Multiscale modeling shows how 2'-deoxy-ATP rescues ventricular function in heart failure.

2'-deoxy-ATP (dATP) improves cardiac function by increasing the rate of crossbridge cycling and Ca[Formula: see text] transient decay. However, the mechanisms of these effects and how therapeutic responses to dATP are achieved when dATP is only a small fraction of the total ATP pool remain poorly understood. Here, we used a multiscale computational modeling approach to analyze the mechanisms by which dATP improves ventricular function. We integrated atomistic simulations of prepowerstroke myosin and actomyosin association, filament-scale Markov state modeling of sarcomere mechanics, cell-scale analysis of myocyte Ca[Formula: see text] dynamics and contraction, organ-scale modeling of biventricular mechanoenergetics, and systems level modeling of circulatory dynamics. Molecular and Brownian dynamics simulations showed that dATP increases the actomyosin association rate by 1.9 fold. Markov state models predicted that dATP increases the pool of myosin heads available for crossbridge cycling, increasing steady-state force development at low dATP fractions by 1.3 fold due to mechanosensing and nearest-neighbor cooperativity. This was found to be the dominant mechanism by which small amounts of dATP can improve contractile function at myofilament to organ scales. Together with faster myocyte Ca[Formula: see text] handling, this led to improved ventricular contractility, especially in a failing heart model in which dATP increased ejection fraction by 16% and the energy efficiency of cardiac contraction by 1%. This work represents a complete multiscale model analysis of a small molecule myosin modulator from single molecule to organ system biophysics and elucidates how the molecular mechanisms of dATP may improve cardiovascular function in heart failure with reduced ejection fraction.

Multiscale Simulations Examining Glycan Shield Effects on Drug Binding to Influenza Neuraminidase.

Influenza neuraminidase is an important drug target. Glycans are present on neuraminidase and are generally considered to inhibit antibody binding via their glycan shield. In this work, we studied the effect of glycans on the binding kinetics of antiviral drugs to the influenza neuraminidase. We created all-atom in silico systems of influenza neuraminidase with experimentally derived glycoprofiles consisting of four systems with different glycan conformations and one system without glycans. Using Brownian dynamics simulations, we observe a two- to eightfold decrease in the rate of ligand binding to the primary binding site of neuraminidase due to the presence of glycans. These glycans are capable of covering much of the surface area of neuraminidase, and the ligand binding inhibition is derived from glycans sterically occluding the primary binding site on a neighboring monomer. Our work also indicates that drugs preferentially bind to the primary binding site (i.e., the active site) over the secondary binding site, and we propose a binding mechanism illustrating this. These results help illuminate the complex interplay between glycans and ligand binding on the influenza membrane protein neuraminidase.

Predicting the effects of dATP on cardiac contraction using multiscale modeling of the sarcomere.

2'-deoxy-ATP (dATP) is a naturally occurring small molecule that has shown promise as a therapeutic because it significantly increases cardiac myocyte force development even at low dATP/ATP ratios. To investigate mechanisms by which dATP alters myosin crossbridge dynamics, we used Brownian dynamics simulations to calculate association rates between actin and ADP- or dADP-bound myosin. These rates were then directly incorporated in a mechanistic Monte Carlo Markov Chain model of cooperative sarcomere contraction. A unique combination of increased powerstroke and detachment rates was required to match experimental steady-state and kinetic data for dATP force production in rat cardiac myocytes when the myosin attachment rate in the model was constrained by the results of a Brownian dynamics simulation. Nearest-neighbor cooperativity was seen to contribute to, but not fully explain, the steep relationship between dATP/ATP ratio and steady-state force-development observed at lower dATP concentrations. Dynamic twitch simulations performed using measured calcium transients as inputs showed that the effects of dATP on the crossbridge alone were not sufficient to explain experimentally observed enhancement of relaxation kinetics by dATP treatment. Hence, dATP may also affect calcium handling even at low concentrations. By enabling the effects of dATP on sarcomere mechanics to be predicted, this multi-scale modeling framework may elucidate the molecular mechanisms by which dATP can have therapeutic effects on cardiac contractile dysfunction.

