Simulating the electrostatic guidance of the vectorial translocations in hexameric helicases and translocases

Machines on Genes through the Computational Microscope

Macromolecular machines acting on genes are at the core of life's fundamental processes, including DNA replication and repair, gene transcription and regulation, chromatin packaging, RNA splicing, and genome editing. Here, we report the increasing role of computational biophysics in characterizing the mechanisms of "machines on genes", focusing on innovative applications of computational methods and their integration with structural and biophysical experiments. We showcase how state-of-the-art computational methods, including classical and ab initio molecular dynamics to enhanced sampling techniques, and coarse-grained approaches are used for understanding and exploring gene machines for real-world applications. As this review unfolds, advanced computational methods describe the biophysical function that is unseen through experimental techniques, accomplishing the power of the "computational microscope", an expression coined by Klaus Schulten to highlight the extraordinary capability of computer simulations. Pushing the frontiers of computational biophysics toward a pragmatic representation of large multimegadalton biomolecular complexes is instrumental in bridging the gap between experimentally obtained macroscopic observables and the molecular principles playing at the microscopic level. This understanding will help harness molecular machines for medical, pharmaceutical, and biotechnological purposes.

Computationally exploring the mechanism of bacteriophage T7 gp4 helicase translocating along ssDNA

Bacteriophage T7 gp4 helicase has served as a model system for understanding mechanisms of hexameric replicative helicase translocation. The mechanistic basis of how nucleoside 5'-triphosphate hydrolysis and translocation of gp4 helicase are coupled is not fully resolved. Here, we used a thermodynamically benchmarked coarse-grained protein force field, Associative memory, Water mediated, Structure and Energy Model (AWSEM), with the single-stranded DNA (ssDNA) force field 3SPN.2C to investigate gp4 translocation. We found that the adenosine 5'-triphosphate (ATP) at the subunit interface stabilizes the subunit-subunit interaction and inhibits subunit translocation. Hydrolysis of ATP to adenosine 5'-diphosphate enables the translocation of one subunit, and new ATP binding at the new subunit interface finalizes the subunit translocation. The LoopD2 and the N-terminal primase domain provide transient protein-protein and protein-DNA interactions that facilitate the large-scale subunit movement. The simulations of gp4 helicase both validate our coarse-grained protein-ssDNA force field and elucidate the molecular basis of replicative helicase translocation.

Simulating the directional translocation of a substrate by the AAA+ motor in the 26S proteasome

This work explored the molecular origin of substrate translocation by the AAA+ motor of the 26S proteasome. This exploration was performed by combining different simulation approaches including calculations of binding free energies, coarse-grained simulations, and considerations of the ATP hydrolysis energy. The simulations were used to construct the free energy landscape for the translocation process. This included the evaluation of the conformational barriers in different translocation steps. Our simulation reveals that the substrate translocation by the AAA+ motor is guided in part by electrostatic interactions. We also validated the experimental observation that bulkier residues in pore loop 1 are responsible for substrate translocation. However, our calculation also reveals that the lysine residues prior to the bulkier residues (conserved along pore loop 1) are also important for the translocation process. We believe that this computational study can help in guiding the ongoing research of the proteasome.

Revisiting the protomotive vectorial motion of F0-ATPase

The elucidation of the detailed mechanism used by F₀ to convert proton gradient to torque and rotational motion presents a major puzzle despite significant biophysical and structural progress. Although the conceptual model has advanced our understanding of the working principles of such systems, it is crucial to explore the actual mechanism using structure-based models that actually reproduce a unidirectional proton-driven rotation. Our previous work used a coarse-grained (CG) model to simulate the action of F₀ However, the simulations were based on a very tentative structural model of the interaction between subunit a and subunit c. Here, we again use a CG model but with a recent cryo-EM structure of cF₁F₀ and also explore the proton path using our water flooding and protein dipole Langevin dipole semimacroscopic formalism with its linear response approximation version (PDLD/S-LRA) approaches. The simulations are done in the combined space defined by the rotational coordinate and the proton transport coordinate. The study reproduced the effect of the protomotive force on the rotation of the F₀ while establishing the electrostatic origin of this effect. Our landscape reproduces the correct unidirectionality of the synthetic direction of the F₀ rotation and shows that it reflects the combined electrostatic coupling between the proton transport path and the c-ring conformational change. This work provides guidance for further studies in other proton-driven mechanochemical systems and should lead (when combined with studies of F₁) to a complete energy transduction picture of the F₀F₁-ATPase system.

