Coarse-Grain Modeling of Shear-Induced Binding between von Willebrand Factor and Collagen

Von Willebrand factor (VWF) is a large multimeric protein that aids in blood clotting. Near injury sites, hydrodynamic force from increased blood flow elongates VWF, exposing binding sites for platelets and collagen. To investigate VWF binding to collagen that is exposed on injured arterial surfaces, Brownian dynamics simulations are performed with a coarse-grain molecular model. Accounting for hydrodynamic interactions in the presence of a stationary surface, shear flow conditions are modeled. Binding between beads in coarse-grain VWF and collagen sites on the surface is described via reversible ligand-receptor-type bond formation, which is governed via Bell model kinetics. For conditions in which binding is energetically favored, the model predicts a high probability for binding at low shear conditions; this is counter to experimental observations but in agreement with what prior modeling studies have revealed. To address this discrepancy, an additional binding criterion that depends on the conformation of a submonomer feature in the model local to a given VWF binding site is implemented. The modified model predicts shear-induced binding, in very good agreement with experimental observations; this is true even for conditions in which binding is significantly favored energetically. Biological implications of the model modification are discussed in terms of mechanisms of VWF activity.     

Monte Carlo analysis of neck linker extension in kinesin molecular motors

Kinesin stepping is thought to involve both concerted conformational changes and diffusive movement, but the relative roles played by these two processes are not clear. The neck linker docking model is widely accepted in the field, but the remainder of the step--diffusion of the tethered head to the next binding site--is often assumed to occur rapidly with little mechanical resistance. Here, we investigate the effect of tethering by the neck linker on the diffusive movement of the kinesin head, and focus on the predicted behavior of motors with naturally or artificially extended neck linker domains. The kinesin chemomechanical cycle was modeled using a discrete-state Markov chain to describe chemical transitions. Brownian dynamics were used to model the tethered diffusion of the free head, incorporating resistive forces from the neck linker and a position-dependent microtubule binding rate. The Brownian dynamics and chemomechanical cycle were coupled to model processive runs consisting of many 8 nm steps. Three mechanical models of the neck linker were investigated: Constant Stiffness (a simple spring), Increasing Stiffness (analogous to a Worm-Like Chain), and Reflecting (negligible stiffness up to a limiting contour length). Motor velocities and run lengths from simulated paths were compared to experimental results from Kinesin-1 and a mutant containing an extended neck linker domain. When tethered by an increasingly stiff spring, the head is predicted to spend an unrealistically short amount of time within the binding zone, and extending the neck is predicted to increase both the velocity and processivity, contrary to experiments. These results suggest that the Worm-Like Chain is not an adequate model for the flexible neck linker domain. The model can be reconciled with experimental data if the neck linker is either much more compliant or much stiffer than generally assumed, or if weak kinesin-microtubule interactions stabilize the diffusing head near its binding site.     

Brownian dynamics theory for predicting internal and external blockages of tetraethylammonium in the KcsA potassium channel

The theory of Brownian dynamics is used to model permeation and the blocking of KcsA potassium channels by tetraethylammonium (TEA). A novel Brownian dynamics simulation algorithm is implemented that comprises two free energy profiles; one profile is seen by the potassium ions and the other by the TEA molecules whose shape is approximated by a sphere. Our simulations reveal that internally applied TEA blocks the passage of K⁺ ions by physically occluding the pore. A TEA molecule in the external reservoir encounters an attractive energy-well created by four tyrosine residues at position 82, in addition to all other attractive and repulsive forces impinging on it. Using Brownian dynamics, we investigate how deep the energy-well needs to be to reproduce the experimentally determined inhibitory constant k_i for the TEA blockade of KcsA or the mutant Shaker T449Y. The one-dimensional free energy profile obtained from molecular dynamics is first converted into a one-dimensional potential energy profile, and is then transformed into a three-dimensional free energy profile in Brownian dynamics by adding the short-range potential from the channel walls. When converted, the free energy profile calculated from molecular dynamics gives a well-depth of ∼10 kT. We systematically alter the depths of the profiles, and then use Brownian dynamics simulations to numerically determine the current versus TEA-concentration curves. We show that the sequence of binding and unbinding events of the TEA molecule to the binding pocket can be modeled by a first-order Markov process. The Brownian dynamics simulations also reveal that the probability of a TEA molecule binding to the binding pocket in KcsA potassium channels increases exponentially with TEA concentration and depends also on the applied potential and the K⁺ concentration in the simulation assembly.     

