Enhanced Coarse-Grained Molecular Dynamics Simulation with a Smoothed Hybrid Potential Using a Neural Network Model.

In all-atom (AA) molecular dynamics (MD) simulations, the rugged energy profile of the force field makes it challenging to reproduce spontaneous structural changes in biomolecules within a reasonable calculation time. Existing coarse-grained (CG) models, in which the energy profile is set to a global minimum around the initial structure, are unsuitable to explore the structural dynamics between metastable states far away from the initial structure without any bias. In this study, we developed a new hybrid potential composed of an artificial intelligence (AI) potential and minimal CG potential related to the statistical bond length and excluded volume interactions to accelerate the transition dynamics while maintaining the protein character. The AI potential is trained by energy matching using a diverse structural ensemble sampled via multicanonical (Mc) MD simulation and the corresponding AA force field energy, profile of which is smoothed by energy minimization. By applying the new methodology to chignolin and TrpCage, we showed that the AI potential can predict the AA energy with significantly high accuracy, as indicated by a correlation coefficient (R-value) between the true and predicted energies exceeding 0.89. In addition, we successfully demonstrated that CGMD simulation based on the smoothed hybrid potential can significantly enhance the transition dynamics between various metastable states while preserving protein properties compared to those obtained with conventional CGMD and AAMD.

A thermodynamically consistent monte carlo cross-bridge model with a trapping mechanism reveals the role of stretch activation in heart pumping.

Changes in intracellular calcium concentrations regulate heart beats. However, the decline in the left ventricular pressure during early diastole is much sharper than that of the Ca2+ transient, resulting in a rapid supply of blood to the left ventricle during the diastole. At the tissue level, cardiac muscles have a distinct characteristic, known as stretch activation, similar to the function of insect flight muscles. Stretch activation, which is a delayed increase in force following a rapid muscle length increase, has been thought to be related to autonomous control in these muscles. In this numerical simulation study, we introduced a molecular mechanism of stretch activation and investigated the role of this mechanism in the pumping function of the heart, using the previously developed coupling multiple-step active stiffness integration scheme for a Monte Carlo (MC) cross-bridge model and a bi-ventricular finite element model. In the MC cross-bridge model, we introduced a mechanism for trapping the myosin molecule in its post-power stroke state. We then determined the rate constants of transitions for trapping and escaping in a thermodynamically consistent manner. Based on our numerical analysis, we draw the following conclusions regarding the stretch activation mechanism: (i) the delayed force becomes larger than the original isometric force because the population of trapped myosin molecules and their average force increase after stretching; (ii) the delayed force has a duration of more than a few seconds owing to a fairly small rate constant of escape from the trapped state. For the role of stretch activation in heart pumping, we draw the following conclusions: (iii) for the regions in which the contraction force decreases earlier than the neighboring region in the end-systole phase, the trapped myosin molecules prevent further lengthening of the myocytes, which then prevents further shortening of neighboring myocytes; (iv) as a result, the contraction forces are sustained longer, resulting in a larger blood ejection, and their degeneration is synchronized.

Protein-ligand binding affinity prediction of cyclin-dependent kinase-2 inhibitors by dynamically averaged fragment molecular orbital-based interaction energy.

Fragment molecular orbital (FMO) method is a powerful computational tool for structure-based drug design, in which protein-ligand interactions can be described by the inter-fragment interaction energy (IFIE) and its pair interaction energy decomposition analysis (PIEDA). Here, we introduced a dynamically averaged (DA) FMO-based approach in which molecular dynamics simulations were used to generate multiple protein-ligand complex structures for FMO calculations. To assess this approach, we examined the correlation between the experimental binding free energies and DA-IFIEs of six CDK2 inhibitors whose net charges are zero. The correlation between the experimental binding free energies and snapshot IFIEs for X-ray crystal structures was R2  = 0.75. Using the DA-IFIEs, the correlation significantly improved to 0.99. When an additional CDK2 inhibitor with net charge of -1 was added, the DA FMO-based scheme with the dispersion energies still achieved R2  = 0.99, whereas R2 decreased to 0.32 employing all the energy terms of PIEDA.

Enhanced Conformational Sampling with an Adaptive Coarse-Grained Elastic Network Model Using Short-Time All-Atom Molecular Dynamics.

