Structure-based Coarse-grained Model Research Articles

It is theoretically possible to avoid misfolding into non-covalent lasso entanglements using small molecule drugs.

A novel class of protein misfolding characterized by either the formation of non-native noncovalent lasso entanglements in the misfolded structure or loss of native entanglements has been predicted to exist and found circumstantial support through biochemical assays and limited-proteolysis mass spectrometry data. Here, we examine whether it is possible to design small molecule compounds that can bind to specific folding intermediates and thereby avoid these misfolded states in computer simulations under idealized conditions (perfect drug-binding specificity, zero promiscuity, and a smooth energy landscape). Studying two proteins, type III chloramphenicol acetyltransferase (CAT-III) and D-alanyl-D-alanine ligase B (DDLB), that were previously suggested to form soluble misfolded states through a mechanism involving a failure-to-form of native entanglements, we explore two different drug design strategies using coarse-grained structure-based models. The first strategy, in which the native entanglement is stabilized by drug binding, failed to decrease misfolding because it formed an alternative entanglement at a nearby region. The second strategy, in which a small molecule was designed to bind to a non-native tertiary structure and thereby destabilize the native entanglement, succeeded in decreasing misfolding and increasing the native state population. This strategy worked because destabilizing the entanglement loop provided more time for the threading segment to position itself correctly to be wrapped by the loop to form the native entanglement. Further, we computationally identified several FDA-approved drugs with the potential to bind these intermediate states and rescue misfolding in these proteins. This study suggests it is possible for small molecule drugs to prevent protein misfolding of this type.

Intrinsically Disordered Regions Function as a Cervical Collar to Remotely Regulate the Nodding Dynamics of SARS-CoV-2 Prefusion Spike Heads.

The SARS-CoV-2 prefusion spike heads (receptor binding domains, RBDs) frequently nod down and up to interact with host cell receptors. As the spike protein is a trimeric unit of significant size, to understand its large-scale structural dynamics associated with the nodding mechanism and the mutational impact on the same, we develop a topological symmetry-information-loaded coarse-grained structure-based model of a spike trimer using recent cryo-EM structural data. Our study reveals the control of two distant intrinsically disordered regions (IDRs), namely, 630 and FPPR loops, over the nodding dynamics of spike heads. We find that the order-disorder transition of IDRs becomes more evident in the variants of concern (VOCs) that are associated with the characteristic mutation, D614G, in the proximity of these IDRs. In some VOCs, the two other mutations A570D and S982A also show an integral effect. The driver mutation D614G instigates a salt-bridge disruption, altering the order-disorder dynamics of both 630 and FPPR loops and their interaction with the C-terminal domains (CTD1/CTD2). This altered connectivity in these mutants allows the two IDRs to act collectively as a "cervical collar" for the RBD, supporting various spike head postures, consistent with cryo-EM results available for specific cases. The IDRs' control over the spike structure and dynamics presents an exciting opportunity where they can be targeted as remote operational switches to artificially maneuver the nod for effective therapeutic interventions.

Potential Self-Peptide Inhibitors of the SARS-CoV-2 Main Protease.

The SARS-CoV-2 main protease (Mpro) plays an essential role in viral replication, cleaving viral polyproteins into functional proteins. This makes Mpro an important drug target. Mpro consists of an N-terminal catalytic domain and a C-terminal α-helical domain (MproC). Previous studies have shown that peptides derived from a given protein sequence (self-peptides) can affect the folding and, in turn, the function of that protein. Since the SARS-CoV-1 MproC is known to stabilize its Mpro and regulate its function, we hypothesized that SARS-CoV-2 MproC-derived self-peptides may modulate the folding and the function of SARS-CoV-2 Mpro. To test this, we studied the folding of MproC in the presence of various self-peptides using coarse-grained structure-based models and molecular dynamics simulations. In these simulations of MproC and one self-peptide, we found that two self-peptides, the α1-helix and the loop between α4 and α5 (loop4), could replace the equivalent native sequences in the MproC structure. Replacement of either sequence in full-length Mpro should, in principle, be able to perturb Mpro function albeit through different mechanisms. Some general principles for the rational design of self-peptide inhibitors emerge: The simulations show that prefolded self-peptides are more likely to replace native sequences than those which do not possess structure. Additionally, the α1-helix self-peptide is kinetically stable and once inserted rarely exchanges with the native α1-helix, while the loop4 self-peptide is easily replaced by the native loop4, making it less useful for modulating function. In summary, a prefolded α1-derived peptide should be able to inhibit SARS-CoV-2 Mpro function.

