Intrinsically disordered proteins (IDPs) are a class of proteins with wide-ranging

significance in signaling and disease that do not adopt a dominant folded structure as

monomers. Rather, the structures of IDPs in solution are best described as ensembles of

conformational states that may range from being fully random coil to partially ordered.

This structural plasticity of IDPs is theorized to facilitate regulation of their interaction

with other species, as in signal transduction or aggregation of IDPs into ordered fibrils.

Characterizing the structural ensembles of IDPs in the free, solvated state is key to

understanding the mechanisms of these interactions, and correspondingly the role an IDP

species plays in signaling or disease.

The rapid interconversion between conformational states, however, complicates the

experimental study of IDPs because most experimental signals report highly averaged

information. Computational modeling with validation through comparison to experiment

has therefore been a main approach to characterizing IDP structure and dynamics. The

focus of my dissertation is on the development of new methods for computational study of

IDPs, facilitating better and less expensive de novo generation of IDP structural ensembles

and improving the metrics used to evaluate the degree of agreement between a simulated

ensemble and a set of experimental data.

Despite vast improvements in computational power and efficiency, molecular

dynamics (MD) simulations of IDPs for generating conformational ensembles are still

limited by the expense of calculations. In Chapter 2 I present the development of a new

enhanced sampling method – temperature cool walking (TCW) – and comparison of its

performance against a standard method – temperature replica exchange (TREx). The TCW

method accelerates the rate of convergence to the equilibrium conformational ensemble

with increased sampling acceleration relative to TREx at greatly reduced computational

cost.

The second major limitation in MD is the accuracy of the force field. Most classical

fixed charge force fields were parameterized using data from folded proteins, and have

been thought to be biased to overly collapsed and structured conformations. This has

motivated the development of IDP-tailored force fields that sample greater disorder, at the

potential expense of the ability to model stabilizing interactions between an IDP and its

binding partners. In Chapter 3, I assess to what degree the shortcomings assigned to

standard force fields may be due to insufficient sampling by characterizing the

performance of standard and newly modified force fields on the Alzheimer’s peptide

amyloid-β using both TREx and TCW. We find that with improved sampling, standard and

modified force fields produce similar structural ensembles, suggesting that both are

appropriate for simulation of the disordered state. In Chapter 4 I present preliminary

results building off of this work by characterizing the performance of a polarizable force

field modeling a synthetic peptide that demonstrates complete loss of helical content with

increasing temperature. Inclusion of polarization effects has been thought to be key for

accurate modeling of such multicomponent systems, especially when there is a shift in the

electrostatic environment as is the case for the unfolding peptide. Our early results, while

limited by current lack of convergence for tests using the polarizable force field and

needing further confirmation, match that expectation by finding early evidence of greater

response to temperature by the polarizable force field than fixed charge comparators.

The last work presented here is in the development of new methods for calculating

the degree of agreement between a simulated IDP ensemble and experimental data. Backcalculation

of experimental data from structure can be very imprecise, motivating the

development in Chapter 5 of scoring formalisms that account for variable uncertainties in

both back-calculation and experiment for diverse experimental data types. In summary, the

methods described in this dissertation seek to improve computational study of IDPs by

facilitating better, less expensive generation of IDP ensembles and producing more

informative metrics for evaluating their agreement with experiment.

Proteins are biomolecules involved in cellular structure as well as function. These molecules are long chain polymers consisting of amino acids, which are organic compounds containing many different functional groups such as amine (−NH2) and carboxylic acids (−COOH). Actin proteins form part of the cellular structure, membrane proteins act as channels for transfer of ions, and enzymes catalyze critical cellular reactions. While structure is a well- appreciated determinant of function, the role of dynamics of proteins and solvent are less well studied. In my thesis work, I have studied the statistical fluctuations and dynamics of the basic amino acids in water and up to the full complexity of enzymes. The combination of experimental and computational techniques is a powerful combination for obtaining insight into dynamical events. I have used force-field based classical molecular dynamics simulations using an advanced polarizable force field to study the behaviour of these biomolecules in so- lution and have simulated experimental observables to understand conformational motions.

In the first part of my thesis, I have characterized the dynamical modes of a basic pro- tein unit - a single zwitterionic amino acid in solution - to make quantitative comparisons to the low frequency Terahertz (THz) absorption spectra. An analysis protocol for decom- posing the THz absorption spectrum has been previously developed for analyzing zwitterion simulations performed using ab-initio molecular dynamics (AIMD). In this work we extend the analysis method to simulations performed by force field molecular dynamics, which are computationally far less intensive, and setting the stage for decomposing the THz spectra for larger proteins that are not affordable by AIMD. We also show that the main impact of the solvation on the dynamical modes of zwitterions comes from the first solvation shell around the zwitterion only, and presence of waters further out does not affect the dynamics of these molecules significantly.