Building Transcription Factor Binding Site Models to Understand Gene Regulation in Plants

Transcription factors (TFs) are key cellular components that control gene expression. They recognize specific DNA sequences, the TF binding sites (TFBSs), and thus are targeted to specific regions of the genome where they can recruit transcriptional co-factors and/or chromatin regulators to fine-tune spatiotemporal gene regulation. Therefore, the identification of TFBSs in genomic sequences and their subsequent quantitative modeling is of crucial importance for understanding and predicting gene expression. Here, we review how TFBSs can be determined experimentally, how the TFBS models can be constructed in silico, and how they can be optimized by taking into account features such as position interdependence within TFBSs, DNA shape, and/or by introducing state-of-the-art computational algorithms such as deep learning methods. In addition, we discuss the integration of context variables into the TFBS modeling, including nucleosome positioning, chromatin states, methylation patterns, 3D genome architectures, and TF cooperative binding, in order to better predict TF binding under cellular contexts. Finally, we explore the possibilities of combining the optimized TFBS model with technological advances, such as targeted TFBS perturbation by CRISPR, to better understand gene regulation, evolution, and plant diversity.

Molecular Mechanisms of DNA Replication and Repair Machinery: Insights from Microscopic Simulations

Reproduction, the hallmark of biological activity, requires making an accurate copy of the genetic material to allow the progeny to inherit parental traits. In all living cells, the process of DNA replication is carried out by a concerted action of multiple protein species forming a loose protein-nucleic acid complex, the replisome. Proofreading and error correction generally accompany replication but also occur independently, safeguarding genetic information through all phases of the cell cycle. Advances in biochemical characterization of intracellular processes, proteomics and the advent of single-molecule biophysics have brought about a treasure trove of information awaiting to be assembled into an accurate mechanistic model of the DNA replication process. In this review, we describe recent efforts to model elements of DNA replication and repair processes using computer simulations, an approach that has gained immense popularity in many areas of molecular biophysics but has yet to become mainstream in the DNA metabolism community. We highlight the use of diverse computational methods to address specific problems of the fields and discuss unexplored possibilities that lie ahead for the computational approaches in these areas.

The FOF1 ATP synthase: from atomistic three-dimensional structure to the rotary-chemical function

Molecular motors are multi-subunit complexes that are indispensable for accomplishing various tasks of the living cells. One such molecular motor is the F_OF₁ ATP synthase that synthesizes ATP at the expense of the membrane proton gradient. Elucidating the molecular origin of the motor function is challenging despite significant advances in various experimental fields. Currently atomic simulations of whole motor complexes cannot reach to functionally relevant time scales that extend beyond the millisecond regime. Moreover, to reveal the underlying molecular origin of the function, one must model the coupled chemical and conformational events using physically and chemically meaningful multiscaling techniques. In this review, we discuss our approach to model the action of the F₁ and F_O molecular motors, where emphasis is laid on elucidating the molecular origin of the driving force that leads to directional rotation at the expense of ATP hydrolysis or proton gradients. We have used atomic structures of the motors and used hierarchical multiscaling techniques to generate low dimensional functional free energy surfaces of the complete mechano-chemical process. These free energy surfaces were studied further to calculate important characteristics of the motors, such as, rotational torque, temporal dynamics, occurrence of intermittent dwell states, etc. We also studied the result of mutating various parts of the motor domains and our observations correspond very well with the experimental findings. Overall, our studies have generated a cumulative understanding of the motor action, and especially highlight the crucial role of electrostatics in establishing the mechano-chemical coupling.