The role of C-terminal helix in the conformational transition of an arginine binding protein

The thermotoga maritima arginine binding protein (TmArgBP) is a periplasmic binding protein that has a short helix at the C-terminal end (CTH), which is swapped between the two chains. We apply a coarse-grained structure-based model (SBM) and all-atom MD simulation on this protein to understand the mechanism and the role of CTH in the conformational transition. When the results of SBM simulations of TmArgBP in the presence and absence of CTH are compared, we find that CTH is strategically located at the back of the binding pocket restraining the open-state conformation thereby disengaging access to the closed-state. We also ran all-atom MD simulations of open-state TmArgBP with and without CTH and discovered that in the absence of CTH the protein could reach the closed-state within 250 ns, while in its presence, the protein remained predominantly in its open-state conformation. In the simulation started from unliganded closed-state conformation without CTH, the protein exhibited multiple transitions between the two states, suggesting CTH as an essential structural element to stabilize the open-state conformation. In another simulation that began with an unliganded closed-state conformation with CTH, the protein was able to access the open-state. In this simulation the CTH was observed to reorient itself to interact with the protein emphasizing its role in assisting the conformational change. Based on our findings, we believe that CTH not only acts as a structural element that constraints the protein in its open-state but it may also guide the protein back to its open-state conformation upon ligand unbinding.

Molecular Simulations of Intrinsically Disordered Proteins and Their Binding Mechanisms.

Intrinsically disordered proteins (IDPs) lack well-defined secondary or tertiary structures in solution but are found to be involved in a wide range of critical cellular processes that highlight their functional importance. IDPs usually undergo folding upon binding to their targets. Such binding coupled to folding behavior has widened our perspective on the protein structure-dynamics-function paradigm in molecular biology. However, characterizing the folding upon binding mechanism of IDPs experimentally remains quite challenging. Molecular simulations emerge as a potentially powerful tool that offers information complementary to experiments. Here we present a general computational framework for the molecular simulations of IDP folding upon binding processes that combines all-atom molecular dynamics (MD) and coarse-grained simulations. The classical all-atom molecular dynamics approach using GPU acceleration allows the researcher to explore the properties of the IDP conformational ensemble, whereas coarse-grained structure-based models implemented with parameters carefully calibrated to available experimental measurements can be used to simulate the entire folding upon binding process. We also discuss a set of tools for the analysis of MD trajectories and describe the details of the computational protocol to follow so that it can be adapted by the user to study any IDP in isolation and in complex with partners.

Understanding the Folding Mediated Assembly of the Bacteriophage MS2 Coat Protein Dimers

The capsids of RNA viruses such as MS2 are great models for studying protein self-assembly because they are made almost entirely of multiple copies of a single coat protein (CP). Although CP is the minimal repeating unit of the capsid, previous studies have shown that CP exists as a homodimer (CP2) even in an acid-disassembled system, indicating that CP2 is an obligate dimer. Here, we investigate the molecular basis of this obligate dimerization using coarse-grained structure-based models and molecular dynamics simulations. We find that, unlike monomeric proteins of similar size, CP populates a single partially folded ensemble whose "foldedness" is sensitive to denaturing conditions. In contrast, CP2 folds similarly to single-domain proteins populating only the folded and the unfolded ensembles, separated by a prominent folding free energy barrier. Several intramonomer contacts form early, but the CP2 folding barrier is crossed only when the intermonomer contacts are made. A dissection of the structure of CP2 through mutant folding simulations shows that the folding barrier arises both from the topology of CP and the interface contacts of CP2. Together, our results show that CP2 is an obligate dimer because of kinetic stability, that is, dimerization induces a folding barrier and that makes it difficult for proteins in the dimer minimum to partially unfold and access the monomeric state without completely unfolding. We discuss the advantages of this obligate dimerization in the context of dimer design and virus stability.

Coarse-Grained Modeling of Multiple Pathways in Conformational Transitions of Multi-Domain Proteins.