In the second part of my thesis work, I have explored the role of statistical fluctuations of solvation for artificial enzymes - which have poor activity - and have evaluated how the entropic features change upon mutation through laboratory directed evolution in which the enzymes show much greater activity. I have used two Kemp Eliminases (KE07 and KE70) and show that the active sites of these two enzymes have starkly contrasting interactions with solvent. KE07 incorporates the water into the active site to enhance the catalysis of the Kemp Elimination reaction while KE70 creates a strong hydrophobic pocket leading to the catalysis being driven entirely by the protein residues at the active site. Different entropic species of waters based on their vibrational dynamics are identified, and we observe varying behaviour of waters between mutants, as well as with the presence of the ligand.

In the final part of my thesis, I have looked at the dynamical correlations between residues in KE07 and have evaluated how the dynamical correlations change upon mutation through laboratory directed evolution. In particular, I have characterized the residue-residue inter- actions where we find that there is correlated motion between surface loops in KE07, which potentially could modulate access of the ligand to the active site of the enzyme; we observe that the binding of the ligand increases the correlation between the residues of the protein in the higher performing variants of the enzyme.

Abstract

Understanding and Improving Designed Enzymes by Computer Simulations

By

Asmit Bhowmick

Doctor of Philosophy in Chemical Engineering

University of California, Berkeley

Professor Teresa Head-Gordon, Chair

The ability to control for protein structure, electrostatics and dynamical motions is a fundamental problem that limits our ability to rationally design catalysts for new chemical reactions not known to have a natural biocatalyst. Current computational approaches for de novo enzyme design seek to engineer a small catalytic construct into an accommodating protein scaffold as exemplified by the Rosetta strategy. Here we consider 3 designed enzymes for the Kemp elimination reaction (KE07, KE70 and KE15) that showed minimal catalytic activity. KE07 and KE70 were subsequently improved by 2 orders of magnitude in catalytic efficiency by directed evolution and highlighted the shortcomings of the design process. This work studies two keys issues plaguing the designs – side chain conformational variability and electrostatics.

For the first part, a new Monte Carlo sampling method was developed that uses a physical forcefield and coupled with backbone variability and a backbone dependent rotamer library. Using transition state theory with energies/entropies calculated from Monte Carlo simulations, it is shown that in both KE07 and KE70, the initial design was over-optimized to stabilize the enzyme-substrate complex. Mutations introduced by directed evolutions led to destabilization of the enzyme-substrate complex and stabilization of the transition state. Furthermore, analysis of residue correlations via mutual information yielded hotspots, several of which were mutations during directed evolution. Laboratory mutations of these hotspots in the best variant of KE07 led to a drop in catalytic performance, demonstrating their importance. The metrics identified in KE07/KE70 studies were used to predict mutations to improve enzyme KE15 that had not been improved prior to this study. Several mutants, all predicted through computer simulations have now yielded better catalytic activity in the laboratory with the best one 10-fold better than the starting enzyme.

In order to quantify the role of electrostatics, a new method was developed using the AMOEBA polarizable forcefield that allowed splitting the contribution of electric field at the substrate by residues and solvent. The improvement in KE07 series could be tracked directly through changes in electric field at the substrate. In comparison, KE70 did not show a significant shift in electrostatic field, suggesting other factors like substrate binding may have been the reason for enhancement of activity. However, the common theme in both enzymes was the lack of participation (and in fact detrimental role) of the scaffold in the reaction. Future design efforts would benefit from an expanded theozyme and careful selection of scaffold based on electrostatic properties.

Generating efficient biocatalysts without using laboratory directed evolution would be an inflection point in the field of enzyme design. This work is a step in that direction.

Polarization is the ability of a molecule’s electron density to respond to and influence its environment and is the leading order many-body interaction for advanced electrostatics used in classical molecular simulation. It has proven to be an important interaction that is necessary to accurately simulate certain molecular systems. Polarization helps to capture intermolecular interactions of ligand-macromolecule complexes, heterogeneity at interfaces, electric field environments of heterogeneous systems such as proteins, and structure and dynamics of peptide-water solutions. In general, systems that can benefit most from the inclusion of polarization effects are heterogeneous, non-bulk systems that give rise to asymmetric environments. Additionally, polarization has been shown to be more transferable across the phase diagram beyond regions where the force field was initially parameterized.

The main drawback of including polarization in molecular simulation, however, is the computational expense of calculating explicit polarization interactions. The most common approach is to approximate the polarization solution using an iterative self- consistent field (SCF) method, which accounts for about half the cost of a polarizable simulation. Another approach is that of extended Lagrangians (EL), which treat polarization degrees of freedom dynamically and do not require iterations. EL methods, however, suffer from instability and require prohibitively small simulation time steps.