Simulating the dynamics of the mechanochemical cycle of myosin-V

The detailed dynamics of the cycle of myosin-V are explored by simulation approaches, examining the nature of the energy-driven motion. Our study started with Langevin dynamics (LD) simulations on a very coarse landscape with a single rate-limiting barrier and reproduced the stall force and the hand-over-hand dynamics. We then considered a more realistic landscape and used time-dependent Monte Carlo (MC) simulations that allowed trajectories long enough to reproduce the force/velocity characteristic sigmoidal correlation, while also reproducing the hand-over-hand motion. Overall, our study indicated that the notion of a downhill lever-up to lever-down process (popularly known as the powerstroke mechanism) is the result of the energetics of the complete myosin-V cycle and is not the source of directional motion or force generation on its own. The present work further emphasizes the need to use well-defined energy landscapes in studying molecular motors in general and myosin in particular.

Physics-Based Potentials for Coarse-Grained Modeling of Protein-DNA Interactions

Physics-based potentials have been developed for the interactions between proteins and DNA for simulations with the UNRES + NARES-2P force field. The mean-field interactions between a protein and a DNA molecule can be divided into eight categories: (1) nonpolar side chain–DNA base, (2) polar uncharged side chain–DNA base, (3) charged side chain–DNA base, (4) peptide group–phosphate group, (5) peptide group–DNA base, (6) nonpolar side chain–phosphate group, (7) polar uncharged side chain–phosphate group, and (8) charged side chain–phosphate group. Umbrella-sampling molecular dynamics simulations in explicit TIP3P water using the AMBER force field were carried out to determine the potentials of mean force (PMF) for all 105 pairs of interacting components. Approximate analytical expressions for the mean-field interaction energy of each pair of the different kinds of interacting molecules were then fitted to the PMFs to obtain the parameters of the analytical expressions. These analytical expressions can reproduce satisfactorily the PMF curves corresponding to different orientations of the interacting molecules. The results suggest that the physics-based mean-field potentials of amino acid–nucleotide interactions presented here can be used in coarse-grained simulation of protein–DNA interactions.

Protein-DNA and ion-DNA interactions revealed through contrast variation SAXS

Understanding how DNA carries out its biological roles requires knowledge of its interactions with biological partners. Since DNA is a polyanionic polymer, electrostatic interactions contribute significantly. These interactions are mediated by positively charged protein residues or charge compensating cations. Direct detection of these partners and/or their effect on DNA conformation poses challenges, especially for monitoring conformational dynamics in real time. Small-angle x-ray scattering (SAXS) is uniquely sensitive to both the conformation and local environment (i.e. protein partner and associated ions) of the DNA. The primary challenge of studying multi-component systems with SAXS lies in resolving how each component contributes to the measured scattering. Here, we review two contrast variation (CV) strategies that enable targeted studies of the structures of DNA or its associated partners. First, solution contrast variation enables measurement of DNA conformation within a protein-DNA complex by masking out the protein contribution to the scattering profile. We review a specific example, in which the real-time unwrapping of DNA from a nucleosome core particle is measured during salt-induced disassembly. The second method, heavy atom isomorphous replacement, reports the spatial distribution of the cation cloud around duplex DNA by exploiting changes in the scattering strength of cations with varying atomic numbers. We demonstrate the application of this approach to provide the spatial distribution of monovalent cations (Na+, K+, Rb+, Cs+) around a standard 25-base pair DNA. The CV strategies presented here are valuable tools for understanding DNA interactions with its biological partners.

