Multistep Brownian dynamics: application to short wormlike chains

Brownian dynamics simulations of short wormlike chains are carried out using the method of Ermak and McCammon [(1978) J. Chem. Phys. 69 , 1352–1360]. Following Hagerman and Zimm [(1981) Biopolymers 20 , 1481–1502], the wormlike chain is modeled as a string of beads. In each simulation, the dynamic evolution of an ensemble of 100 randomly generated chains is calculated for a period of from 3 to 200 ns. Two different “experiments,” fluorescence depolarization and dynamic light scattering, were performed in these simulations. Since we are primarily interested in the bending motions and not the torsional motions in this work, we have placed the transition moments along the local symmetry axis of the wormlike chain in the fluorescence depolarization “experiment.” As predicted by the Barkley and Zimm theory [(1979) J. Chem. Phys. 70 , 2991–3008], a considerable amount of rapid bending motion was detected by fluorescence depolarization, though not as much as predicted by theory. We conclude that these differences are primarily due to differences between the model used in the theory and the simulations. The light-scattering experiment was found to be insensitive to internal motion in the low scattering angle limit.     

Kinetics of association of anti-lysozyme monoclonal antibody D44.1 and hen-egg lysozyme

Association rate constants for antigen/antibody associations have been computed by Brownian Dynamics simulations of D. L. Ermak and J. A. McCammon, J. Chem. Phys. 69:1352-1360, 1978. The model of monoclonal antibody (mAb) D44.1 is based on crystallographic data (B. C. Braden et al., J. Mol. Biol. 243:767-781, 1994). Electrostatic forces that steer the antigen to the antibody-combining site are computed by solving the linearized Poisson-Boltzmann equation. D44. 1-HEL complex displays very similar association motifs to a related anti-lysozyme antibody, HyHEL-5-HEL system. The computed association rate constants are comparable in the two systems, although the experimental affinity constants differ by three orders of magnitude (D. Tello et al., Biochem. Soc. Trans. 21:943-946, 1993; K. A. Hibbits et al., Biochemistry. 33:3584-3590, 1994). Simulations suggest that the origin of the differences in the affinity come from dissociation rate constants. We have also carried out simulation experiments on a number of mutant antibody fragment-HEL associations to address the role of electrostatics and, to a limited extent, the orientational aspects of association.     

Intrinsic conformational flexibility of acetylcholinesterase

Proteins have been metaphorically described - due to the introduction and extraordinary advances in biomolecular dynamics and computational biophysics over the past decades - as "kicking and screaming" molecules [G. Weber, Adv. Protein Chem. 29 (1975) 1-83]. In fact, dynamic fluctuations in protein structural conformation have been known to play an important role in protein function. However, fundamental mechanisms by which protein fluctuations couple with catalytic function of particular enzymes remain poorly understood. To understand the dynamical properties of acetylcholinesterase (AChE) in rapid termination of cationic neurotransmitter, acetylcholine at neurosynaptic junctions, multiple molecular dynamics (MD) trajectories of AChE in the presence and absence of its inhibitors [J.M. Bui, J.A. McCammon, Proc. Natl. Acad. Sci. U.S.A. 103 (2006) 15451-15456; J.M. Bui, Z. Radic, P. Taylor, J.A. McCammon, Biophys. J. 90 (2006) 3280-3287; J.M. Bui, K. Tai, J.A. McCammon, J. Am. Chem. Soc. 126 (2004) 7198-7205; J.M. Bui, R.H. Henchman, J.A. McCammon, Biophys. J. 85 (2003) 2267-2272] have been conducted and correlated with its inhibitory mechanisms. The intrinsic flexibilities of AChE, particularly of the long omega loop, are important in facilitating the ligand's inhibition of the enzyme.     

