Deciphering the Cofilin Oligomers via Intermolecular Disulfide Bond Formation: A Coarse-Grained Molecular Dynamics Approach to Understanding Cofilin's Regulation on Actin Filaments.

Cofilin, a key actin-binding protein, orchestrates the dynamics of the actomyosin network through its actin-severing activity and by promoting the recycling of actin monomers. Recent experiments suggest that cofilin forms functionally distinct oligomers via thiol post-translational modifications (PTMs) that promote actin nucleation and assembly. Despite these advances, the structural conformations of cofilin oligomers that modulate actin activity remain elusive because there are combinatorial ways to oxidize thiols in cysteines to form disulfide bonds rapidly. This study employs molecular dynamics simulations to investigate human cofilin 1 as a case study for exploring cofilin dimers via disulfide bond formation. Utilizing a biasing scheme in simulations, we focus on analyzing dimer conformations conducive to disulfide bond formation. Additionally, we explore potential PTMs arising from the examined conformational ensemble. Using the free energy profiling, our simulations unveil a range of probable cofilin dimer structures not represented in current Protein Data Bank entries. These candidate dimers are characterized by their distinct population distributions and relative free energies. Of particular note is a dimer featuring an interface between cysteines 139 and 147 residues, which demonstrates stable free energy characteristics and intriguingly symmetrical geometry. In contrast, the experimentally proposed dimer structure exhibits a less stable free energy profile. We also evaluate frustration quantification based on the energy landscape theory in the protein-protein interactions at the dimer interfaces. Notably, the 39-39 dimer configuration emerges as a promising candidate for forming cofilin tetramers, as substantiated by frustration analysis. Additionally, docking simulations with actin filaments further evaluate the stability of these cofilin dimer-actin complexes. Our findings thus offer a computational framework for understanding the role of thiol PTM of cofilin proteins in regulating oligomerization, and the subsequent cofilin-mediated actin dynamics in the actomyosin network.

PTM-Psi: A python package to facilitate the computational investigation of post-translational modification on protein structures and their impacts on dynamics and functions.

Post-translational modification (PTM) of a protein occurs after it has been synthesized from its genetic template, and involves chemical modifications of the protein's specific amino acid residues. Despite of the central role played by PTM in regulating molecular interactions, particularly those driven by reversible redox reactions, it remains challenging to interpret PTMs in terms of protein dynamics and function because there are numerous combinatorially enormous means for modifying amino acids in response to changes in the protein environment. In this study, we provide a workflow that allows users to interpret how perturbations caused by PTMs affect a protein's properties, dynamics, and interactions with its binding partners based on inferred or experimentally determined protein structure. This Python-based workflow, called PTM-Psi, integrates several established open-source software packages, thereby enabling the user to infer protein structure from sequence, develop force fields for non-standard amino acids using quantum mechanics, calculate free energy perturbations through molecular dynamics simulations, and score the bound complexes via docking algorithms. Using the S-nitrosylation of several cysteines on the GAP2 protein as an example, we demonstrated the utility of PTM-Psi for interpreting sequence-structure-function relationships derived from thiol redox proteomics data. We demonstrate that the S-nitrosylated cysteine that is exposed to the solvent indirectly affects the catalytic reaction of another buried cysteine over a distance in GAP2 protein through the movement of the two ligands. Our workflow tracks the PTMs on residues that are responsive to changes in the redox environment and lays the foundation for the automation of molecular and systems biology modeling.

Experiment and Simulation Reveal Residue Details for How Target Binding Tunes Calmodulin's Calcium-Binding Properties.