Mechanism of substrate translocation by a ring-shaped ATPase motor at millisecond resolution

Ring-shaped, hexameric ATPase motors fulfill key functions in cellular processes, such as genome replication, transcription, or protein degradation, by translocating a long substrate through their central pore powered by ATP hydrolysis. Despite intense research efforts, the atomic-level mechanism transmitting chemical energy from hydrolysis into mechanical force that translocates the substrate is still unclear. Here we employ all-atom molecular dynamics simulations combined with advanced path sampling techniques and milestoning analysis to characterize how mRNA substrate is translocated by an exemplary homohexameric motor, the transcription termination factor Rho. We find that the release of hydrolysis product (ADP + Pi) triggers the force-generating process of Rho through a 0.1 millisecond-long conformational transition, the time scale seen also in experiment. The calculated free energy profiles and kinetics show that Rho unidirectionally translocates the single-stranded RNA substrate via a population shift of the conformational states of Rho; upon hydrolysis product release, the most favorable conformation shifts from the pretranslocation state to the post-translocation state. Via two previously unidentified intermediate states, the RNA chain is seen to be pulled by six K326 side chains, whose motions are induced by highly coordinated relative translation and rotation of Rho's six subunits. The present study not only reveals in new detail the mechanism employed by ring-shaped ATPase motors, for example the use of loosely bound and tightly bound hydrolysis reactant and product states to coordinate motor action, but also provides an effective approach to identify allosteric sites of multimeric enzymes in general.

Evidence for an electrostatic mechanism of force generation by the bacteriophage T4 DNA packaging motor

How viral packaging motors generate enormous forces to translocate DNA into viral capsids remains unknown. Recent structural studies of the bacteriophage T4 packaging motor have led to a proposed mechanism wherein the gp17 motor protein translocates DNA by transitioning between extended and compact states, orchestrated by electrostatic interactions between complimentarily charged residues across the interface between the N- and C-terminal subdomains. Here we show that site-directed alterations in these residues cause force dependent impairments of motor function including lower translocation velocity, lower stall force and higher frequency of pauses and slips. We further show that the measured impairments correlate with computed changes in free-energy differences between the two states. These findings support the proposed structural mechanism and further suggest an energy landscape model of motor activity that couples the free-energy profile of motor conformational states with that of the ATP hydrolysis cycle.

Electrostatically accelerated encounter and folding for facile recognition of intrinsically disordered proteins

Achieving facile specific recognition is essential for intrinsically disordered proteins (IDPs) that are involved in cellular signaling and regulation. Consideration of the physical time scales of protein folding and diffusion-limited protein-protein encounter has suggested that the frequent requirement of protein folding for specific IDP recognition could lead to kinetic bottlenecks. How IDPs overcome such potential kinetic bottlenecks to viably function in signaling and regulation in general is poorly understood. Our recent computational and experimental study of cell-cycle regulator p27 (Ganguly et al., J. Mol. Biol. (2012)) demonstrated that long-range electrostatic forces exerted on enriched charges of IDPs could accelerate protein-protein encounter via "electrostatic steering" and at the same time promote "folding-competent" encounter topologies to enhance the efficiency of IDP folding upon encounter. Here, we further investigated the coupled binding and folding mechanisms and the roles of electrostatic forces in the formation of three IDP complexes with more complex folded topologies. The surface electrostatic potentials of these complexes lack prominent features like those observed for the p27/Cdk2/cyclin A complex to directly suggest the ability of electrostatic forces to facilitate folding upon encounter. Nonetheless, similar electrostatically accelerated encounter and folding mechanisms were consistently predicted for all three complexes using topology-based coarse-grained simulations. Together with our previous analysis of charge distributions in known IDP complexes, our results support a prevalent role of electrostatic interactions in promoting efficient coupled binding and folding for facile specific recognition. These results also suggest that there is likely a co-evolution of IDP folded topology, charge characteristics, and coupled binding and folding mechanisms, driven at least partially by the need to achieve fast association kinetics for cellular signaling and regulation.