Time-resolved fluorescence polarization anisotropy of short restriction fragments: the friction factor for rotation of DNA about its symmetry axis

The time-resolved fluorescence polarization anisotropy (FPA) of ethidium dye intercalated in 43 and 69 base pair (bp) restriction fragments is measured, and the friction factor per bp for rotation of DNA about its symmetry axis is determined. The same value of the hydrodynamic radius, a = 12.0 ± 0.6 Å, is obtained for both the 43- and 69-bp fragments, but only when (1) the twisting correlation functions appropriate for such short filaments are used: (2) the correct amplitude is employed for the uniform tumbling mode decays: and (3) the data analysis is restricted to times after the internal bending modes have died away leaving just reduced amplitudes of the exponentially decaying uniform tumbling modes. The present value of the hydrodynamic radius is significantly larger than that implied by the cross-sectional area perpendicular to the symmetry axis. This strongly suggests that a significant fraction of water in the major and minor groves is rotating more or less rigidly with the DNA on this time scale. The correct expression for the amplitude D_n(∞) of the uniform mode decay of the tumbling correlation function, including the average over all sites to which the dye could bind, is derived in the appendix. The present theory for D_n(∞) is compared with that of Barkley and Zimm [(1979) J. Chem. Phys. 70 , 2991–3007], and with recent Brownian simulations of discrete wormlike chains by Allison and co-workers [S. A. Allison and J. A. McCammon (1984) Biopolymers 23 , 363–375; S. A. Allison (1986) Macromolecules 19 , 118–124].     

Normal mode theory for the Brownian dynamics of a weakly bending rod: Comparison with Brownian dynamics simulations

A normal mode theory is developed for the Brownian dynamics of weakly bending rods with preset hydrodynamic interactions. The rod is replaced by a chain of contiguous spheres whose radius is chosen to yield the appropriate uniform translational and rotational diffusion coefficients. Despite the inclusion of preset hydrodynamic interactions in the dynamical operator, its normal modes are not coupled by the potential energy, so their amplitudes remain pairwise “orthogonal” under equilibrium averaging. The uniform translational and rotational diffusion coefficients obtained from Langevin theory are shown to be identical to those obtained from the Kirkwood algorithm, despite their rather different appearance. An expression is given for the mean squared angular displacement 〈Δ_xm(t)²〉 of the mth bond vector around the instantaneous x axis (perpendicular to the end-to-end vector z). Necessary algorithms are presented for the numerical evaluation of all quantities. The normal mode theory is compared with Brownian dynamics simulations for the same model by examining 3〈Δ_xm(t)²〉 for the central bond vector of rods comprising 10 and 30 subunits with various persistence lengths. The normal mode theory works very well for all times for L/P ? 0.6, where P = κ/k_BT is the persistence length and κ is the bending rigidity. With increasing flexibility, the domain of validity of the normal mode theory is restricted to shorter times, where violations of the weak bending approximation are less severe. However, increasing the length of the rod from 10 to 30 subunits yields improved agreement with the simulations for the same and even longer times. This latter effect is tentatively attributed to the greater fluctuating tension in the longer chains, which acts to retard the rotational relaxation in the simulations, but is not taken into account in the present normal mode theory.     

Direct Measurement of Hydration-Related Dynamic Changes in Lysozyme using Inelastic Neutron Scattering Spectroscopy

Abstract

Inelastic neutron scattering spectroscopy is used to investigate dynamic changes in lysozyme powder at two different low D,0 hydrations (0.07g D²,O/g protein and 0,20 g D²,O/g protein). In the higher hydration sample, the inelastic scattering between 0.8 and 4.0 cm^?1 energy transfer is increased and the elastic scattering is decreased. The decreased elastic scattering suggests increased atomic amplitudes of motion and the increased 0.8 to 4.0 cm^?1 scattering suggests increased motions in this frequency range. Comparison with normal mode models of lysozyme dynamics shows that the inelastic difference occurs in the frequency region predicted for the lowest frequency, largest amplitude, global modes of the molccule[M. Levitt, C. Sanderand P. S. Stern, J. Mol. Biol. 181. 423 (1985). B.Brooks and M.Karplus.Prot. Natl Acad. Sci (U.S.A) 82. 4995 (1985), R.E. Bruccoleri, M. Karplus and J.A. McCammon, Biopolymers 25 1767 (1986)]. Our results are consistent with a model in which an increased number of low frequency global modes are present in the higher hydrated sample.     