We aim to elucidate the molecular mechanism of the reciprocal relation of calmodulin's (CaM) target binding and its affinity for calcium ions (Ca2+), which is central to decoding CaM-dependent Ca2+ signaling in a cell. We employed stopped-flow experiments and coarse-grained molecular simulations that learn the coordination chemistry of Ca2+ in CaM from first-principle calculations. The associative memories as part of the coarse-grained force fields built on known protein structures further influence CaM's selection of its polymorphic target peptides in the simulations. We modeled the peptides from the Ca2+/CaM-binding domain of Ca2+/CaM-dependent kinase II (CaMKII), CaMKIIp (293-310) and selected distinctive mutations at the N-terminus. Our stopped-flow experiments have shown that the CaM's affinity for Ca2+ in the bound complex of Ca2+/CaM/CaMKIIp decreased significantly when Ca2+/CaM bound to the mutant peptide (296-AAA-298) compared to that bound to the wild-type peptide (296-RRK-298). The coarse-grained molecular simulations revealed that the 296-AAA-298 mutant peptide destabilized the structures of Ca2+-binding loops at the C-domain of CaM (c-CaM) due to both loss of electrostatic interactions and differences in polymorphic structures. We have leveraged a powerful coarse-grained approach to advance a residue-level understanding of the reciprocal relation in CaM, that could not be possibly achieved by other computational approaches.

Graph identification of proteins in tomograms (GRIP-Tomo).

In this study, we present a method of pattern mining based on network theory that enables the identification of protein structures or complexes from synthetic volume densities, without the knowledge of predefined templates or human biases for refinement. We hypothesized that the topological connectivity of protein structures is invariant, and they are distinctive for the purpose of protein identification from distorted data presented in volume densities. Three-dimensional densities of a protein or a complex from simulated tomographic volumes were transformed into mathematical graphs as observables. We systematically introduced data distortion or defects such as missing fullness of data, the tumbling effect, and the missing wedge effect into the simulated volumes, and varied the distance cutoffs in pixels to capture the varying connectivity between the density cluster centroids in the presence of defects. A similarity score between the graphs from the simulated volumes and the graphs transformed from the physical protein structures in point data was calculated by comparing their network theory order parameters including node degrees, betweenness centrality, and graph densities. By capturing the essential topological features defining the heterogeneous morphologies of a network, we were able to accurately identify proteins and homo-multimeric complexes from 10 topologically distinctive samples without realistic noise added. Our approach empowers future developments of tomogram processing by providing pattern mining with interpretability, to enable the classification of single-domain protein native topologies as well as distinct single-domain proteins from multimeric complexes within noisy volumes.

Effects of Protein Crowders and Charge on the Folding of Superoxide Dismutase 1 Variants: A Computational Study.

The neurodegenerative disease amyotrophic lateral sclerosis (ALS) is associated with the misfolding and aggregation of the metalloenzyme protein superoxide dismutase 1 (SOD1) via mutations that destabilize the monomer-dimer interface. In a cellular environment, crowding and electrostatic screening play essential roles in the folding and aggregation of the SOD1 monomers. Despite numerous studies on the effects of mutations on SOD1 folding, a clear understanding of the interplay between crowding, folding, and aggregation in vivo remains lacking. Using a structure-based minimal model for molecular dynamics simulations, we investigate the role of self-crowding and charge on the folding stability of SOD1 and the G41D mutant where experimentalists were intrigued by an alteration of the folding mechanism by a single point mutation from glycine to charged aspartic acid. We show that unfolded SOD1 configurations are significantly affected by charge and crowding, a finding that would be extremely costly to achieve with all-atom simulations, while the native state is not significantly altered. The mutation at residue 41 alters the interactions between proteins in the unfolded states instead of those within a protein. This paper suggests electrostatics may play an important role in the folding pathway of SOD1 and modifying the charge via mutation and ion concentration may change the dominant interactions between proteins, with potential impacts for aggregation of the mutants. This work provides a plausible reason for the alteration of the unfolded states to address why the mutant G41D causes the changes to the folding mechanism of SOD1 that have intrigued experimentalists.

A generalized Flory-Stockmayer kinetic theory of connectivity percolation and rigidity percolation of cytoskeletal networks.