Compared to all-atom molecular dynamics (AA-MD) simulations, coarse-grained (CG) MD simulations can significantly reduce calculation costs. However, existing CG-MD methods are unsuitable for sampling structures that depart significantly from the initial structure without any biased force. In this study, we developed a new adaptive CG elastic network model (ENM), in which the dynamic cross-correlation coefficient based on short-time AA-MD of at most ns order is considered. By applying Bayesian optimization to search for a suitable parameter among the vast parameter space of adaptive CG-ENM, we succeeded in reducing the searching cost to approximately 10% of those for random sampling and exhaustive sampling. To evaluate the performance of adaptive CG-ENM, we applied the new methodology to adenylate kinase (ADK) and glutamine binding protein (GBP) in the apo state. The results showed that the structural ensembles explored by adaptive CG-ENM could be considerably more diverse than those by conventional ENMs with enhanced sampling such as temperature replica exchange MD and long-time AA-MD of 1 µs. In particular, some of the structures sampled by adaptive ENM are relatively close to the holo-type structures of ADK and GBP. Furthermore, as a challenging task, to demonstrate the advantages of the CG model with lower calculation cost, we applied our new methodology to a larger biomolecule, integrin (αV) in the inactive state. Then, we sampled various structural ensembles, including extended structures that are apparently different from inactive ones.

Semi-Implicit Time Integration with Hessian Eigenvalue Corrections for a Larger Time Step in Molecular Dynamics Simulations.

In molecular dynamics simulations, the limited time step size has been a barrier to simulating long-time behaviors. Implicit time integration methods allow markedly larger time steps than the standard explicit time method, although they have major drawbacks such as overheads solving linear systems and instability of Newton iterations. To overcome these issues, we propose a semi-implicit time integration scheme, the semi-implicit Hessian correction (SimHec) scheme, for overdamped Langevin dynamics. The method focuses on the Hessian matrices of bonded and nonbonded interactions, where components with large negative Hessian eigenvalues are cut off in the linear approximation of momentum equations to avoid instability. The narrow band Hessian matrix enables an efficient parallelized linear solution with an overlapping approximation. We tested SimHec for the interdomain fluctuations in adenylate kinase and the powerstroke transition of myosin II using a coarse-grained protein model. SimHec reproduced the same dynamics as the explicit method, although the transition dynamics tended to be accelerated and fluctuations in bonded potentials were slightly reduced. These deviations were corrected using a hybrid method, SimHec-H, which adds explicit time steps after the semi-implicit time step. The proposed scheme allowed us to use time steps 50-200 times larger than those in explicit time integration, which resulted in a speedup factor of 7-30 taking the overhead into account.

Microsecond-timescale MD simulation of EGFR minor mutation predicts the structural flexibility of EGFR kinase core that reflects EGFR inhibitor sensitivity.

Approximately 15-30% of patients with lung cancer harbor mutations in the EGFR gene. Major EGFR mutations (>90% of EGFR-mutated lung cancer) are highly sensitive to EGFR tyrosine kinase inhibitors (TKIs). Many uncommon EGFR mutations have been identified, but little is known regarding their characteristics, activation, and sensitivity to various EGFR-TKIs, including allosteric inhibitors. We encountered a case harboring an EGFR-L747P mutation, originally misdiagnosed with EGFR-del19 mutation using a routine diagnostic EGFR mutation test, which was resistant to EGFR-TKI gefitinib. Using this minor mutation and common EGFR-activating mutations, we performed the binding free energy calculations and microsecond-timescale molecular dynamic (MD) simulations, revealing that the L747P mutation considerably stabilizes the active conformation through a salt-bridge formation between K745 and E762. We further revealed why several EGFR inhibitors, including the allosteric inhibitor, were ineffective. Our computational structural analysis strategy would be beneficial for future drug development targeting the EGFR minor mutations.

High-Precision Atomic Charge Prediction for Protein Systems Using Fragment Molecular Orbital Calculation and Machine Learning.

Here, we have constructed neural network-based models that predict atomic partial charges with high accuracy at low computational cost. The models were trained using high-quality data acquired from quantum mechanics calculations using the fragment molecular orbital method. We have succeeded in obtaining highly accurate atomic partial charges for three representative molecular systems of proteins, including one large biomolecule (approx. 2000 atoms). The novelty of our approach is the ability to take into account the electronic polarization in the system, which is a system-dependent phenomenon, being important in the field of drug design. Our high-precision models are useful for the prediction of atomic partial charges and expected to be widely applicable in structure-based drug designs such as structural optimization, high-speed and high-precision docking, and molecular dynamics calculations.