A Stochastic Multiscale Model of Cardiac Thin Filament Activation Using Brownian-Langevin Dynamics.

We use Brownian-Langevin dynamics principles to derive a coarse-graining multiscale myofilament model that can describe the thin-filament activation process during contraction. The model links atomistic molecular simulations of protein-protein interactions in the thin-filament regulatory unit to sarcomere-level activation dynamics. We first calculate the molecular interaction energy between tropomyosin and actin surface using Brownian dynamics simulations. This energy profile is then generalized to account for the observed tropomyosin transitions between its regulatory stable states. The generalized energy landscape then served as a basis for developing a filament-scale model using Langevin dynamics. This integrated analysis, spanning molecular to thin-filament scales, is capable of tracking the events of the tropomyosin conformational changes as it moves over the actin surface. The tropomyosin coil with flexible overlap regions between adjacent tropomyosins is represented in the model as a system of coupled stochastic ordinary differential equations. The proposed multiscale approach provides a more detailed molecular connection between tropomyosin dynamics, the trompomyosin-actin interaction-energy landscape, and the generated force by the sarcomere.

Hybrid finite element and Brownian dynamics method for charged particles.

Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.

Electrostatic channeling in P. falciparum DHFR-TS: Brownian dynamics and Smoluchowski modeling.

We perform Brownian dynamics simulations and Smoluchowski continuum modeling of the bifunctional Plasmodium falciparum dihydrofolate reductase-thymidylate synthase (P. falciparum DHFR-TS) with the objective of understanding the electrostatic channeling of dihydrofolate generated at the TS active site to the DHFR active site. The results of Brownian dynamics simulations and Smoluchowski continuum modeling suggest that compared to Leishmania major DHFR-TS, P. falciparum DHFR-TS has a lower but significant electrostatic-mediated channeling efficiency (?15-25%) at physiological pH (7.0) and ionic strength (150 mM). We also find that removing the electric charges from key basic residues located between the DHFR and TS active sites significantly reduces the channeling efficiency of P. falciparum DHFR-TS. Although several protozoan DHFR-TS enzymes are known to have similar tertiary and quaternary structure, subtle differences in structure, active-site geometry, and charge distribution appear to influence both electrostatic-mediated and proximity-based substrate channeling.

Electrostatically biased binding of kinesin to microtubules.

The minimum motor domain of kinesin-1 is a single head. Recent evidence suggests that such minimal motor domains generate force by a biased binding mechanism, in which they preferentially select binding sites on the microtubule that lie ahead in the progress direction of the motor. A specific molecular mechanism for biased binding has, however, so far been lacking. Here we use atomistic Brownian dynamics simulations combined with experimental mutagenesis to show that incoming kinesin heads undergo electrostatically guided diffusion-to-capture by microtubules, and that this produces directionally biased binding. Kinesin-1 heads are initially rotated by the electrostatic field so that their tubulin-binding sites face inwards, and then steered towards a plus-endwards binding site. In tethered kinesin dimers, this bias is amplified. A 3-residue sequence (RAK) in kinesin helix alpha-6 is predicted to be important for electrostatic guidance. Real-world mutagenesis of this sequence powerfully influences kinesin-driven microtubule sliding, with one mutant producing a 5-fold acceleration over wild type. We conclude that electrostatic interactions play an important role in the kinesin stepping mechanism, by biasing the diffusional association of kinesin with microtubules.

Assessing the two-body diffusion tensor calculated by the bead models.

The diffusion tensor of complex macromolecules in Stokes flow is often approximated by the bead models. The bead models are known to reproduce the experimental diffusion coefficients of a single macromolecule, but the accuracy of their calculation of the whole multi-body diffusion tensor, which is important for Brownian dynamics simulations, has not been closely investigated. As a first step, we assess the accuracy of the bead model calculated diffusion tensor of two spheres. Our results show that the bead models produce very accurate diffusion tensors for two spheres where a reasonable number of beads are used and there is no bead overlap.