Simulating the pulling of stalled elongated peptide from the ribosome by the translocon

The nature of the coupling between the stalling of the elongated nascent peptide chain in the ribosome and its insertion through the translocon is analyzed, focusing on the recently discovered biphasic force that overcomes the stalling barrier. The origin of this long-range coupling is explored by coarse-grained simulations that combine the translocon (TR) insertion profile and the effective chemical barrier for the extension of the nascent chain in the ribosome. Our simulation determined that the inserted H segment is unlikely to climb the TR barrier in parallel with the peptide synthesis chemical step and that the nascent chain should first overcome the chemical barriers and move into the ribosome-TR gap region before the insertion into the TR tunnel. Furthermore, the simulations indicate that the coupled TR-chemistry free energy profile accounts for the biphasic force. Apparently, although the overall elongation/insertion process can be depicted as a tug-of-war between the forces of the TR and the ribosome, it is actually a reflection of the combined free-energy landscape. Most importantly, the present study helps to relate the experimental observation of the biphasic force to crucial information about the elusive path and barriers of the TR insertion process.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Realistic simulations of the coupling between the protomotive force and the mechanical rotation of the F0-ATPase

The molecular origin of the action of the F(0) proton gradient-driven rotor presents a major puzzle despite significant structural advances. Although important conceptual models have provided guidelines of how such systems should work, it has been challenging to generate a structure-based molecular model using physical principles that will consistently lead to the unidirectional proton-driven rotational motion during ATP synthesis. This work uses a coarse-grained (CG) model to simulate the energetics of the F(0)-ATPase system in the combined space defined by the rotational coordinate and the proton transport (PTR) from the periplasmic side (P) to the cytoplasmic side (N). The model establishes the molecular origin of the rotation, showing that this effect is due to asymmetry in the energetics of the proton path rather than only the asymmetry of the interaction of the Asp on the c-ring helices and Arg on the subunit-a. The simulation provides a clear conceptual background for further exploration of the electrostatic basis of proton-driven mechanochemical systems.

Electrostatically accelerated coupled binding and folding of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) are now recognized to be prevalent in biology, and many potential functional benefits have been discussed. However, the frequent requirement of peptide folding in specific interactions of IDPs could impose a kinetic bottleneck, which could be overcome only by efficient folding upon encounter. Intriguingly, existing kinetic data suggest that specific binding of IDPs is generally no slower than that of globular proteins. Here, we exploited the cell cycle regulator p27(Kip1) (p27) as a model system to understand how IDPs might achieve efficient folding upon encounter for facile recognition. Combining experiments and coarse-grained modeling, we demonstrate that long-range electrostatic interactions between enriched charges on p27 and near its binding site on cyclin A not only enhance the encounter rate (i.e., electrostatic steering) but also promote folding-competent topologies in the encounter complexes, allowing rapid subsequent formation of short-range native interactions en route to the specific complex. In contrast, nonspecific hydrophobic interactions, while hardly affecting the encounter rate, can significantly reduce the efficiency of folding upon encounter and lead to slower binding kinetics. Further analysis of charge distributions in a set of known IDP complexes reveals that, although IDP binding sites tend to be more hydrophobic compared to the rest of the target surface, their vicinities are frequently enriched with charges to complement those on IDPs. This observation suggests that electrostatically accelerated encounter and induced folding might represent a prevalent mechanism for promoting facile IDP recognition.

Electrostatic origin of the mechanochemical rotary mechanism and the catalytic dwell of F1-ATPase

Understanding the nature of energy transduction in life processes requires a quantitative description of the energetics of the conversion of ATP to ADP by ATPases. Previous attempts to do so have provided an interesting insight but could not account for the rotary mechanism by a nonphenomenological structure/energy description. In particular it has been very challenging to account for the observations of the 80° and 40° rotational substates, without any prior information about such states in the simulation procedure. Here we use a coarse-grained model of F1-ATPase and generate, without the adjustment of phenomenological parameters, a structure-based free energy landscape that reproduces the energetics of the mechanochemical process. It is found that the landscape along the relevant rotary path is determined by the electrostatic free energy and not by steric effects. Furthermore, the generated surface and the corresponding Langevin dynamics simulations identify a hidden conformational barrier that provides a new fundamental interpretation of the catalytic dwell and illuminate the nature of the energy conversion process.