The reliability of relative anion-cation permeabilities deduced from reversal (Dilution) potential measurements in ion channel studies

Measurements of anion-cation permeability ratios (e.g., P _Cl/P _Na) are most readily made by measuring changes in zero-current reversal potential when the salt concentration on one side of the membrane (e.g., external NaCl) is decreased. This is particularly useful for measuring changes in ion selectivity in wild-type and mutant channels, such as those of the ligand-gated ion channel superfamily, and has shown that many of these channels have a significant permeability to counter-ions. One Brownian dynamics study of ion permeation through such narrow ion channels failed to observe such counter-ion movement, although later, another Brownian dynamics study did observe counter-ion movement through simulations of the same channels. The question has been raised as to the reliability of such reversal potential measurements for determining permeability ratios, particularly given the use of an equation such as the Goldman-Hodgkin-Katz (GHK) equation, which is often used to calculate such ratios. A new derivation of the GHK equation in terms of activity coefficients is also included. The application of irreversible thermodynamics will be shown to qualitatively support the reliability of such experimental anion-cation permeability values derived from reversal potential measurements. It will then be shown that for such zero-current situations, different electrodiffusion models, with very different underlying assumptions, produce almost identical relative permeabilities (and reversal potentials). Finally, the results of the two Brownian dynamics simulation studies and the relationship between reversal potentials and relative permeability will be discussed.     

A New Coarse-Grained Model for E. coli Cytoplasm: Accurate Calculation of the Diffusion Coefficient of Proteins and Observation of Anomalous Diffusion

A new coarse-grained model of the E. coli cytoplasm is developed by describing the proteins of the cytoplasm as flexible units consisting of one or more spheres that follow Brownian dynamics (BD), with hydrodynamic interactions (HI) accounted for by a mean-field approach. Extensive BD simulations were performed to calculate the diffusion coefficients of three different proteins in the cellular environment. The results are in close agreement with experimental or previously simulated values, where available. Control simulations without HI showed that use of HI is essential to obtain accurate diffusion coefficients. Anomalous diffusion inside the crowded cellular medium was investigated with Fractional Brownian motion analysis, and found to be present in this model. By running a series of control simulations in which various forces were removed systematically, it was found that repulsive interactions (volume exclusion) are the main cause for anomalous diffusion, with a secondary contribution from HI.     

The relaxed complex method: Accommodating receptor flexibility for drug design with an improved scoring scheme

An extension of the new computational methodology for drug design, the "relaxed complex" method (J.-H. Lin, A. L. Perryman, J. R. Schames, and J. A. McCammon, Journal of the American Chemical Society, 2002, vol. 24, pp. 5632-5633), which accommodates receptor flexibility, is described. This relaxed complex method recognizes that ligand may bind to conformations that occur only rarely in the dynamics of the receptor. We have shown that the ligand-enzyme binding modes are very sensitive to the enzyme conformations, and our approach is capable of finding the best ligand enzyme complexes. Rapid docking serves as an efficient initial filtering method to screen a myriad of docking modes to a limited set, and it is then followed by more accurate scoring with the MM/PBSA (Molecular Mechanics/Poisson Boltzmann Surface Area) approach to find the best ligand-receptor complexes. The MM/PBSA scorings consistently indicate that the calculated binding modes that are most similar to those observed in the x-ray crystallographic complexes are the ones with the lowest free energies.     