Large-scale conformational transitions in multi-domain proteins are often essential for their functions. To investigate the transitions, it is necessary to explore multiple potential pathways, which involve different intermediate structures. Here, we present a multi-basin (MB) coarse-grained (CG) structure-based Go̅ model for describing transitions in proteins with more than two moving domains. This model is an extension of our dual-basin Go̅ model in which system-dependent parameters are determined systematically using the multistate Bennett acceptance ratio method. In the MB Go̅ model for multi-domain proteins, we assume that intermediate structures may have partial inter-domain native contacts. This approach allows us to search multiple transition pathways that involve distinct intermediate structures using the CG molecular dynamics (MD) simulations. We apply this scheme to an enzyme, adenylate kinase (AdK), which has three major domains and can move along two different pathways. Using the optimized mixing parameters for each pathway, AdK shows frequent transitions between the Open, Closed, and the intermediate basins and samples a wide variety of conformations within each basin. The explored multiple transition pathways could be compared with experimental data and examined in more detail by atomistic MD simulations.

Shedding Light on the Inhibitory Mechanisms of SARS-CoV-1/CoV-2 Spike Proteins by ACE2-Designed Peptides.

Angiotensin-converting enzyme 2 (ACE2) is the host cellular receptor that locks onto the surface spike protein of the 2002 SARS coronavirus (SARS-CoV-1) and of the novel, highly transmissible and deadly 2019 SARS-CoV-2, responsible for the COVID-19 pandemic. One strategy to avoid the virus infection is to design peptides by extracting the human ACE2 peptidase domain α1-helix, which would bind to the coronavirus surface protein, preventing the virus entry into the host cells. The natural α1-helix peptide has a stronger affinity to SARS-CoV-2 than to SARS-CoV-1. Another peptide was designed by joining α1 with the second portion of ACE2 that is far in the peptidase sequence yet grafted in the spike protein interface with ACE2. Previous studies have shown that, among several α1-based peptides, the hybrid peptidic scaffold is the one with the highest/strongest affinity for SARS-CoV-1, which is comparable to the full-length ACE2 affinity. In this work, binding and folding dynamics of the natural and designed ACE2-based peptides were simulated by the well-known coarse-grained structure-based model, with the computed thermodynamic quantities correlating with the experimental binding affinity data. Furthermore, theoretical kinetic analysis of native contact formation revealed the distinction between these processes in the presence of the different binding partners SARS-CoV-1 and SARS-CoV-2 spike domains. Additionally, our results indicate the existence of a two-state folding mechanism for the designed peptide en route to bind to the spike proteins, in contrast to a downhill mechanism for the natural α1-helix peptides. The presented low-cost simulation protocol demonstrated its efficiency in evaluating binding affinities and identifying the mechanisms involved in the neutralization of spike-ACE2 interaction by designed peptides. Finally, the protocol can be used as a computer-based screening of more potent designed peptides by experimentalists searching for new therapeutics against COVID-19.

The Molecular Mechanism of Domain Swapping of the C-Terminal Domain of the SARS-Coronavirus Main Protease

In three-dimensional domain swapping, two protein monomers exchange a part of their structures to form an intertwined homodimer, whose subunits resemble the monomer. Several viral proteins domain swap to increase their structural complexity or functional avidity. The main protease (Mpro) of the severe acute respiratory syndrome (SARS) coronavirus proteolyzes viral polyproteins and has been a target for anti-SARS drug design. Domain swapping in the α-helical C-terminal domain of Mpro (MproC) locks Mpro into a hyperactive octameric form that is hypothesized to promote the early stages of viral replication. However, in the absence of a complete molecular understanding of the mechanism of domain swapping, investigations into the biological relevance of this octameric Mpro have stalled. Isolated MproC can exist as a monomer or a domain-swapped dimer. Here, we investigate the mechanism of domain swapping of MproC using coarse-grained structure-based models and molecular dynamics simulations. Our simulations recapitulate several experimental features of MproC folding. Further, we find that a contact between a tryptophan in the MproC domain-swapping hinge and an arginine elsewhere forms early during folding, modulates the folding route, and promotes domain swapping to the native structure. An examination of the sequence and the structure of the tryptophan containing hinge loop shows that it has a propensity to form multiple secondary structures and contacts, indicating that it could be stabilized into either the monomer- or dimer-promoting conformations by mutations or ligand binding. Finally, because all residues in the tryptophan loop are identical in SARS-CoV and SARS-CoV-2, mutations that modulate domain swapping may provide insights into the role of octameric Mpro in the early-stage viral replication of both viruses.

Role of AAA3 Domain in Allosteric Communication of Dynein Motor Proteins.