Multiscale computational modeling of the effects of 2'-deoxy-ATP on cardiac muscle calcium handling.

2'-Deoxy-ATP (dATP), a naturally occurring near analog of ATP, is a well-documented myosin activator that has been shown to increase contractile force, improve pump function, and enhance lusitropy in the heart. Calcium transients in cardiomyocytes with elevated levels of dATP show faster calcium decay compared with cardiomyocytes with basal levels of dATP, but the mechanisms behind this are unknown. Here, we design and utilize a multiscale computational modeling framework to test the hypothesis that dATP acts on the sarcoendoplasmic reticulum calcium-ATPase (SERCA) pump to accelerate calcium re-uptake into the sarcoplasmic reticulum during cardiac relaxation. Gaussian accelerated molecular dynamics simulations of human cardiac SERCA2A in the E1 apo, ATP-bound and dATP-bound states showed that dATP forms more stable contacts in the nucleotide binding pocket of SERCA and leads to increased closure of cytosolic domains. These structural changes ultimately lead to changes in calcium binding, which we assessed using Brownian dynamics simulations. We found that dATP increases calcium association rate constants to SERCA and that dATP binds to apo SERCA more rapidly than ATP. Using a compartmental ordinary differential equation model of human cardiomyocyte excitation-contraction coupling, we found that these increased association rate constants contributed to the accelerated rates of calcium transient decay observed experimentally. This study provides clear mechanistic evidence of enhancements in cardiac SERCA2A pump function due to interactions with dATP.

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Investigating Intrinsically Disordered Proteins With Brownian Dynamics.

Intrinsically disordered proteins (IDPs) have recently become systems of great interest due to their involvement in modulating many biological processes and their aggregation being implicated in many diseases. Since IDPs do not have a stable, folded structure, however, they cannot be easily studied with experimental techniques. Hence, conducting a computational study of these systems can be helpful and be complementary with experimental work to elucidate their mechanisms. Thus, we have implemented the coarse-grained force field for proteins (COFFDROP) in Browndye 2.0 to study IDPs using Brownian dynamics (BD) simulations, which are often used to study large-scale motions with longer time scales and diffusion-limited molecular associations. Specifically, we have checked our COFFDROP implementation with eight naturally occurring IDPs and have investigated five (Glu-Lys)25 IDP sequence variants. From measuring the hydrodynamic radii of eight naturally occurring IDPs, we found the ideal scaling factor of 0.786 for non-bonded interactions. We have also measured the entanglement indices (average C α distances to the other chain) between two (Glu-Lys)25 IDP sequence variants, a property related to molecular association. We found that entanglement indices decrease for all possible pairs at excess salt concentration, which is consistent with long-range interactions of these IDP sequence variants getting weaker at increasing salt concentration.

Browndye: A Software Package for Brownian Dynamics.

A new software package, Browndye, is presented for simulating the diffusional encounter of two large biological molecules. It can be used to estimate second-order rate constants and encounter probabilities, and to explore reaction trajectories. Browndye builds upon previous knowledge and algorithms from software packages such as UHBD, SDA, and Macrodox, while implementing algorithms that scale to larger systems.

Brownian Dynamics Simulations of Biological Molecules.

Brownian dynamics (BD) is a technique for carrying out computer simulations of physical systems that are driven by thermal fluctuations. Biological systems at the macromolecular and cellular level, while falling in the gap between well-established atomic-level models and continuum models, are especially suitable for such simulations. We present a brief history, examples of important biological processes that are driven by thermal motion, and those that have been profitably studied by BD. We also present some of the challenges facing developers of algorithms and software, especially in the attempt to simulate larger systems more accurately and for longer times.

Continuum simulations of acetylcholine consumption by acetylcholinesterase: a Poisson-Nernst-Planck approach.