Frustration in protein-DNA binding influences conformational switching and target search kinetics

Rapid recognition of DNA target sites involves facilitated diffusion through which alternative sites are searched on genomic DNA. A key mechanism facilitating the localization of the target by a DNA-binding protein (DBP) is one-dimensional diffusion (sliding) in which electrostatic forces attract the protein to the DNA. As the protein reaches its target DNA site, it switches from purely electrostatic binding to a specific set of interactions with the DNA bases that also involves hydrogen bonding and van der Waals forces. High overlap between the DBP patches used for nonspecific and specific interactions with DNA may enable an immediate transition between the two binding modes following target site localization. By contrast, an imperfect overlap may result in greater frustration between the two potentially competing binding modes and consequently slower switching between them. A structural analysis of 125 DBPs indicates frustration between the two binding modes that results in a large difference between the orientations of the protein to the DNA when it slides compared to when it specifically interacts with DNA. Coarse-grained molecular dynamics simulations of in silico designed peptides comprising the full range of frustrations between the two interfaces show slower transition from nonspecific to specific DNA binding as the overlap between the patches involved in the two binding modes decreases. The complex search kinetics may regulate the search by eliminating trapping of the protein in semispecific sites while sliding.

Coarse-grained (multiscale) simulations in studies of biophysical and chemical systems

Recent years have witnessed an explosion in computational power, leading to attempts to model ever more complex systems. Nevertheless, there remain cases for which the use of brute-force computer simulations is clearly not the solution. In such cases, great benefit can be obtained from the use of physically sound simplifications. The introduction of such coarse graining can be traced back to the early usage of a simplified model in studies of proteins. Since then, the field has progressed tremendously. In this review, we cover both key developments in the field and potential future directions. Additionally, particular emphasis is given to two general approaches, namely the renormalization and reference potential approaches, which allow one to move back and forth between the coarse-grained (CG) and full models, as these approaches provide the foundation for CG modeling of complex systems.

Paradynamics: an effective and reliable model for ab initio QM/MM free-energy calculations and related tasks

Recent years have seen tremendous effort in the development of approaches with which to obtain quantum mechanics/molecular mechanics (QM/MM) free energies for reactions in the condensed phase. Nevertheless, there remain significant challenges to address, particularly, the high computational cost involved in performing proper configurational sampling and, in particular, in obtaining ab initio QM/MM (QM(ai)/MM) free-energy surfaces. One increasingly popular approach that seems to offer an ideal way to progress in this direction is the elegant metadynamics (MTD) approach. However, in the current work, we point out the subtle efficiency problems associated with this approach and illustrate that we have at hand what is arguably a more powerful approach. More specifically, we demonstrate the effectiveness of an updated version of our original idea of using a classical reference potential for QM(ai)/MM calculations [J. Phys. Chem. 1995, 99, 17516)], which we refer to as paradynamics (PD). This approach is based on the use of an empirical valence bond (EVB) reference potential, which is already similar to the real ab initio potential. The reference potential is fitted to the ab initio potential by an iterative and, to a great degree, automated refinement procedure. The corresponding free-energy profile is then constructed using the refined EVB potential, and the linear response approximation (LRA) is used to evaluate the QM(ai)/MM activation free-energy barrier. The automated refinement of the EVB surface (and thus the reduction of the difference between the reference and ab initio potentials) is a key factor in accelerating the convergence of the LRA approach. We apply our PD approach to a test reaction, namely, the S(N)2 reaction between a chloride ion and methyl chloride, and demonstrate that, at present, this approach is far more powerful and cost-effective than the metadynamics approach (at least in its current implementation). We also discuss the general features of the PD approach in terms of its ability to explore complex systems and clarify that it is not a specialized approach limited to only accelerating QM(ai)/MM calculations with proper sampling, but rather can be used in a wide variety of applications. In fact, we point out that the use of a reference (CG) potential coupled with its PD refinement, as well as our renormalization approach, provides very general and powerful strategies that can be used very effectively to explore any property that has been studied by the MTD approach.