Orientational steering in enzyme-substrate association: Ionic strength dependence of hydrodynamic torque effects

The effect of hydrodynamic torques on the association rate constants for enzyme-ligand complexation is investigated by Brownian dynamics simulations. Our hydrodynamic models of the enzyme and ligand are composed of spherical elements with friction forces acting at their centers. A quantitative measure of hydrodynamic torque orientational effects is introduced by choosing, as a reference system, an enzyme-ligand model with the same average hydrodynamic interactions but without orientational dependence. Our simple models show a 15% increase in the rate constant caused by hydrodynamic torques at physiological ionic strength. For more realistic hydrodynamic models, which are not computationally feasible at present, this effect is probably higher. The most important finding of this work is that hydrodynamic complementarity in shape (i.e. like the fitting together of pieces of a puzzle) is most effective for interactions between molecules at physiological ionic strength. Correspondence to: J.M. Briggs     

The hinge-bending mode of a lysozyme-inhibitor complex

The hinge-bending mode of hen egg white lysozyme is studied by a constrained minimization technique. Results with and without a bound inhibitor, tri-N-acetyl-glucosamine, are obtained. The frequency of the mode with the inhibitor is found to be 4.3 cm^?1, in contrast to 3.0 cm^?1 for the free enzyme. Also, the hinge-bending angle with the lowest energy is shifted 10° towards a more closed cleft in the bound species. The main contribution to these differences arise from interactions with the residues lining the cleft and those on the back side of it. Structural details that account for the energetics are presented. The method of calculation is somewhat different from a previous study [J. A. McCammon, B. R. Gelin, M. Karplus & P. G. Wolynes, (1976) Nature 262 , 325–326] to reduce the likelihood of artifacts in the results.     

A Method for Molecular Dynamics on Curved Surfaces

Dynamics simulations of constrained particles can greatly aid in understanding the temporal and spatial evolution of biological processes such as lateral transport along membranes and self-assembly of viruses. Most theoretical efforts in the field of diffusive transport have focused on solving the diffusion equation on curved surfaces, for which it is not tractable to incorporate particle interactions even though these play a crucial role in crowded systems. We show here that it is possible to take such interactions into account by combining standard constraint algorithms with the classical velocity Verlet scheme to perform molecular dynamics simulations of particles constrained to an arbitrarily curved surface. Furthermore, unlike Brownian dynamics schemes in local coordinates, our method is based on Cartesian coordinates, allowing for the reuse of many other standard tools without modifications, including parallelization through domain decomposition. We show that by applying the schemes to the Langevin equation for various surfaces, we obtain confined Brownian motion, which has direct applications to many biological and physical problems. Finally we present two practical examples that highlight the applicability of the method: 1) the influence of crowding and shape on the lateral diffusion of proteins in curved membranes; and 2) the self-assembly of a coarse-grained virus capsid protein model.     

Kinesin‐2 differentially regulates the anterograde axonal transports of acetylcholinesterase and choline acetyltransferase in Drosophila

Choline acetyltransferase (ChAT) and acetylcholinesterase (AChE) are involved in acetylcholine synthesis and degradation at pre‐ and postsynaptic compartments, respectively. Here we show that their anterograde transport in Drosophila larval ganglion is microtubule‐dependent and occurs in two different time profiles. AChE transport is constitutive while that of ChAT occurs in a brief pulse during third instar larva stage. Mutations in the kinesin‐2 motor subunit Klp64D and separate siRNA‐mediated knock‐outs of all the three kinesin‐2 subunits disrupt the ChAT and AChE transports, and these antigens accumulate in discrete nonoverlapping punctae in neuronal cell bodies and axons. Quantification analysis further showed that mutations in Klp64D could independently affect the anterograde transport of AChE even before that of ChAT. Finally, ChAT and AChE were coimmunoprecipitated with the kinesin‐2 subunits but not with each other. Altogether, these suggest that kinesin‐2 independently transports AChE and ChAT within the same axon. It also implies that cargo availability could regulate the rate and frequency of transports by kinesin motors. © 2006 Wiley Periodicals, Inc. J Neurobiol, 2006     