Cytoplasmic dynein, an AAA+ motif containing motor, generates force and movement along the microtubule to execute important biological functions including intracellular material transport and cell division by hydrolyzing ATP. Among the six AAA+ domains, AAA1 is the primary ATPase site where a single ATP hydrolysis generates a single step. Nucleotide states in AAA3 gate dynein’s activity, suggesting that AAA3 acts as a regulatory switch. However, the comprehensive structural perspective of AAA3 in dynein’s mechanochemical cycle remains unclear. Here, we explored the allosteric transition path of dynein involving AAA3 using a coarse-grained structure-based model. ATP binding to the AAA1 domain creates a cascade of conformational changes through the other domains of the ring, which leads to the pre-power stroke formation. The linker domain, which is the mechanical element of dynein, shifts from a straight to a bent conformation during this process. In our present study, we observe that AAA3 gates the allosteric communication from AAA1 to the microtubule binding domain (MTBD) through AAA4 and AAA5. The MTBD is linked to the AAA+ ring via a coiled-coil stalk and a buttress domain, which are extended from AAA4 and AAA5, respectively. Further analysis also uncovers the role of AAA3 in the linker movement. The free energy calculation shows that the linker prefers the straight conformation when AAA3 remains in the ATP-bound condition. As AAA3 restricts the motion of AAA4 and AAA5, the linker/AAA5 interactions get stabilized, and the linker cannot move to the pre-power stroke state that halts the complete structural transition required for the mechanochemical cycle. Therefore, we suggest that AAA3 governs dynein’s mechanochemical cycle and motility by controlling the AAA4 and AAA5 domains that further regulate the linker movement and the power stroke formation.

Phase Equilibria Modeling with Systematically Coarse-Grained Models-A Comparative Study on State Point Transferability.

Coarse-grained (CG) models for soft matter systems can be parameterized using a variety of approaches. In systematic coarse-graining procedures, effective interactions are calculated using a reference fine-grained simulation. The degree to which thermodynamical and structural properties of the reference system are reproduced depends critically on the coarse-graining method used to parameterize the model. In this article, a comparative study is presented on the capability of different CG models to reproduce vapor-liquid equilibrium thermodynamics of hexane and perfluorohexane systems. CG models are developed using coarse-graining methods based on the reproduction of (a) structure and (b) coupling free energies. Although the structure-based models show an overestimation of the pressure and therefore perform relatively poorly in reproducing the vapor-liquid thermodynamics, it is shown that methods based on coupling free energies, in particular the conditional reversible work method, are capable of better reproducing the vapor-liquid phase diagram of the united-atom reference simulations, while reproducing the liquid structure almost as accurately as the structure-based CG model. This illustrates the state point transferability of the interaction potentials calculated using these methods, as the resulting CG model (which has been parameterized at 300 K) is capable of accurately modeling the thermodynamic properties up to the critical point.

Structural consequences of hereditary spastic paraplegia disease-related mutations in kinesin

A wide range of mutations in the kinesin motor Kif5A have been linked to a neuronal disorder called hereditary spastic paraplegia (HSP). The position of these mutations can vary, and a range of different motile behaviors have been observed, indicating that the HSP mutants can alter distinct aspects of kinesin mechanochemistry. While focusing on four key HSP-associated mutants, this study examined the structural and dynamic perturbations that arise from these mutations using a series of different computational methods, ranging from bioinformatics analyses to all-atom simulations, that account for solvent effects explicitly. We show that two catalytic domain mutations (R280S and K253N) reduce the microtubule (MT) binding affinity of the kinesin head domains appreciably, while N256S has a much smaller impact. Bioinformatics analysis suggests that the stalk mutation A361V perturbs motor dimerization. Subsequent integration of these effects into a coarse-grained structure-based model of dimeric kinesin revealed that the order-disorder transition of the neck linker is substantially affected, indicating a hampered directionality and processivity of kinesin. The present analyses therefore suggest that, in addition to kinesin-MT binding and coiled-coil dimerization, HSP mutations affecting motor stepping transitions and processivity can lead to disease.

Molecular mechanisms of the interhead coordination by interhead tension in cytoplasmic dyneins

Cytoplasmic dyneins play a major role in retrograde cellular transport by moving vesicles and organelles along microtubule filaments. Dyneins are multidomain motor proteins with two heads that coordinate their motion via their interhead tension. Compared with the leading head, the trailing head has a higher detachment rate from microtubules, facilitating the movement. However, the molecular mechanism of such coordination is unknown. To elucidate this mechanism, we performed molecular dynamics simulations on a cytoplasmic dynein with a structure-based coarse-grained model that probes the effect of the interhead tension on the structure. The tension creates a torque that influences the head rotating about its stalk. The conformation of the stalk switches from the α registry to the β registry during the rotation, weakening the binding affinity to microtubules. The directions of the tension and the torque of the leading head are opposite to those of the trailing head, breaking the structural symmetry between the heads. The leading head transitions less often to the β registry than the trailing head. The former thus has a greater binding affinity to the microtubule than the latter. We measured the moment arm of the torque from a dynein structure in the simulations to develop a phenomenological model that captures the influence of the head rotating about its stalk on the differential detachment rates of the two heads. Our study provides a consistent molecular picture for interhead coordination via interhead tension.