Actin networks are essential for living cells to move, reproduce, and sense their environments. The dynamic and rheological behavior of actin networks is modulated by actin-binding proteins such as α-actinin, Arp2/3, and myosin. There is experimental evidence that actin-binding proteins modulate the cooperation of myosin motors by connecting the actin network. In this work, we present an analytical mean field model, using the Flory-Stockmayer theory of gelation, to understand how different actin-binding proteins change the connectivity of the actin filaments as the networks are formed. We follow the kinetics of the networks and estimate the concentrations of actin-binding proteins that are needed to reach connectivity percolation as well as to reach rigidity percolation. We find that Arp2/3 increases the actomyosin connectivity in the network in a non-monotonic way. We also describe how changing the connectivity of actomyosin networks modulates the ability of motors to exert forces, leading to three possible phases of the networks with distinctive dynamical characteristics: a sol phase, a gel phase, and an active phase. Thus, changes in the concentration and activity of actin-binding proteins in cells lead to a phase transition of the actin network, allowing the cells to perform active contraction and change their rheological properties.

Correlating Interfacial Charge Transfer Rates with Interfacial Molecular Structure in the Tetraphenyldibenzoperiflanthene/C70 Organic Photovoltaic System.

Organic photovoltaics (OPV) is an emerging solar cell technology that offers vast advantages such as low-cost manufacturing, transparency, and solution processability. However, because the performance of OPV devices is still disappointing compared to their inorganic counterparts, better understanding of how controlling the molecular-level morphology can impact performance is needed. To this end, one has to overcome significant challenges that stem from the complexity and heterogeneity of the underlying electronic structure and molecular morphology. In this Letter, we address this challenge in the context of the DBP/C70 OPV system by employing a modular workflow that combines recent advances in electronic structure, molecular dynamics, and rate theory. We show how the wide range of interfacial pairs can be classified into four types of interfacial donor-acceptor geometries and find that the least populated interfacial geometry gives rise to the fastest charge transfer (CT) rates.

Forecasting Avalanches in Branched Actomyosin Networks with Network Science and Machine Learning.

We explored the dynamic and structural effects of actin-related proteins 2/3 (Arp2/3) on actomyosin networks using mechanochemical simulations of active matter networks. On the nanoscale, the Arp2/3 complex alters the topology of actomyosin by nucleating a daughter filament at an angle with respect to a mother filament. At a subcellular scale, they orchestrate the formation of a branched actomyosin network. Using a coarse-grained approach, we sought to understand how an actomyosin network temporally and spatially reorganizes itself by varying the concentration of the Arp2/3 complexes. Driven by motor dynamics, the network stalls at a high concentration of Arp2/3 and contracts at a low Arp2/3 concentration. At an intermediate Arp2/3 concentration, however, the actomyosin network is formed by loosely connected clusters that may collapse suddenly when driven by motors. This physical phenomenon is called an "avalanche" largely due to the marginal instability inherent to the morphology of a branched actomyosin network when the Arp2/3 complex is present. While embracing the data science approaches, we unveiled the higher-order patterns in the branched actomyosin networks and discovered a sudden change in the "social" network topology of actomyosin, which is a new type of avalanche in addition to the two types of avalanches associated with a sudden change in the size or shape of the whole actomyosin network, as shown in a previous investigation. Our new finding promotes the importance of using network theory and machine learning models to forecast avalanches in actomyosin networks. The mechanisms of the Arp2/3 complexes in shaping the architecture of branched actomyosin networks obtained in this paper will help us better understand the emergent reorganization of the topology in dense actomyosin networks that are difficult to detect in experiments.

Coarse-Grained Modeling and Molecular Dynamics Simulations of Ca2+-Calmodulin.

Calmodulin (CaM) is a calcium-binding protein that transduces signals to downstream proteins through target binding upon calcium binding in a time-dependent manner. Understanding the target binding process that tunes CaM's affinity for the calcium ions (Ca2+), or vice versa, may provide insight into how Ca2+-CaM selects its target binding proteins. However, modeling of Ca2+-CaM in molecular simulations is challenging because of the gross structural changes in its central linker regions while the two lobes are relatively rigid due to tight binding of the Ca2+ to the calcium-binding loops where the loop forms a pentagonal bipyramidal coordination geometry with Ca2+. This feature that underlies the reciprocal relation between Ca2+ binding and target binding of CaM, however, has yet to be considered in the structural modeling. Here, we presented a coarse-grained model based on the Associative memory, Water mediated, Structure, and Energy Model (AWSEM) protein force field, to investigate the salient features of CaM. Particularly, we optimized the force field of CaM and that of Ca2+ ions by using its coordination chemistry in the calcium-binding loops to match with experimental observations. We presented a "community model" of CaM that is capable of sampling various conformations of CaM, incorporating various calcium-binding states, and carrying the memory of binding with various targets, which sets the foundation of the reciprocal relation of target binding and Ca2+ binding in future studies.