Multiscale modeling of biological functions

Recent years have witnessed a tremendous explosion in computational power, which in turn has resulted in great progress in the complexity of the biological and chemical problems that can be addressed by means of all-atom simulations. Despite this, however, our computational time is not infinite, and in fact many of the key problems of the field were resolved long before the existence of the current levels of computational power. This review will start by presenting a brief historical overview of the use of multiscale simulations in biology, and then present some key developments in the field, highlighting several cases where the use of a physically sound simplification is clearly superior to a brute-force approach. Finally, some potential future directions will be discussed.

Renormalizing SMD: the renormalization approach and its use in long time simulations and accelerated PMF calculations of macromolecules

Simulations of long time process in condensed phases, in general, and in biomolecules, in particular, present a major challenge that cannot be overcome at present by brute force molecular dynamics (MD) approaches. This work takes the renormalization method, intruded by us sometime ago, and establishes its reliability and potential in extending the time scale of molecular simulations. The validation involves a truncated gramicidin system in the gas phase. This system is small enough to allow for very long explicit simulations and sufficiently complex to present the physics of realistic ion channels. The renormalization approach is found to be reliable and arguably presents the first approach that allows one to exploit the otherwise problematic steered molecular dynamics (SMD) treatments in quantitative and meaningful studies. It is established that we can reproduce the long time behavior of large systems by using Langevin dynamics (LD) simulations of a renormalized implicit model. This is done without spending the enormous time needed to obtain such trajectories in the explicit system. The present study also provides a promising advance in accelerated evaluation of free energy barriers. This is done by adjusting the effective potential in the implicit model to reproduce the same passage time as that obtained in the explicit model under the influence of an external force. Here having a reasonable effective friction provides a way to extract the potential of mean force (PMF) without investing the time needed for regular PMF calculations. The renormalization approach, which is illustrated here in realistic calculations, is expected to provide a major help in studies of complex landscapes and in exploring long time dynamics of biomolecules.

Hexameric helicase deconstructed: interplay of conformational changes and substrate coupling

Hexameric helicases are molecular motor proteins that utilize energy obtained from ATP hydrolysis to translocate along and/or unwind nucleic acids. In this study, we investigate the dynamic behavior of the Simian Virus 40 hexameric helicase bound to DNA by performing molecular dynamics simulations employing a coarse-grained model. Our results elucidate the two most important molecular features of the helicase motion. First, the attractive interactions between the DNA-binding domain of the helicase and the DNA backbone are essential for the helicase to exhibit a unidirectional motion along the DNA strand. Second, the sequence of ATP binding at multiple binding pockets affects the helicase motion. Specifically, concerted ATP binding does not generate a unidirectional motion of the helicase. It is only when the binding of ATP occurs sequentially from one pocket to the next that the helicase moves unidirectionally along the DNA. Interestingly, in the reverse order of sequential ATP binding, the helicase also moves unidirectionally but in the opposite direction. These observations suggest that in nature ATP molecules must distinguish between different available ATP binding pockets of the hexameric helicase in order to function efficiently. To this end, simulations reveal that the binding of ATP in one pocket induces an opening of the next ATP-binding pocket and such an asymmetric deformation may coordinate the sequential ATP binding in a unidirectional manner. Overall, these findings may provide clues toward understanding the mechanism of substrate translocation in other motor proteins.

Multiscale simulations of protein landscapes: using coarse-grained models as reference potentials to full explicit models

Evaluating the free-energy landscape of proteins and the corresponding functional aspects presents a major challenge for computer simulation approaches. This challenge is due to the complexity of the landscape and the enormous computer time needed for converging simulations. The use of simplified coarse-grained (CG) folding models offers an effective way of sampling the landscape but such a treatment, however, may not give the correct description of the effect of the actual protein residues. A general way around this problem that has been put forward in our early work (Fan et al., Theor Chem Acc 1999;103:77-80) uses the CG model as a reference potential for free-energy calculations of different properties of the explicit model. This method is refined and extended here, focusing on improving the electrostatic treatment and on demonstrating key applications. These applications include: evaluation of changes of folding energy upon mutations, calculations of transition-states binding free energies (which are crucial for rational enzyme design), evaluations of catalytic landscape, and evaluations of the time-dependent responses to pH changes. Furthermore, the general potential of our approach in overcoming major challenges in studies of structure function correlation in proteins is discussed.