Metal cofactor modulated folding and target recognition of HIV-1 NCp7.

The HIV-1 nucleocapsid 7 (NCp7) plays crucial roles in multiple stages of HIV-1 life cycle, and its biological functions rely on the binding of zinc ions. Understanding the molecular mechanism of how the zinc ions modulate the conformational dynamics and functions of the NCp7 is essential for the drug development and HIV-1 treatment. In this work, using a structure-based coarse-grained model, we studied the effects of zinc cofactors on the folding and target RNA(SL3) recognition of the NCp7 by molecular dynamics simulations. After reproducing some key properties of the zinc binding and folding of the NCp7 observed in previous experiments, our simulations revealed several interesting features in the metal ion modulated folding and target recognition. Firstly, we showed that the zinc binding makes the folding transition states of the two zinc fingers less structured, which is in line with the Hammond effect observed typically in mutation, temperature or denaturant induced perturbations to protein structure and stability. Secondly, We showed that there exists mutual interplay between the zinc ion binding and NCp7-target recognition. Binding of zinc ions enhances the affinity between the NCp7 and the target RNA, whereas the formation of the NCp7-RNA complex reshapes the intrinsic energy landscape of the NCp7 and increases the stability and zinc affinity of the two zinc fingers. Thirdly, by characterizing the effects of salt concentrations on the target RNA recognition, we showed that the NCp7 achieves optimal balance between the affinity and binding kinetics near the physiologically relevant salt concentrations. In addition, the effects of zinc binding on the inter-domain conformational flexibility and folding cooperativity of the NCp7 were also discussed.

Exploration of Multistate Conformational Dynamics upon Ligand Binding of a Monomeric Enzyme Involved in Pyrophosphoryl Transfer.

HPPK (6-hydroxymethyl-7,8-dihydropterin pyrophosphokinase) is a monomeric protein with 158 residues, which undergoes large-scale conformational changes between apo, open, and holo states responding to ligand binding for its function. It has been explored widely as an excellent target for potential antibacterial drug development. However, little is known about how conformational dynamics between the native states influences the substrate recognition and the functionality of enzymatic catalysis. Here, we report a coarse-grained triple-basin structure-based model upon ligand binding to describe such multiple-state system by the molecular dynamics simulation. With our model, we have made theoretical predictions that are in good agreement with the experimental measurements. Our results revealed the intrinsic conformational fluctuations between apo and open states without ligand binding. We found that HPPK can switch to the activated holo state upon the ordered binding of the two ligands (ATP and HP). We uncovered the underlying mechanism by which major induced fit and minor population shift pathways coexist upon ligand binding by quantitative flux analysis. Additionally, we pointed out the structural origin for the conformational changes and identified the key residues as well as contact interactions. We further explored the temperature effect on the conformational distributions and pathway weights. It gave strong support that higher temperatures promote population shift, while the induced fit pathway is always the predominant activation route of the HPPK system. These findings will provide significant insights of the mechanisms of the multistate conformational dynamics of HPPK upon ligand binding.

On the folding of a structurally complex protein to its metastable active state

For successful protease inhibition, the reactive center loop (RCL) of the two-domain serine protease inhibitor, α1-antitrypsin (α1-AT), needs to remain exposed in a metastable active conformation. The α1-AT RCL is sequestered in a β-sheet in the stable latent conformation. Thus, to be functional, α1-AT must always fold to a metastable conformation while avoiding folding to a stable conformation. We explore the structural basis of this choice using folding simulations of coarse-grained structure-based models of the two α1-AT conformations. Our simulations capture the key features of folding experiments performed on both conformations. The simulations also show that the free energy barrier to fold to the latent conformation is much larger than the barrier to fold to the active conformation. An entropically stabilized on-pathway intermediate lowers the barrier for folding to the active conformation. In this intermediate, the RCL is in an exposed configuration, and only one of the two α1-AT domains is folded. In contrast, early conversion of the RCL into a β-strand increases the coupling between the two α1-AT domains in the transition state and creates a larger barrier for folding to the latent conformation. Thus, unlike what happens in several proteins, where separate regions promote folding and function, the structure of the RCL, formed early during folding, determines both the conformational and the functional fate of α1-AT. Further, the short 12-residue RCL modulates the free energy barrier and the folding cooperativity of the large 370-residue α1-AT. Finally, we suggest experiments to test the predicted folding mechanism for the latent state.