Coarse-Grained Diffraction Template Matching Model to Retrieve Multiconformational Models for Biomolecule Structures from Noisy Diffraction Patterns.

Biomolecular imaging using X-ray free-electron lasers (XFELs) has been successfully applied to serial femtosecond crystallography. However, the application of single-particle analysis for structure determination using XFELs with 100 nm or smaller biomolecules has two practical problems: the incomplete diffraction data sets for reconstructing 3D assembled structures and the heterogeneous conformational states of samples. A new diffraction template matching method is thus presented here to retrieve a plausible 3D structural model based on single noisy target diffraction patterns, assuming candidate structures. Two concepts are introduced here: prompt candidate diffraction, generated by enhanced sampled coarse-grain (CG) candidate structures, and efficient molecular orientation searching for matching based on Bayesian optimization. A CG model-based diffraction-matching protocol is proposed that achieves a 100-fold speed increase compared to exhaustive diffraction matching using an all-atom model. The conditions that enable multiconformational analysis were also investigated by simulated diffraction data for various conformational states of chromatin and ribosomes. The proposed method can enable multiconformational analysis, with a structural resolution of at least 20 Å for 270-800 Å flexible biomolecules, in experimental single-particle structure analyses that employ XFELs.

Exploring Successful Parameter Region for Coarse-Grained Simulation of Biomolecules by Bayesian Optimization and Active Learning.

Accompanied with an increase of revealed biomolecular structures owing to advancements in structural biology, the molecular dynamics (MD) approach, especially coarse-grained (CG) MD suitable for macromolecules, is becoming increasingly important for elucidating their dynamics and behavior. In fact, CG-MD simulation has succeeded in qualitatively reproducing numerous biological processes for various biomolecules such as conformational changes and protein folding with reasonable calculation costs. However, CG-MD simulations strongly depend on various parameters, and selecting an appropriate parameter set is necessary to reproduce a particular biological process. Because exhaustive examination of all candidate parameters is inefficient, it is important to identify successful parameters. Furthermore, the successful region, in which the desired process is reproducible, is essential for describing the detailed mechanics of functional processes and environmental sensitivity and robustness. We propose an efficient search method for identifying the successful region by using two machine learning techniques, Bayesian optimization and active learning. We evaluated its performance using F1-ATPase, a biological rotary motor, with CG-MD simulations. We successfully identified the successful region with lower computational costs (12.3% in the best case) without sacrificing accuracy compared to exhaustive search. This method can accelerate not only parameter search but also biological discussion of the detailed mechanics of functional processes and environmental sensitivity based on MD simulation studies.

Stabilization Mechanism for a Nonfibrillar Amyloid ß Oligomer Based on Formation of a Hydrophobic Core Determined by Dissipative Particle Dynamics.

Neurotoxicity caused by nonfibrillar amyloid ß (Aß) oligomers in the brain is suggested to be associated with the onset of Alzheimer's disease (AD). Elucidating the structural features of Aß oligomers is critical for promoting drug discovery research for AD. One of the Aß oligomers, known as Aß*56, is a dodecamer that impairs memory when injected into healthy rats, suggesting that Aß*56 may contribute to cognitive deficits in AD patients. Another dodecamer structure, formed by 20-residue peptide segments derived from the Aß peptide (Aß17-36), has been revealed by X-ray crystallography. The structure of the Aß17-36 dodecamer is composed of trimer units and shows the oligomer antibody A11 reactivity, which are characteristic of Aß*56, indicating that Aß*56 and the Aß17-36 dodecamer share a similar structure. However, the structure of the C-terminal regions (Aß37-42) remains unclear. The C-terminal region, which is abundant in hydrophobic residues, is thought to play a key role in stabilizing the oligomer structure by forming a hydrophobic core. In this study, we employed dissipative particle dynamics, a coarse-grained simulation method with soft core potentials, utilizing the crystal structure information to unravel Aß dodecamer structures with C-terminal regions. The simulation results were validated by the reported experimental data. Hence, an analysis of the simulation results can provide structural insights into Aß oligomers. Our simulations revealed the stabilization mechanism of the dodecamer structure at the molecular level. We showed that C-terminal regions spontaneously form a hydrophobic core in the central cavity, contributing to stabilizing the dodecamer structure. Furthermore, four consecutive hydrophobic residues in the C-terminal region (i.e., Val39-Ala42) are important for core formation.

Nucleosome Crowding in Chromatin Slows the Diffusion but Can Promote Target Search of Proteins.