CTRAMER: An open-source software package for correlating interfacial charge transfer rate constants with donor/acceptor geometries in organic photovoltaic materials.

In this paper, we present CTRAMER (Charge-Transfer RAtes from Molecular dynamics, Electronic structure, and Rate theory)-an open-source software package for calculating interfacial charge-transfer (CT) rate constants in organic photovoltaic (OPV) materials based on ab initio calculations and molecular dynamics simulations. The software is based on identifying representative donor/acceptor geometries within interfacial structures obtained from molecular dynamics simulation of donor/acceptor blends and calculating the corresponding Fermi's golden rule CT rate constants within the framework of the linearized-semiclassical approximation. While the methods used are well established, the integration of these state-of-the-art tools originating from different disciplines to study photoinduced CT processes with explicit treatment of the environment, in our opinion, makes this package unique and innovative. The software also provides tools for investigating other observables of interest. After outlining the features and implementation details, the usage and performance of the software are demonstrated with results from an example OPV system.

Determining the atomic charge of calcium ion requires the information of its coordination geometry in an EF-hand motif.

It is challenging to parameterize the force field for calcium ions (Ca2+) in calcium-binding proteins because of their unique coordination chemistry that involves the surrounding atoms required for stability. In this work, we observed a wide variation in Ca2+ binding loop conformations of the Ca2+-binding protein calmodulin, which adopts the most populated ternary structures determined from the molecular dynamics simulations, followed by ab initio quantum mechanical (QM) calculations on all 12 amino acids in the loop that coordinate Ca2+ in aqueous solution. Ca2+ charges were derived by fitting to the electrostatic potential in the context of a classical or polarizable force field (PFF). We discovered that the atomic radius of Ca2+ in conventional force fields is too large for the QM calculation to capture the variation in the coordination geometry of Ca2+ in its ionic form, leading to unphysical charges. Specifically, we found that the fitted atomic charges of Ca2+ in the context of PFF depend on the coordinating geometry of electronegative atoms from the amino acids in the loop. Although nearby water molecules do not influence the atomic charge of Ca2+, they are crucial for compensating for the coordination of Ca2+ due to the conformational flexibility in the EF-hand loop. Our method advances the development of force fields for metal ions and protein binding sites in dynamic environments.

The Zero-Order Loop in Apoazurin Modulates Folding Mechanism In Silico.

Pseudomonas aeruginosa apoazurin (apo, without the copper cofactor) has a single disulfide bond between residues 3 and 26 and unfolds in a two-state reaction in vitro. The disulfide bond covalently connects the N-termini of ß-strands 1 and 3; thereby, it creates a zero-order loop or a "cinch" that restricts conformational space. Covalent loops and threaded topologies are emerging as important structural elements in folded proteins and may be important for function. In order to understand the role of a zero-order loop in the folding process of a protein, here we used coarse-grained molecular dynamics (CGMD) simulations in silico to compare two variants of apoazurin: one named "loop" which contained the disulfide, and another named "open" in which the disulfide bond between residues 3 and 26 was removed. CGMD simulations were performed to probe the stability and unfolding pathway of the two apoazurin variants at different urea concentrations and temperatures. Our results show that the covalent loop plays a prominent role in the unfolding mechanism of apoazurin; its removal alters both the folding-transition state and the unfolded-state ensemble of conformations. We propose that modulation of azurin's folding landscape by the disulfide bridge may be related to both copper capturing and redox sensing.

Photoinduced Charge Transfer Dynamics in the Carotenoid-Porphyrin-C60 Triad via the Linearized Semiclassical Nonequilibrium Fermi's Golden Rule.