The key role of electrostatic interactions in the induced folding in RNA recognition by DCL1-A.

The intrinsically disordered protein domain DCL1-A is the first report of a complete double stranded RNA binding domain folding upon binding. DCL1-A recognizes the dsRNA by acquiring a well-folded structure after engagement with its interaction partner. Despite the structural characterization of the interaction complex underlying the recognition of dsRNA has been established, the dynamics of disorder-to-order transitions in the binding process remains elusive. Here we have developed a coarse-grained structure-based model with consideration of electrostatic interactions to explore the mechanism of the coupled folding and binding. Our approach led to remarkable agreements with both experimental and theoretical results. We quantified the global binding-folding landscape, which indicates a synergistic binding induced folding mechanism. We further investigated the effect of electrostatic interactions in this coupled folding and binding process. It reveals that non-native electrostatic interactions dominate the initial stage of the recognition. Our results help improve our understanding of the induced folding of the IDP DCL1-A upon binding to dsRNA. Such methods developed here can be applied for further explorations of the dynamics of coupled folding and binding systems.

Exploring the effects of sparse restraints on protein structure prediction.

One of the main barriers to accurate computational protein structure prediction is searching the vast space of protein conformations. Distance restraints or inter-residue contacts have been used to reduce this search space, easing the discovery of the correct folded state. It has been suggested that about 1 contact for every 12 residues may be sufficient to predict structure at fold level accuracy. Here, we use coarse-grained structure-based models in conjunction with molecular dynamics simulations to examine this empirical prediction. We generate sparse contact maps for 15 proteins of varying sequence lengths and topologies and find that given perfect secondary-structural information, a small fraction of the native contact map (5%-10%) suffices to fold proteins to their correct native states. We also find that different sparse maps are not equivalent and we make several observations about the type of maps that are successful at such structure prediction. Long range contacts are found to encode more information than shorter range ones, especially for α and αβ-proteins. However, this distinction reduces for β-proteins. Choosing contacts that are a consensus from successful maps gives predictive sparse maps as does choosing contacts that are well spread out over the protein structure. Additionally, the folding of proteins can also be used to choose predictive sparse maps. Overall, we conclude that structure-based models can be used to understand the efficacy of structure-prediction restraints and could, in future, be tuned to include specific force-field interactions, secondary structure errors and noise in the sparse maps.

Supersymmetric quantum mechanics method for the Fokker–Planck equation with applications to protein folding dynamics

This work developed analytical methods to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding and compared the results with simulation. The Fokker–Planck equation is mapped onto a Schrödinger-type equation due to the well-known solutions of the latter. Through a semi-analytical description, the supersymmetric quantum mechanics formalism is invoked and the time-dependent probability distributions are obtained with numerical calculations by using the variational method. A coarse-grained structure-based model of the two-state protein Tm CSP was simulated at a Cα level of resolution and the thermodynamics and kinetics were fully characterized. Analytical solutions from non-equilibrium conditions were obtained with the simulated double-well free energy potential and kinetic folding times were calculated. It was found that analytical folding time as a function of temperature agrees, quantitatively, with simulations and experiments from the literature of Tm CSP having the well-known ‘U’ shape of the Chevron Plots. The simple analytical model developed in this study has a potential to be used by theoreticians and experimentalists willing to explore, quantitatively, rates and the kinetic behavior of their system by informing the thermally activated barrier. The theory developed describes a stochastic process and, therefore, can be applied to a variety of biological as well as condensed-phase two-state systems.

Self-assembly of model proteins into virus capsids

We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions. Previous studies of the capsid self-assembly involved solid objects of a supramolecular scale, e.g. corresponding to capsomeres, with engineered couplings and stochastic movements. In our approach, a single capsid is dissociated by an application of a high temperature for a variable period and then the system is cooled down to allow for self-assembly. The restoration of the capsid proceeds to various extent, depending on the nature of the dissociated state, but is rarely complete because some proteins depart too far unless the process takes place in a confined space.