The Poisson-Nernst-Planck (PNP) equation provides a continuum description of electrostatic-driven diffusion and is used here to model the diffusion and reaction of acetylcholine (ACh) with acetylcholinesterase (AChE) enzymes. This study focuses on the effects of ion and substrate concentrations on the reaction rate and rate coefficient. To this end, the PNP equations are numerically solved with a hybrid finite element and boundary element method at a wide range of ion and substrate concentrations, and the results are compared with the partially coupled Smoluchowski-Poisson-Boltzmann model. The reaction rate is found to depend strongly on the concentrations of both the substrate and ions; this is explained by the competition between the intersubstrate repulsion and the ionic screening effects. The reaction rate coefficient is independent of the substrate concentration only at very high ion concentrations, whereas at low ion concentrations the behavior of the rate depends strongly on the substrate concentration. Moreover, at physiological ion concentrations, variations in substrate concentration significantly affect the transient behavior of the reaction. Our results offer a reliable estimate of reaction rates at various conditions and imply that the concentrations of charged substrates must be coupled with the electrostatic computation to provide a more realistic description of neurotransmission and other electrodiffusion and reaction processes.

HIERARCHICAL ORTHOGONAL MATRIX GENERATION AND MATRIX-VECTOR MULTIPLICATIONS IN RIGID BODY SIMULATIONS.

In this paper, we apply the hierarchical modeling technique and study some numerical linear algebra problems arising from the Brownian dynamics simulations of biomolecular systems where molecules are modeled as ensembles of rigid bodies. Given a rigid body p consisting of n beads, the 6×3n transformation matrix Z that maps the force on each bead to p's translational and rotational forces (a 6 × 1 vector), and V the row space of Z, we show how to explicitly construct the (3n - 6) × 3n matrix Q ˜ consisting of (3n - 6) orthonormal basis vectors of V ⊥ (orthogonal complement of V) using only O ( n log n ) operations and storage. For applications where only the matrix-vector multiplications Q ˜ V and Q ˜ T V are needed, we introduce asymptotically optimal O ( n ) hierarchical algorithms without explicitly forming Q ˜ . Preliminary numerical results are presented to demonstrate the performance and accuracy of the numerical algorithms.

Brownian dynamic study of an enzyme metabolon in the TCA cycle: Substrate kinetics and channeling.

Malate dehydrogenase (MDH) and citrate synthase (CS) are two pacemaking enzymes involved in the tricarboxylic acid (TCA) cycle. Oxaloacetate (OAA) molecules are the intermediate substrates that are transferred from the MDH to CS to carry out sequential catalysis. It is known that, to achieve a high flux of intermediate transport and reduce the probability of substrate leaking, a MDH-CS metabolon forms to enhance the OAA substrate channeling. In this study, we aim to understand the OAA channeling within possible MDH-CS metabolons that have different structural orientations in their complexes. Three MDH-CS metabolons from native bovine, wild-type porcine, and recombinant sources, published in recent work, were selected to calculate OAA transfer efficiency by Brownian dynamics (BD) simulations and to study, through electrostatic potential calculations, a possible role of charges that drive the substrate channeling. Our results show that an electrostatic channel is formed in the metabolons of native bovine and recombinant porcine enzymes, which guides the oppositely charged OAA molecules passing through the channel and enhances the transfer efficiency. However, the channeling probability in a suggested wild-type porcine metabolon conformation is reduced due to an extended diffusion length between the MDH and CS active sites, implying that the corresponding arrangements of MDH and CS result in the decrease of electrostatic steering between substrates and protein surface and then reduce the substrate transfer efficiency from one active site to another.

A Computational Assay that Explores the Hemagglutinin/Neuraminidase Functional Balance Reveals the Neuraminidase Secondary Site as a Novel Anti-Influenza Target.