The focus of this dissertation is the reduction of the computational cost of polarizable classical molecular simulations while maintaining the high level of accuracy associated with these simulations. I present several new methods that combine the stability of SCF methods with the iteration-free dynamics of EL methods into a hybrid EL/SCF framework. The key to these EL/SCF methods is the introduction of auxiliary polarization degrees of freedom, which can be dynamically integrated and drive the real polarization degrees of freedom. The first approach is a relatively simple method for polarization that reduces the number of iterative cycles required for an SCF solution. This method also introduces thermostat control of auxiliary variables and is called iEL/SCF. A more sophisticated approach that eliminates the need for SCF iteration altogether, iEL/0-SCF, is also presented. This method is developed for both induced dipole and Drude polarization models. I also present a generalized and complete theory for classical iteration-free polarizable EL/SCF dynamics and explore combining iteration- free dynamics with other advanced high efficiency methods such as RESPA multi-time stepping and stochastic-isokinetic integration, which work complementarily with EL/SCF to further increase computational efficiency.

In summary, the developments presented in this dissertation are methods and theories that significantly reduce the cost of classical polarizable molecular dynamics without sacrificing accuracy. This work represents an important step in moving the scientific community toward the broader adoption of advanced potential energy surfaces embodied by polarizable force fields.

Theoretical studies of molecules have historically relied on deterministic algorithms, stochastic simulations, and physical models. Recently modern data-driven methods are starting to infiltrate into various fields of molecular science, opening new possibilities for solving problems that are difficult to tackle through traditional approaches. The accumulation of data, advancement of machine learning algorithms and improvement in hardware enables a plethora of data-driven approaches to surpass traditional methods in terms of accuracy and efficiency, but questions remain about how well these data-driven methods can generalize to unseen data to do true prediction. In this dissertation, I will show that when data-driven models are combined with physics-based approaches, through either feature design, or exerting constrains on the machine learning models, new standards can be established in the fields of molecule characterization and generation.

Nuclear magnetic resonance (NMR) chemical shifts (CS) are extremely sensitive to the local atomic environments for different nuclei in a molecule, and therefore is a common technique in molecule characterization. In chapter 2, I focus on the design of the UCBShift predictor for CSs for proteins in aqueous solution. The UCBShift method uniquely fuses a transfer prediction module, which employs sequence and structure alignments to select reference chemical shifts from a database, with a machine learning model that uses carefully curated and physics-inspired features, to predict CSs for proteins with higher accuracy and better reliability compared to all popular methods such as SHIFTX2 and SPARTA+. This chapter further delineates how UCBShift benefits from realistic data that has not been heavily curated, and surpasses existing CS calculators in terms of real-world performance without eliminating test predictions ad hoc.

However, in order to achieve rigorous and consistent improvement for an arbitrary molecular system, carefully curated feature sets specifically for proteins can be limiting, and we seek features from theoretical calculations. In Chapter 3 I describe the development of a novel neural network model which employs quantum mechanical (QM) features from affordable Density Functional Theory (DFT) calculations, along with geometric features of the molecular systems, to predict NMR chemical shieldings. The resulting iShiftML model predicts chemical shieldings approaching the highest level of accuracy under the modern theoretical framework of CCSD(T) in the complete basis set limit, but without the computational burden that limits its applicability to large systems. Not only does the iShiftML model demonstrate excellent predictive performance when compared with small molecule gas phase experimental CSs, but it also offers a capability to predict chemical shifts for much more complex natural products, and can be used for differentiating diasteromers based on chemical shift assignments. This chapter unveils new possibilities for integrating machine learning and QM calculations for accurate and transferable molecular characterization.

In Chapters 4 an 5, my research addresses fundamental issues for large and small molecule generation relevant to proteins and drug molecules. Chapter 4 describes the Int2Cart method that uses a recurrent neural network to predict the correlations between bond lengths, bond angles and backbone torsion angles and amino acid sequence of a protein. By incorporating these correlations, proteins reconstructed from just torsion angles display not only physically more accurate bond lengths and bond angles, but the reconstructed proteins are closer to their crystal structures than under the common assumption that bond lengths and bond angles are fixed, or that coming from a static library that only relies on local residue geometries. I have also shown potential applications of this method in estimating model quality for AlphaFold2 predicted structures, and reconstructing intrinsically disordered protein (IDP) ensembles with decreased steric overlap. Chapter 5 describes the combination of deep generative networks trained by reinforcement learning and physical docking study. I developed the iMiner method, which generates de novo drug-like molecules with an augmented binding potency towards specific protein targets, facilitating the discovery of potential new therapeutic targets. SARS-COV-2 Main Protease was used as an example to show that our generated molecules cover a broader chemical space than crowdsourcing efforts, and the newly generated molecules exert optimized interactions and correct shape for the compatibility with the binding pocket.

To summarize, this dissertation contains multiple methods that harmonize data-driven models and physics-based approaches in the area of NMR spectroscopy, protein structure modelling and de novo drug discovery, which provides a new perspective for researchers striving to leverage computational methods in molecular science and chemical biology.