The effect of shear stress on protein conformation: Physical forces operating on biochemical systems: The case of von Willebrand factor

Macromolecules and cells exposed to blood flow in the circulatory tree experience hydrodynamic forces that affect their structure and function. After introducing the general theory of the effects of shear forces on protein conformation, selected examples are presented in this review for biological macromolecules sensitive to shear stress. In particular, the biochemical effects of shear stress in controlling the von Willebrand Factor (VWF) conformation are extensively described. This protein, together with blood platelets, is the main actor of the early steps of primary haemostasis. Under the effect of shear forces > 30 dyn/cm², VWF unfolding occurs and the protein exhibits an extended chain conformation oriented in the general direction of the shear stress field. The stretched VWF conformation favors also a process of self aggregation, responsible for the formation of a spider web network, particularly efficient in the trapping process of flowing platelets. Thus, the effect of shear stress on conformational changes in VWF shows a close structure-function relationship in VWF for platelet adhesion and thrombus formation in arterial circulation, where high shear stress is present. The investigation of biophysical effects of shear forces on VWF conformation contributes to unraveling the molecular interaction mechanisms involved in arterial thrombosis.     

Intradimer forces and their implication for conformations of von Willebrand factor multimers

The largest blood glycoprotein von Willebrand factor (VWF) responds to hydrodynamic stresses in the bloodstream with abrupt conformation changes, thus increasing its adhesivity to platelets and collagen. Arterial and microvascular hemostasis relies on mechanical and physicochemical properties of this macromolecule. Recently, it was discovered that the mechanical properties of VWF are controlled by multiple pH-dependent interactions with opposite trends within dimeric subunits. In this work, computer simulations reveal the effect of these intradimer forces on the conformation of VWF multimers in various hydrodynamic conditions. A coarse-grained computer model of VWF has been proposed and parameterized to give a good agreement with experimental data. The simulations suggest that strong attraction between VWF D4 domains increases the resistance to elongation under shear stress, whereas even intermediate attraction between VWF C domains contributes to VWF compaction in nonsheared fluid. It is hypothesized that the detailed subdimer dynamics of VWF concatamers may be one of the biophysical regulators of initial hemostasis and arterial thrombosis.     

Influence of protein flexibility on the electrostatic energy landscape in gramicidin A

We describe an electrostatic model of the gramicidin A channel that allows protein atoms to move in response to the presence of a permeating ion. To do this, molecular dynamics simulations are carried out with a permeating ion at various positions within the channel. Then an ensemble of atomic coordinates taken from the simulations are used to construct energy profiles using macroscopic electrostatic calculations. The energy profiles constructed are compared to experimentally-determined conductance data by inserting them into Brownian dynamics simulations. We find that the energy landscape seen by a permeating ion changes significantly when we allow the protein atoms to move rather than using a rigid protein structure. However, the model developed cannot satisfactorily reproduce all of the experimental data. Thus, even when protein atoms are allowed to move, the dielectric model used in our electrostatic calculations breaks down when modeling the gramicidin channel.     

Brownian dynamics simulation of the unsaturated lipidic molecules oleic and docosahexaenoic acid confined in a cellular membrane

A Brownian dynamics (BD) simulation of two unsaturated molecules, oleic and docosahexaenoic acid, in an environment that reproduces a cellular membrane, is presented. The results of the simulations, performed using mean-field potentials, were calibrated with experimental results obtained for oleic acid in a cellular membrane. The agreement between simulation and experimental results is excellent which validates subsequent simulation outcome for docosahexaenoic acid. This molecule is a major component of several cellular membranes thought to be involved in specific biological functions that require conformational changes of membrane components. The results for docosahexaenoic acid indicate that it is minimally influenced by temperature changes and that it presents great conformational variability.     