Studies of pathogen-host specificity, virulence, and transmissibility are critical for basic research as well as for assessing the pandemic potential of emerging infectious diseases. This is especially true for viruses such as influenza, which continue to affect millions of people annually through both seasonal and occasional pandemic events. Although the influenza virus has been fairly well studied for decades, our understanding of host-cell binding and its relation to viral transmissibility and infection is still incomplete. Assessing the binding mechanisms of complex biological systems with atomic-scale detail is challenging given current experimental limitations. Much remains to be learned, for example, about how the terminal residue of influenza-binding host-cell receptors (sialic acid) interacts with the viral surface. Here, we present an integrative structural-modeling and physics-based computational assay that reveals the sialic acid association rate constants (k on) to three influenza sites: the hemagglutinin (HA), neuraminidase (NA) active, and NA secondary binding sites. We developed a series of highly detailed (atomic-resolution) structural models of fully intact influenza viral envelopes. Brownian dynamics simulations of these systems showed how structural properties, such as stalk height and secondary-site binding, affect sialic acid k on values. Comparing the k on values of the three sialic acid binding sites across different viral strains suggests a detailed model of encounter-complex formation and indicates that the secondary NA binding site may play a compensatory role in host-cell receptor binding. Our method elucidates the competition among these sites, all present on the same virion, and provides a new technology for directly studying the functional balance between HA and NA.

Electrostatic Steering Accelerates C3d:CR2 Association.

Electrostatic effects are ubiquitous in protein interactions and are found to be pervasive in the complement system as well. The interaction between complement fragment C3d and complement receptor 2 (CR2) has evolved to become a link between innate and adaptive immunity. Electrostatic interactions have been suggested to be the driving factor for the association of the C3d:CR2 complex. In this study, we investigate the effects of ionic strength and mutagenesis on the association of C3d:CR2 through Brownian dynamics simulations. We demonstrate that the formation of the C3d:CR2 complex is ionic strength-dependent, suggesting the presence of long-range electrostatic steering that accelerates the complex formation. Electrostatic steering occurs through the interaction of an acidic surface patch in C3d and the positively charged CR2 and is supported by the effects of mutations within the acidic patch of C3d that slow or diminish association. Our data are in agreement with previous experimental mutagenesis and binding studies and computational studies. Although the C3d acidic patch may be locally destabilizing because of unfavorable Coulombic interactions of like charges, it contributes to the acceleration of association. Therefore, acceleration of function through electrostatic steering takes precedence to stability. The site of interaction between C3d and CR2 has been the target for delivery of CR2-bound nanoparticle, antibody, and small molecule biomarkers, as well as potential therapeutics. A detailed knowledge of the physicochemical basis of C3d:CR2 association may be necessary to accelerate biomarker and drug discovery efforts.

Electrostatic steering enhances the rate of cAMP binding to phosphodiesterase: Brownian dynamics modeling.

Signaling in cells often involves co-localization of the signaling molecules. Most experimental evidence has shown that intracellular compartmentalization restricts the range of action of the second messenger, 3'-5'-cyclic adenosine monophosphate (cAMP), which is degraded by phosphodiesterases (PDEs). The objective of this study is to understand the details of molecular encounter that may play a role in efficient operation of the cAMP signaling apparatus. The results from electrostatic potential calculations and Brownian dynamics simulations suggest that positive potential of the active site from PDE enhances capture of diffusing cAMP molecules. This electrostatic steering between cAMP and the active site of a PDE plays a major role in the enzyme-substrate encounter, an effect that may be of significance in sequestering cAMP released from a nearby binding site or in attracting more freely diffusing cAMP molecules.

Integrative biological modelling in silico.

In silico models of biological systems provide a powerful tool for integrative analysis of physiological function. Using the computational models of the heart as examples, we discuss three types of integration: structural integration implies integration across physical scales of biological organization from protein molecule to whole organ; functional integration of interacting physiological processes such as signalling, metabolism, excitation and contraction; and the synthesis of experimental observation with physicochemical and mathematical principles.