Dynamics of nuclear proteins in crowded chromatin has only been poorly understood. Here, we address the diffusion, target search, and structural dynamics of three proteins in a model chromatin using coarse-grained molecular simulations run on the K computer. We prepared two structures of chromatin made of 20 nucleosomes with different nucleosome densities and investigated dynamics of two transcription factors, HMGB1 and p53, and one signaling protein, ERK, embedded in the chromatin. We found fast and normal diffusion of the nuclear proteins in the low-density chromatins and slow and subdiffusional movements in the high-density chromatin. The diffusion of the largest transcription factor, p53, is slowed by high-density chromatin most markedly. The on rates and off rates for DNA binding are increased and decreased, respectively, in the high-density chromatin. To our surprise, the DNA sequence search was faster in chromatin with high nucleosome density, though the diffusion is slower. We also found that the three nuclear proteins preferred to bind on the linker DNA and the entry and exit regions of nucleosomal DNA. In addition to these regions, HMGB1 and p53 also bound to the dyad.

Molecular dynamics simulation-guided drug sensitivity prediction for lung cancer with rare EGFR mutations.

Next generation sequencing (NGS)-based tumor profiling identified an overwhelming number of uncharacterized somatic mutations, also known as variants of unknown significance (VUS). The therapeutic significance of EGFR mutations outside mutational hotspots, consisting of >50 types, in nonsmall cell lung carcinoma (NSCLC) is largely unknown. In fact, our pan-nation screening of NSCLC without hotspot EGFR mutations (n = 3,779) revealed that the majority (>90%) of cases with rare EGFR mutations, accounting for 5.5% of the cohort subjects, did not receive EGFR-tyrosine kinase inhibitors (TKIs) as a first-line treatment. To tackle this problem, we applied a molecular dynamics simulation-based model to predict the sensitivity of rare EGFR mutants to EGFR-TKIs. The model successfully predicted the diverse in vitro and in vivo sensitivities of exon 20 insertion mutants, including a singleton, to osimertinib, a third-generation EGFR-TKI (R2 = 0.72, P = 0.0037). Additionally, our model showed a higher consistency with experimentally obtained sensitivity data than other prediction approaches, indicating its robustness in analyzing complex cancer mutations. Thus, the in silico prediction model will be a powerful tool in precision medicine for NSCLC patients carrying rare EGFR mutations in the clinical setting. Here, we propose an insight to overcome mutation diversity in lung cancer.

Prediction of ALK mutations mediating ALK-TKIs resistance and drug re-purposing to overcome the resistance.

BACKGROUND: Alectinib has shown a greater efficacy to ALK-rearranged non-small-cell lung cancers in first-line setting; however, most patients relapse due to acquired resistance, such as secondary mutations in ALK including I1171N and G1202R. Although ceritinib or lorlatinib was shown to be effective to these resistant mutants, further resistance often emerges due to ALK-compound mutations in relapse patients following the use of ceritinib or lorlatinib. However, the drug for overcoming resistance has not been established yet. METHODS: We established lorlatinib-resistant cells harboring ALK-I1171N or -G1202R compound mutations by performing ENU mutagenesis screening or using an in vivo mouse model. We performed drug screening to overcome the lorlatinib-resistant ALK-compound mutations. To evaluate these resistances in silico, we developed a modified computational molecular dynamic simulation (MP-CAFEE). FINDINGS: We identified 14 lorlatinib-resistant ALK-compound mutants, including several mutants that were recently discovered in lorlatinib-resistant patients. Some of these compound mutants were found to be sensitive to early generation ALK-TKIs and several BCR-ABL inhibitors. Using our original computational simulation, we succeeded in demonstrating a clear linear correlation between binding free energy and in vitro experimental IC50 value of several ALK-TKIs to single- or compound-mutated EML4-ALK expressing Ba/F3 cells and in recapitulating the tendency of the binding affinity reduction by double mutations found in this study. Computational simulation revealed that ALK-L1256F single mutant conferred resistance to lorlatinib but increased the sensitivity to alectinib. INTERPRETATION: We discovered lorlatinib-resistant multiple ALK-compound mutations and an L1256F single mutation as well as the potential therapeutic strategies for these ALK mutations. Our original computational simulation to calculate the binding affinity may be applicable for predicting resistant mutations and for overcoming drug resistance in silico. FUND: This work was mainly supported by MEXT/JSPS KAKENHI Grants and AMED Grants.

