i enzymer. De parametrar vi publicerat kan beskriva experimentellt bestämda egenskaper som solveringsenergi, koordi- nationsnummer och avstånd mellan en metalljon och det omgivande vattnet. Särskilt viktigt för att kunna beskriva reaktioner är att vår modell kan genomgå ligand-utbyte: Det är möjligt att byta ut till exempel en vattenmolekyl mot en annan bindningspartner. Förutom detta är vår modell också enkel att överföra till andra system. Dessa egenskaper har tidigare modeller inte kunna uppfylla med samma noggrannhet och utan begränsningar.
51 För det andra har jag forskat på ett enzym från potatis. Enzym är biokatalys- atorer som, likt en katalysator i en bil, gör en kemisk reaktion snabbare. Detta potatisenzym kan omvandla så kallade epoxider mycket selektivt. Epoxider är molekyler som har en tre-ring av två kolatomer och en syreatom. Epoxider kan användas som råmaterial till olika finkemikalier och läkemedel. I min första artikel om StEH1, Solanum tuberosum epoxidhydrolas, har jag undersökt i detalj hur enzymet genomför reaktionen. Vi har funnit och publicerat reak- tionsmekanismen, och dessutom funnit att det är mycket sannolikt att en viss histidin aminosyra i enzymet är joniserad, samt att detta histidin också finns på motsvarande plats i närbesläktade enzymer. I tidigare datorstudier av lik- nande system har detta histidin ignorerats eller modellerats felaktigt. Genom mitt nästa steg, och tredje vetenskapliga arbete, har vi kunnat förstå en mycket intressant egenskap hos StEH1 bättre. Denna egenskap kallas enantiokonver- gens. Enkelt förklarat finns det molekyler som är spegelbilder av varandra. I fall man genomför en reaktion och får två spegelvända produkter men endast är intresserad av den ena, så förlorar man en stor del av produkten! Därför använ- der man ofta så kallade enantioselektiva katalysatorer vilka främst omvandlar substratet till den ena produkten (och inte dess spegelbild). StEH1, vårt pota- tisenzym, är en sådan. Men mycket mer spännande för oss var att StEH1 kan omvandla två spegelvända molekyler till en enda produkt, därav benämningen enantiokonvergens. Experiment med StEH1 har visat att selektiviteten till och med kan vändas. Vi har därför undersökt enantioselektiviteten hos StEH1. I vår modell har vi kunnat återskapa fenomenet och bättre kunnat förklara varför StEH1 är enantiokonvergent.
I mitt tredje projekt, och fjärde publikation, har jag utvecklat CADEE, vilket står för Computer-Aided Directed Evolution of Enzymes (ung. datorstödd styrd evolution av enzym). CADEE är ett vetenskapligt verktyg för att mer effektivt och mycket snabbare än tidigare simulera enzymvarianter. Med verktyget är det möjligt att inom några veckor skapa hundra- eller tusentals enzymvarianter och göra förutsägelser om hur de kommer bete sig i experiment. Slutligen har jag visat med ett exempel hur enkelt CADEE är att använda.
Sammanfattningsvis har jag med datorers hjälp studerat enzymer och genom CADEE utvidgat möjligheterna att förstå komplexa enzymatiska system.
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A few copies of the complete dissertation are kept at major Swedish research libraries, while the summary alone is distributed internationally through the series Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology. (Prior to January, 2005, the series was published under the title “Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology”.) ACTA UNIVERSITATIS UPSALIENSIS Distribution: publications.uu.se UPPSALA urn:nbn:se:uu:diva-314686 2017