Hydrodynamics of segmentally flexible macromolecules

Segmentally flexible macromolecules are composed of a few rigid subunits linked by joints which are more or less flexible. The dynamics in solution of this type of macromolecule present special aspects that are reviewed here. Three alternative approaches are described. One is the rigid-body treatment, which is shown to be valid for overall dynamic properties such as translational diffusion and intrinsic viscosity. Another approach is the Harvey-Wegener treatment, which is particularly suited for rotational diffusion. The simplest version of this treatment, which ignores hydrodynamic interaction (HI) effects, is found to be quite accurate when compared to a more rigorous version including HI. A third approach is the Brownian dynamics simulation that, albeit at some computational cost, might describe rigorously cases of arbitrary complexity. This technique has been used to test the approximations in the rigid-body and Harvey-Wegener treatments, thus allowing a better understanding of their validity. Brownian trajectories of simplified models such as the trumbbell and the broken rod have been simulated. The comparison of the decay rates of some correlation functions with the predictions of the two treatments leads to a general conclusion: the Harvey-Wegener treatment determines the initial rate, while the long-time behavior is dominated by the rigid-body relaxation time. As an example of application to a specific biological macromolecule, we present a simulation of an immunoglobulin molecule, showing how Brownian Dynamics can be used to predict rotational and internal dynamics. Another typical example is myosin. Literature data of hydrodynamic properties of whole myosin and the myosin rod are compared with predictions from the Harvey-Wegener and rigid-body treatments. The present situation of the problem on myosin flexibility is analyzed, and some indications are given for future experimental and simulation work.     

Kinetic properties of ASC protein aggregation in epithelial cells

Apoptosis‐associated speck‐like protein with CARD domain (ASC), an adaptor protein composed of caspase recruitment and pyrin domains, can efficiently self‐associate to form a large spherical structure, called a speck. Although ASC aggregation is generally involved with both inflammatory processes and apoptosis, the detailed dynamics of speck formation have not been characterized. In this report, speck formation in HeLa cells transfected with ASC is examined by time‐lapse live‐imaging by confocal laser scanning microscopy. The results show that ASC aggregation is a very rapid and tightly regulated process. Prior to speck formation, soluble ASC aggregation is a low probability event, and the affinity of ASC subunits for one another is very low. Following a speck nucleation event, the affinity for further addition of ASC subunits increases dramatically, and aggregation is a highly energetically favorable reaction (Gibbs free energy ～ ?40 kJ/mol). This leads to a rapid depletion of soluble ASC, making it highly unlikely that a second speck will form inside the same cell and assuring that speck formation is “all or none,” with a well‐defined end point. Comparison with kinetic models of the aggregation process indicates diffusion, instead of active transport, is the dominant process for speck growth. Though speck formation and aggresome formation share some properties, we show that the two processes are distinct. J. Cell. Physiol. 222: 738–747, 2010. © 2009 Wiley‐Liss, Inc.     

Computational electrophysiology: the molecular dynamics of ion channel permeation and selectivity in atomistic detail

Presently, most simulations of ion channel function rely upon nonatomistic Brownian dynamics calculations, indirect interpretation of energy maps, or application of external electric fields. We present a computational method to directly simulate ion flux through membrane channels based on biologically realistic electrochemical gradients. In close analogy to single-channel electrophysiology, physiologically and experimentally relevant timescales are achieved. We apply our method to the bacterial channel PorB from pathogenic Neisseria meningitidis, which, during Neisserial infection, inserts into the mitochondrial membrane of target cells and elicits apoptosis by dissipating the membrane potential. We show that our method accurately predicts ion conductance and selectivity and elucidates ion conduction mechanisms in great detail. Handles for overcoming channel-related antibiotic resistance are identified.     