Coupling Langevin Dynamics With Continuum Mechanics: Exposing the Role of Sarcomere Stretch Activation Mechanisms to Cardiac Function.

High-performance computing approaches that combine molecular-scale and macroscale continuum mechanics have long been anticipated in various fields. Such approaches may enrich our understanding of the links between microscale molecular mechanisms and macroscopic properties in the continuum. However, there have been few successful examples to date owing to various difficulties associated with overcoming the large spatial (from 1 nm to 10 cm) and temporal (from 1 ns to 1 ms) gaps between the two scales. In this paper, we propose an efficient parallel scheme to couple a microscopic model using Langevin dynamics for a protein motor with a finite element continuum model of a beating heart. The proposed scheme allows us to use a macroscale time step that is an order of magnitude longer than the microscale time step of the Langevin model, without loss of stability or accuracy. This reduces the overhead required by the imbalanced loads of the microscale computations and the communication required when switching between scales. An example of the Langevin dynamics model that demonstrates the usefulness of the coupling approach is the molecular mechanism of the actomyosin system, in which the stretch-activation phenomenon can be successfully reproduced. This microscopic Langevin model is coupled with a macroscopic finite element ventricle model. In the numerical simulations, the Langevin dynamics model reveals that a single sarcomere can undergo spontaneous oscillation (15 Hz) accompanied by quick lengthening due to cooperative movements of the myosin molecules pulling on the common Z-line. Also, the coupled simulations using the ventricle model show that the stretch-activation mechanism contributes to the synchronization of the quick lengthening of the sarcomeres at the end of the systolic phase. By comparing the simulation results given by the molecular model with and without the stretch-activation mechanism, we see that this synchronization contributes to maintaining the systolic blood pressure by providing sufficient blood volume without slowing the diastolic process.

Modeling Structural Dynamics of Biomolecular Complexes by Coarse-Grained Molecular Simulations.

Due to hierarchic nature of biomolecular systems, their computational modeling calls for multiscale approaches, in which coarse-grained (CG) simulations are used to address long-time dynamics of large systems. Here, we review recent developments and applications of CG modeling methods, focusing on our methods primarily for proteins, DNA, and their complexes. These methods have been implemented in the CG biomolecular simulator, CafeMol. Our CG model has resolution such that ∼10 non-hydrogen atoms are grouped into one CG particle on average. For proteins, each amino acid is represented by one CG particle. For DNA, one nucleotide is simplified by three CG particles, representing sugar, phosphate, and base. The protein modeling is based on the idea that proteins have a globally funnel-like energy landscape, which is encoded in the structure-based potential energy function. We first describe two representative minimal models of proteins, called the elastic network model and the classic Go̅ model. We then present a more elaborate protein model, which extends the minimal model to incorporate sequence and context dependent local flexibility and nonlocal contacts. For DNA, we describe a model developed by de Pablo's group that was tuned to well reproduce sequence-dependent structural and thermodynamic experimental data for single- and double-stranded DNAs. Protein-DNA interactions are modeled either by the structure-based term for specific cases or by electrostatic and excluded volume terms for nonspecific cases. We also discuss the time scale mapping in CG molecular dynamics simulations. While the apparent single time step of our CGMD is about 10 times larger than that in the fully atomistic molecular dynamics for small-scale dynamics, large-scale motions can be further accelerated by two-orders of magnitude with the use of CG model and a low friction constant in Langevin dynamics. Next, we present four examples of applications. First, the classic Go̅ model was used to emulate one ATP cycle of a molecular motor, kinesin. Second, nonspecific protein-DNA binding was studied by a combination of elaborate protein and DNA models. Third, a transcription factor, p53, that contains highly fluctuating regions was simulated on two perpendicularly arranged DNA segments, addressing intersegmental transfer of p53. Fourth, we simulated structural dynamics of dinucleosomes connected by a linker DNA finding distinct types of internucleosome docking and salt-concentration-dependent compaction. Finally, we discuss many of limitations in the current approaches and future directions. Especially, more accurate electrostatic treatment and a phospholipid model that matches our CG resolutions are of immediate importance.

Nucleotide-dependent structural fluctuations and regulation of microtubule-binding affinity of KIF1A.