Slackness between vessel and myocardium is necessary for coronary flow reserve

Tone regulation in coronary microvessels has largely been studied in isolated vessels in the absence of myocardial tethering. Here, the potential effect of radial tethering and interstitial space connective tissue (ISCT) between coronary microvessels and the surrounding myocardium was studied. We hypothesized that rigid tethering between microvessels and the myocardium would constrain the active contraction of arterioles and is not compatible with the observed tone regulation. The ISCT between coronary microvessels and myocardium in five swine was found to increase exponentially from 0.22 ± 0.02 μm in capillaries (modified Strahler order 0) of the endocardium to 34.9 ± 7.1 μm in epicardial vessels (order 10). Microvessels with both soft tethering and ISCT gap were capable of significant changes in vessel resistance (up to an ～1,600% increase), consistent with experimental measurements of high coronary flow reserve. Additionally, the mechanical energy required for myogenic contraction was estimated. The results indicate that rigid tethering requires up to four times more mechanical energy than soft tethering in the absence of a gap. Hence, the experimental measurements and model predictions suggest that effectiveness and efficiency in tone regulation can be achieved only if the vessel is both softly tethered to and separated from the myocardium in accordance with the experimental findings of ISCT gap. These results have fundamental implications on future simulations of coronary circulation.     

Brownian dynamics simulation of the unsaturated lipidic molecules oleic and docosahexaenoic acid confined in a cellular membrane

A Brownian dynamics (BD) simulation of two unsaturated molecules, oleic and docosahexaenoic acid, in an environment that reproduces a cellular membrane, is presented. The results of the simulations, performed using mean-field potentials, were calibrated with experimental results obtained for oleic acid in a cellular membrane. The agreement between simulation and experimental results is excellent which validates subsequent simulation outcome for docosahexaenoic acid. This molecule is a major component of several cellular membranes thought to be involved in specific biological functions that require conformational changes of membrane components. The results for docosahexaenoic acid indicate that it is minimally influenced by temperature changes and that it presents great conformational variability.     

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.     

Mechanisms of permeation and selectivity in calcium channels

The mechanisms underlying ion transport and selectivity in calcium channels are examined using electrostatic calculations and Brownian dynamics simulations. We model the channel as a rigid structure with fixed charges in the walls, representing glutamate residues thought to be responsible for ion selectivity. Potential energy profiles obtained from multi-ion electrostatic calculations provide insights into ion permeation and many other observed features of L-type calcium channels. These qualitative explanations are confirmed by the results of Brownian dynamics simulations, which closely reproduce several experimental observations. These include the current-voltage curves, current-concentration relationship, block of monovalent currents by divalent ions, the anomalous mole fraction effect between sodium and calcium ions, attenuation of calcium current by external sodium ions, and the effects of mutating glutamate residues in the amino acid sequence.     

Computational approach to site-directed ligand discovery

A computational approach, Systematic Conformational Search & Induced Fit (SCI&FI), to site-directed ligand discovery (Tethering) is presented. SCI&FI has the ability to predict the binding site, binding mode, and bound dynamics of small molecule fragments covalently tethered to a protein. The SCI&FI method was engineered with the ability to model induced fit conformational changes of the protein because of the binding of the tether. SCI&FI generates comprehensive picture of the binding preferences of the tether to the protein by elucidating potential binding sites of the tether and by describing regions of receptor space capable of conformational change because of the binding of the tether. The SCI&FI method provides a complementary approach to experimental tethering. Initial validation of the SCI&FI method is reported by predicting the 3D structure of two Interleukin-2 and an Interleukin-4 tethered-protein systems.     