A computational analysis of ATP binding of SV40 large tumor antigen helicase motor

Simian Virus 40 Large Tumor Antigen (LTag) is an efficient helicase motor that unwinds and translocates DNA. The DNA unwinding and translocation of LTag is powered by ATP binding and hydrolysis at the nucleotide pocket between two adjacent subunits of an LTag hexamer. Based on the set of high-resolution hexameric structures of LTag helicase in different nucleotide binding states, we simulated a conformational transition pathway of the ATP binding process using the targeted molecular dynamics method and calculated the corresponding energy profile using the linear response approximation (LRA) version of the semi-macroscopic Protein Dipoles Langevin Dipoles method (PDLD/S). The simulation results suggest a three-step process for the ATP binding from the initial interaction to the final tight binding at the nucleotide pocket, in which ATP is eventually “locked” by three pairs of charge-charge interactions across the pocket. Such a “cross-locking” ATP binding process is similar to the binding zipper model reported for the F1-ATPase hexameric motor. The simulation also shows a transition mechanism of Mg²⁺ coordination to form the Mg-ATP complex during ATP binding, which is accompanied by the large conformational changes of LTag. This simulation study of the ATP binding process to an LTag and the accompanying conformational changes in the context of a hexamer leads to a refined cooperative iris model that has been proposed previously.

The Large Tumor antigen (LTag) encoded by Simian Virus 40 (SV40) is a marvelous molecule that is not only a viral oncogene, but also an efficient molecular machine as a helicase that unwinds double helix DNA for genome replication, an essential process in all living organisms. LTag hexameric helicase uses the energy of ATP to power its conformational switch for DNA unwinding. Understanding how the LTag conformational switch is coupled to the energy from ATP usage by LTag to do the mechanical work of unwinding DNA is of great interest to biologists, and yet remains to be established. Based on our previous high-resolution structures of LTag helicase in different conformational states, we simulated an LTag conformational transition pathway in the ATP binding process using the targeted molecular dynamics method. Our simulation results suggest a three-step process for the ATP binding to the nucleotide pocket, in which ATP is eventually “locked” into the pocket by three pairs of “locker” interactions. We have also quantitatively evaluated the energy profile of ATP binding using a special computational simulation technique. Additionally, our simulation study of ATP binding by LTag and the accompanying conformational switches in the context of a hexamer leads to a refined cooperative iris model that may be used for DNA unwinding.

The minimum replication origin of merkel cell polyomavirus has a unique large T-antigen loading architecture and requires small T-antigen expression for optimal replication

Merkel cell polyomavirus (MCV) is a recently discovered human polyomavirus causing the majority of human Merkel cell carcinomas. We mapped a 71-bp minimal MCV replication core origin sufficient for initiating eukaryotic DNA replication in the presence of wild-type MCV large T protein (LT). The origin includes a poly(T)-rich tract and eight variably oriented, GAGGC-like pentanucleotide sequences (PS) that serve as LT recognition sites. Mutation analysis shows that only four of the eight PS are required for origin replication. A single point mutation in one origin PS from a naturally occurring, tumor-derived virus reduces LT assembly on the origin and eliminates viral DNA replication. Tumor-derived LT having mutations truncating either the origin-binding domain or the helicase domain also prevent LT-origin assembly. Optimal MCV replication requires coexpression of MCV small T protein (sT), together with LT. An intact DnaJ domain on the LT is required for replication but is dispensable on the sT. In contrast, PP2A targeting by sT is required for enhanced replication. The MCV origin provides a novel model for eukaryotic replication from a defined DNA element and illustrates the selective pressure within tumors to abrogate independent MCV replication.