Chloroplast-encoded small subunits of the three multiprotein complexes in photosynthetic electron transport

The photosystem I, photosystem II, and cytochromeb ₆ f complexes that are involved in electron transport of oxygenic photosynthesis consist of a number of subunits encoded by either the chloroplast or nuclear genomes. In addition to the major subunits that carry redox components or photosynthetic pigments, these complexes contain several to more than ten subunits with molecular masses of less than 10 kDa. Directed mutagenesis has served as a powerful tool for investigation of the roles of these small subunits in the organization or function of the complexes. Various chloroplast transformants of the green algaChlamydomonas reinhardtii and mutants of cyanobacteria in which a gene encoding a small subunit was deleted or altered have been constructed. Evidence has accumulated suggesting that these small subunits function in the assembly, stabilization, or protection from photoinhibition of the complexes or in the modulation or regulation of electron transport. This article presents an overview of the properties and functions of the chloroplast-encoded small subunits of the three multiprotein complexes of photosynthetic electron transport that have been mainly analyzed with chloroplast transformants ofC. reinhardtii and the corresponding cyanobacterial transformants. Recipient of the Botanical Society Award for Young Scientists, 1995.     

Dynamics of the acetylcholinesterase tetramer

Acetylcholinesterase rapidly hydrolyzes the neurotransmitter acetylcholine in cholinergic synapses, including the neuromuscular junction. The tetramer is the most important functional form of the enzyme. Two low-resolution crystal structures have been solved. One is compact with two of its four peripheral anionic sites (PAS) sterically blocked by complementary subunits. The other is a loose tetramer with all four subunits accessible to solvent. These structures lacked the C-terminal amphipathic t-peptide (WAT domain) that interacts with the proline-rich attachment domain (PRAD). A complete tetramer model (AChEt) was built based on the structure of the PRAD/WAT complex and the compact tetramer. Normal mode analysis suggested that AChEt could exist in several conformations with subunits fluctuating relative to one another. Here, a multiscale simulation involving all-atom molecular dynamics and Cα-based coarse-grained Brownian dynamics simulations was carried out to investigate the large-scale intersubunit dynamics in AChEt. We sampled the ns-μs timescale motions and found that the tetramer indeed constitutes a dynamic assembly of monomers. The intersubunit fluctuation is correlated with the occlusion of the PAS. Such motions of the subunits “gate” ligand-protein association. The gates are open more than 80% of the time on average, which suggests a small reduction in ligand-protein binding. Despite the limitations in the starting model and approximations inherent in coarse graining, these results are consistent with experiments which suggest that binding of a substrate to the PAS is only somewhat hindered by the association of the subunits.     

On the interpretation and prediction of X-ray scattering profiles of biomolecules in solution

If solution scattering curves can be accurately predicted from structural models, measurements can provide useful tests of predictions of secondary and tertiary structure. We have developed a computational technique for the prediction and interpretation of x-ray scattering profiles of biomolecules in solution. The method employs a Monte Carlo procedure for the generation of length distribution functions and provides predictions to moderate resolution (～5 Å). In addition to facilitating the assignment and interpretation of features in a solution scattering profile, the method also allows the elucidation of the role of protein motion in shaping the final scattering curve. The effect of protein motion on a scattering profile is investigated by generating scattering curves from several consecutive 0.147 ps atomic coordinate frames from a molecular dynamics simulation of the motion of bovine pancreatic trypsin inhibitor (BPTI) [McCammon, J. A. & Karplus, M. (1980) Annu. Rev. Phys. Chem. 31 , 29–45]. The theoretical approach is applied to chicken egg white lysozyme and BPTI, and the overall features in the resulting theoretical scattering profiles match well with the experimental solution scattering curves recorded on film. It is apparent from this study that the scattering profile prediction technique in conjunction with other experimental methods may have value in testing ideas of conformational change based on crystallographic studies; investigations of this type would include a comparison of predicted scattering curves generated from a variety of crystallographic models with an actual scattering profile of the biomolecule in solution.