Modeling the binding of three toxins to the voltage-gated potassium channel (Kv1.3)

The conduction properties of the voltage-gated potassium channel Kv1.3 and its modes of interaction with several polypeptide venoms are examined using Brownian dynamics simulations and molecular dynamics calculations. Employing an open-state homology model of Kv1.3, we first determine current-voltage and current-concentration curves and ascertain that simulated results accord with experimental measurements. We then investigate, using a molecular docking method and molecular dynamics simulations, the complexes formed between the Kv1.3 channel and several Kv-specific polypeptide toxins that are known to interfere with the conducting mechanisms of several classes of voltage-gated K⁺ channels. The depths of potential of mean force encountered by charybdotoxin, α-KTx3.7 (also known as OSK1) and ShK are, respectively, −19, −27, and −25 kT. The dissociation constants calculated from the profiles of potential of mean force correspond closely to the experimentally determined values. We pinpoint the residues in the toxins and the channel that are critical for the formation of the stable venom-channel complexes.     

A particle-based computational model to analyse remodelling of the red blood cell cytoskeleton during malaria infections

Red blood cells can withstand the harsh mechanical conditions in the vasculature only because the bending rigidity of their plasma membrane is complemented by the shear elasticity of the underlying spectrin-actin network. During an infection by the malaria parasite Plasmodium falciparum, the parasite mines host actin from the junctional complexes and establishes a system of adhesive knobs, whose main structural component is the knob-associated histidine rich protein (KAHRP) secreted by the parasite. Here we aim at a mechanistic understanding of this dramatic transformation process. We have developed a particle-based computational model for the cytoskeleton of red blood cells and simulated it with Brownian dynamics to predict the mechanical changes resulting from actin mining and KAHRP-clustering. Our simulations include the three-dimensional conformations of the semi-flexible spectrin chains, the capping of the actin protofilaments and several established binding sites for KAHRP. For the healthy red blood cell, we find that incorporation of actin protofilaments leads to two regimes in the shear response. Actin mining decreases the shear modulus, but knob formation increases it. We show that dynamical changes in KAHRP binding affinities can explain the experimentally observed relocalization of KAHRP from ankyrin to actin complexes and demonstrate good qualitative agreement with experiments by measuring pair cross-correlations both in the computer simulations and in super-resolution imaging experiments.     

Hydrodynamic study of flexibility in immunoglobulin IgG1 using Brownian dynamics and the Monte Carlo simulations of a simple model

A simple bead model is proposed for the antibody molecule immunoglobulin IgG1. The partial flexibility of the hinge is represented by a quadratic potential associated to the angles between arms. Conformational and hydrodynamic properties are calculated using Monte Carlo (rigid-body) and Brownian dynamics simulations. Comparison of experimental and calculated values for some overall properties allows the assignment of dimensions and other model parameters. The Brownian dynamics technique is used next to simulate a rotational correlation function that is comparable with the decay of fluorescence emission anisotropy. This is done with varying flexibility at the hinge. The longest relaxation time shows a threefold decrease when going from the rigid Y-shaped conformation to the completely flexible case. The calculations are in good agreement with the decay times observed for IgG1. A flexibility analysis of the latter indicates that a variability of +/- 55 degrees (standard deviation) in the angle between the Fab arms.     

Application of Fluorescence Spectroscopy to Quantify Shear-Induced Protein Conformation Change

Rapid and robust methods are required to quantify the effect of hydrodynamic shear on protein conformation change. We evaluated such strategies in this work and found that the binding of the fluorescent probe 4,4′-dianilino-1,1′-binaphthyl-5,5′-disulfonic acid (bis-ANS) to hydrophobic pockets in the blood protein von Willebrand factor (VWF) is enhanced upon the application of fluid shear to the isolated protein. Significant structural changes were observed when the protein was sheared at shear rates ≥ 6000/s for ∼3.5 min. The binding of bis-ANS to multimeric VWF, but not dimeric VWF or control protein bovine serum albumin, was enhanced upon fluid shear application. Thus, high-molecular-weight VWF is more susceptible to conformation change upon tensile loading. Although bis-ANS itself did not alter the conformation of VWF, it stabilized protein conformation once it bound the sheared molecule. Bis-ANS binding to VWF was reduced when the sheared protein was allowed to relax before dye addition. Taken together with functional data in the literature, our results suggest that shear-induced conformation changes in VWF reported by bis-ANS correlate well with the normal function of the protein under physiological/pathological fluid flow conditions. Further, this study introduces the fluorescent dye bis-ANS as a tool that may be useful in studies of shear-induced protein conformation change.     