Molecular motors such as kinesin regulate affinity to a rail protein during the ATP hydrolysis cycle. The regulation mechanism, however, is yet to be determined. To understand this mechanism, we investigated the structural fluctuations of the motor head of the single-headed kinesin called KIF1A in different nucleotide states using molecular dynamics simulations of a Go-like model. We found that the helix α4 at the microtubule (MT) binding site intermittently exhibits a large structural fluctuation when MT is absent. Frequency of this fluctuation changes systematically according to the nucleotide states and correlates strongly with the experimentally observed binding affinity to MT. We also showed that thermal fluctuation enhances the correlation and the interaction with the nucleotide suppresses the fluctuation of the helix α4. These results suggest that KIF1A regulates affinity to MT by changing the flexibility of the helix α4 during the ATP hydrolysis process: the binding site becomes more flexible in the strong binding state than in the weak binding state.

Energetics of the single-headed kinesin KIF1A.

KIF1A is a single-headed molecular motor that moves processively and unidirectionally along a microtubule by using the chemical energy released by hydrolyzing adenosine triphosphate (ATP) into adenosine diphosphate (ADP) and inorganic phosphate (P(i)). Although the movement of KIF1A seems to have successfully been explained by a simple Brownian motor model of the flashing ratchet type, this model is not suited to discuss the energetics of KIF1A. We introduce an elaborated model of the ratchet type to investigate how the chemical free energy is converted into mechanical work by taking account of the binding and release of reactant (ATP) and product (ADP and P(i)) molecules to and from the motor. The efficiency of energy transduction, the power output, and other quantities are calculated from the analytically obtained steady-state solution of the Fokker-Planck equations. It turns out that the concentrations of the reactant and product molecules that optimize both the efficiency and the power are close to those in the cell.

Structure-based molecular simulations reveal the enhancement of biased Brownian motions in single-headed kinesin.

Kinesin is a family of molecular motors that move unidirectionally along microtubules (MT) using ATP hydrolysis free energy. In the family, the conventional two-headed kinesin was experimentally characterized to move unidirectionally through "walking" in a hand-over-hand fashion by coordinated motions of the two heads. Interestingly a single-headed kinesin, a truncated KIF1A, still can generate a biased Brownian movement along MT, as observed by in vitro single molecule experiments. Thus, KIF1A must use a different mechanism from the conventional kinesin to achieve the unidirectional motions. Based on the energy landscape view of proteins, for the first time, we conducted a set of molecular simulations of the truncated KIF1A movements over an ATP hydrolysis cycle and found a mechanism exhibiting and enhancing stochastic forward-biased movements in a similar way to those in experiments. First, simulating stand-alone KIF1A, we did not find any biased movements, while we found that KIF1A with a large friction cargo-analog attached to the C-terminus can generate clearly biased Brownian movements upon an ATP hydrolysis cycle. The linked cargo-analog enhanced the detachment of the KIF1A from MT. Once detached, diffusion of the KIF1A head was restricted around the large cargo which was located in front of the head at the time of detachment, thus generating a forward bias of the diffusion. The cargo plays the role of a diffusional anchor, or cane, in KIF1A "walking."

CafeMol: A Coarse-Grained Biomolecular Simulator for Simulating Proteins at Work.

For simulating proteins at work in millisecond time scale or longer, we develop a coarse-grained (CG) molecular dynamics (MD) method and software, CafeMol. At the resolution of one-particle-per-residue, CafeMol equips four structure-based protein models: (1) the off-lattice Go model, (2) the atomic interaction based CG model for native state and folding dynamics, (3) the multiple-basin model for conformational change dynamics, and (4) the elastic network model for quasiharmonic fluctuations around the native structure. Ligands can be treated either explicitly or implicitly. For mimicking functional motions of proteins driven by some external force, CafeMol has various and flexible means to "switch" the energy functions that induce active motions of the proteins. CafeMol can do parallel computation with modest sized PC clusters. We describe CafeMol methods and illustrate it with several examples, such as rotary motions of F1-ATPase and drug exports from a transporter. The CafeMol source code is available at www.cafemol.org .

Theoretical model for motility and processivity of two-headed molecular motors.

The processive motion of two-headed molecular motors is studied theoretically by introducing a model that takes into account the coordinated motion of the constituent heads and the detachment process of heads from linear molecular tracks. The mean velocity, the mean run length, and the mean run time of the motor along the track are calculated numerically based on the Langevin equation. It turns out that the model, with appropriate choice of model parameters, can explain qualitatively the dependence of these quantities on the external load and adenosin triphosphate concentration observed experimentally for kinesin motors. Furthermore, we discuss how the motility and processivity of the motor are affected by various model parameters, which may be tested by experiments.