The nonequilibrium Fermi's golden rule (NE-FGR) describes the time-dependent rate coefficient for electronic transitions when the nuclear degrees of freedom start out in a nonequilibrium state. In this paper, the linearized semiclassical (LSC) approximation of the NE-FGR is used to calculate the photoinduced charge transfer (CT) rates in the carotenoid-porphyrin-C60 molecular triad dissolved in explicit tetrahydrofuran. The initial nonequilibrium state corresponds to impulsive photoexcitation from the equilibrated ground state to the ππ* state, and the porphyrin-to-C60 and carotenoid-to-C60 CT rates are calculated. Our results show that accounting for the nonequilibrium nature of the initial state significantly enhances the transition rate of the porphyrin-to-C60 CT process. We also derive the instantaneous Marcus theory (IMT) from LSC NE-FGR, which casts the CT rate coefficients in terms of a Marcus-like expression, with explicitly time-dependent reorganization energy and reaction free energy. IMT is found to reproduce the CT rates in the system under consideration remarkably well.

On the Interplay between Electronic Structure and Polarizable Force Fields When Calculating Solution-Phase Charge-Transfer Rates.

We present a comprehensive analysis of the interplay between the choice of an electronic structure method and the effect of using polarizable force fields vs. nonpolarizable force fields when calculating solution-phase charge-transfer (CT) rates. The analysis is based on an integrative approach that combines inputs from electronic structure calculations and molecular dynamics simulations and is performed in the context of the carotenoid-porphyrin-C60 molecular triad dissolved in an explicit tetrahydrofuran (THF) liquid solvent. Marcus theory rate constants are calculated for the multiple CT processes that occur in this system based on either polarizable or nonpolarizable force fields, parameterized using density functional theory (DFT) with either the B3LYP or the Baer-Neuhauser-Livshits (BNL) density functionals. We find that the effect of switching from nonpolarizable to polarizable force fields on the CT rates is strongly dependent on the choice of the density functional. More specifically, the rate constants obtained using polarizable and nonpolarizable force fields differ significantly when B3LYP is used, while much smaller changes are observed when BNL is used. It is shown that this behavior can be traced back to the tendency of B3LYP to overstabilize CT states, thereby pushing the underlying electronic transitions to the deep inverted region, where even small changes in the force fields can lead to significant changes in the CT rate constants. Our results demonstrate the importance of combining polarizable force fields with an electronic structure method that can accurately capture the energies of excited CT states when calculating charge-transfer rates.

Charge transfer rate constants for the carotenoid-porphyrin-C60 molecular triad dissolved in tetrahydrofuran: The spin-boson model vs the linearized semiclassical approximation.

Charge transfer rate constants were calculated for the carotenoid-porphyrin-C60 (CPC60) molecular triad dissolved in explicit tetrahydrofuran. The calculation was based on mapping the all-atom anharmonic Hamiltonian of this system onto the spin-boson Hamiltonian. The mapping was based on discretizing the spectral density from the time correlation function of the donor-acceptor potential energy gap, as obtained from all-atom molecular dynamics simulations. Different spin-boson Hamiltonians were constructed for each of the possible transitions between the three excited electronic states in two different triad conformations. The rate constants of three possible transitions were calculated via the quantum-mechanically exact Fermi's golden rule (FGR), as well as a progression of more approximate expressions that lead to the classical Marcus expression. The advantage of the spin-boson approach is that once the mapping is established, the quantum-mechanically exact FGR and the hierarchy of approximations are known in closed form. The classical Marcus charge transfer rate constants obtained with the spin-boson Hamiltonians were found to reproduce those obtained from all-atom simulations with the linearized semiclassical approximation, thereby confirming the equivalence of the two approaches for this system. Within the spin-boson Hamiltonian, we also found that the quantum-mechanically exact FGR rate constants were significantly enhanced compared to the classical Marcus theory rate constants for two out of three transitions in one of the two conformations under consideration. The results confirm that mapping to the spin-boson model can yield accurate predictions for charge transfer rate constants in a system as complex as CPC60 dissolved in tetrahydrofuran.