Numerical simulation of global hydro-dynamics in a pulsatile bioreactor for cardiovascular tissue engineering

Previous numerical simulations of the hydro-dynamic response in the various bioreactor designs were mostly concentrated on the local flow field analysis using computational fluid dynamics, which cannot provide the global hydro-dynamics information to assist the bioreactor design. In this research, a mathematical model is developed to simulate the global hydro-dynamic changes in a pulsatile bioreactor design by considering the flow resistance, the elasticity of the vessel and the inertial effect of the media fluid in different parts of the system. The developed model is used to study the system dynamic response in a typical pulsatile bioreactor design for the culturing of cardiovascular tissues. Simulation results reveal the detailed pressure and flow-rate changes in the different positions of the bioreactor, which are very useful for the evaluation of hydro-dynamic performance in the bioreactor designed. Typical pressure and flow-rate changes simulated agree well with the published experimental data, thus validates the mathematical model developed. The proposed mathematical model can be used for design optimization of other pulsatile bioreactors that work under different experimental conditions and have different system configurations.     

Mg2+-induced compaction of single RNA molecules monitored by tethered particle microscopy

We have applied tethered particle microscopy (TPM) as a single molecule analysis tool to studies of the conformational dynamics of poly-uridine(U) messenger (m)RNA and 16S ribosomal (r)RNA molecules. Using stroboscopic total internal reflection illumination and rigorous selection criteria to distinguish from nonspecific tethering, we have tracked the nanometer-scale Brownian motion of RNA-tethered fluorescent microspheres in all three dimensions at pH 7.5, 22 degrees C, in 10 mM or 100 mM NaCl in the absence or presence of 10 mM MgCl(2). The addition of Mg(2+) to low-ionic strength buffer results in significant compaction and stiffening of poly(U) mRNA, but not of 16S rRNA. Furthermore, the motion of poly(U)-tethered microspheres is more heterogeneous than that of 16S rRNA-tethered microspheres. Analysis of in-plane bead motion suggests that poly(U) RNA, but less so 16S rRNA, can be modeled both in the presence and absence of Mg(2+) by a statistical Gaussian polymer model. We attribute these differences to the Mg(2+)-induced compaction of the relatively weakly structured and structurally disperse poly(U) mRNA, in contrast to Mg(2+)-induced reinforcement of existing secondary and tertiary structure contacts in the highly structured 16S rRNA. Both effects are nonspecific, however, as they are dampened in the presence of higher concentrations of monovalent cations.     

Concerted simulations reveal how peroxidase compound III formation results in cellular oscillations

A major problem in mathematical modeling of the dynamics of complex biological systems is the frequent lack of knowledge of kinetic parameters. Here, we apply Brownian dynamics simulations, based on protein three-dimensional structures, to estimate a previously undetermined kinetic parameter, which is then used in biochemical network simulations. The peroxidase-oxidase reaction involves many elementary steps and displays oscillatory dynamics important for immune response. Brownian dynamics simulations were performed for three different peroxidases to estimate the rate constant for one of the elementary steps crucial for oscillations in the peroxidase-oxidase reaction, the association of superoxide with peroxidase. Computed second-order rate constants agree well with available experimental data and permit prediction of rate constants at physiological conditions. The simulations show that electrostatic interactions depress the rate of superoxide association with myeloperoxidase, bringing it into the range necessary for oscillatory behavior in activated neutrophils. Such negative electrostatic steering of enzyme-substrate association presents a novel control mechanism and lies in sharp contrast to the electrostatically-steered fast association of superoxide and Cu/Zn superoxide dismutase, which is also simulated here. The results demonstrate the potential of an integrated and concerted application of structure-based simulations and biochemical network simulations in cellular systems biology.