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ACTA UNIVERSITATIS

UPSALIENSIS UPPSALA

2017

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

ISSN 1651-6214 ISBN 978-91-554-9816-0 urn:nbn:se:uu:diva-314686

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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

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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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(A) (B)

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-14

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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 bigO

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-17

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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 (N4to

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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