Probing the Transition State of the Allosteric Pathway of the Shaker Kv Channel Pore by Linear Free-Energy Relations

Long-range coupling between distant functional elements of proteins may rely on allosteric communication trajectories lying along the protein structure, as described in the case of the Shaker voltage-activated potassium (Kv) channel model allosteric system. Communication between the distant Kv channel activation and slow inactivation pore gates was suggested to be mediated by a network of local pairwise and higher-order interactions among the functionally unique residues that constitute the allosteric trajectory. The mechanism by which conformational changes propagate along the Kv channel allosteric trajectory to achieve pore opening, however, remains unclear. Such conformational changes may propagate in either a concerted or a sequential manner during the reaction coordinate of channel opening. Residue-level structural information on the transition state of channel gating is required to discriminate between these possibilities. Here, we combine patch-clamp electrophysiology recordings of Kv channel gating and analysis using linear free-energy relations, focusing on a select set of residues spanning the allosteric trajectory of the Kv channel pore. We show that all allosteric trajectory residues tested exhibit an open-like conformation in the transition state of channel opening, implying that coupling interactions occur along the trajectory break in a concerted manner upon moving from the closed to the open state. Energetic coupling between the Kv channel gates thus occurs in a concerted fashion in both the spatial and the temporal dimensions, strengthening the notion that such trajectories correspond to pathways of mechanical deformation along which conformational changes propagate.     

Neotropical rainforest restoration: comparing passive,plantation and nucleation approaches

Neotropical rainforests are global biodiversity hotspots and are challenging to restore. A core part of this challenge is the very long recovery trajectory of the system: recovery of structure can take 20–190 years, species composition 60–500 years, and reestablishment of rare/endemic species thousands of years. Passive recovery may be fraught with instances of arrested succession, disclimax or emergence of novel ecosystems. In these cases, active restoration methods are essential to speed recovery and set a desired restoration trajectory. Tree plantation is the most common active approach to reestablish a high density of native tree species and facilitate understory regeneration. While this approach may speed the successional trajectory, it may not achieve, and possibly inhibit, a long-term restoration trajectory towards the high species diversity characteristic of these forests. A range of nucleation techniques (e.g., tree island planting) are important restoration options: although they may not speed recovery of structure as quickly as plantations, their emphasis on natural regeneration processes may enable greater and more natural patterns of diversity to develop. While more work needs to be done to compare forest restoration techniques in different environmental contexts, it appears that nucleation and, at times, passive restoration may best preserve the diverse legacy of these forested systems (both with lower costs). An integrated approach using both plantation productivity but also the natural functions associated with nucleation may develop composition and diversity trajectory desired in Neotropical conservation efforts.     

On the potential application of DFT methods in predicting the interaction-induced electric properties of molecular complexes. Molecular H-bonded chains as a case of study

A detailed analysis of the selected DFT functionals for the calculations of interaction-induced dipole moment, polarizability and first-order hyperpolarizability has been carried out. The hydrogen-bonded model chains consisting of HF, H(2)CO and H(3)N molecules have been chosen as a case study. The calculations of the components of the static electric properties using the diffuse Dunning's basis set (aug-cc-pVDZ) have been performed employing different types of density functionals (B3LYP, LC-BLYP, PBE0, M06-2X and CAM-B3LYP). Obtained results have been compared with those gained at the CCSD(T) level of theory. The counterpoise correction scheme, namely site-site function counterpoise, has been applied in order to eliminate basis set superposition error. The performed tests allow to conclude that the DFT functionals can provide a useful tool for prediction of the interaction-induced electric properties, however a caution has to be urged to their decomposition to the two- and many-body terms.     

Viscometric flow for a many-body dissipative particle dynamics (MDPD) fluid with Lees–Edwards boundary condition

Viscometric properties of polymer are explored by the many-body dissipative particle dynamics (MDPD) using Lees–Edwards boundary conditions. The equation of state for the MDPD system is modified by fitting the density correction to different values of the cut-off radius. Due to the many-body interactions in MDPD, the viscosity contributed from the conservative force increases considerably with increasing repulsive coefficient, density and cut-off radius, and cannot be ignored compared to the ‘standard’ DPD case. The influence of these parameters on the MDPD viscosity is investigated, and we propose an equation to predict the viscosity in MDPD model. Additionally, the dumbbell polymer suspension model is investigated in the MDPD fluid, and the relations concerning first normal stress difference and shear rate, the relaxation time and spring constant, are consistent to theoretical works. We conclude that the MDPD model can be used to investigate the dynamics of non-Newtonian droplets.     

The Isochronal Fibration: Characterization and Implication in Biology

Limit cycles, because they are constituted of a periodic succession of states (discrete or continuous) constitute a good manner to store information. From any points of the state space reached after a perturbation or stimulation of the cognitive system storing this information, one can aim to join through a more or less long return trajectory a precise neighbourhood of the asymptotic trajectory at a specific moment (or a specific place) on the limit cycle, i.e. where the information of interest stands. We propose that the isochronal fibration, initially imagined and described by A. T. Winfree may be an excellent way to connect directly those two locations. Each isochron is indeed the set of points in temporal phase with one single point of the attractor. The characterisation of the isochronal fibration of various dynamical systems is not easy and until now has principally only been done numerically but not analytically. By integrating the homogeneous solutions of the dynamical system we can solve this fibration in the case of the well known anharmonic pendulum. Other isochronal fibration on classical examples such as the van der Pol system and the non-symmetrical PFK limit cycle are obtained numerically and we also provide the first numerical study on 3-dimentional systems like the anharmonic pendulum with a linear relaxation on its third variable and the Lorenz attractor. The empirical approach seems us useful for dealing with the isochronal fibration which could constitute a powerful tool for understanding and controlling the dynamics of biological or biological-inspired systems.     

Ab initio folding simulation of the Trp-cage mini-protein approaches NMR resolution

Here, we report a 100 ns molecular dynamics simulation of the folding process of a recently designed autonomous-folding mini-protein designated as tc5b with a new AMBER force field parameter set developed based on condensed-phase quantum mechanical calculations and a Generalized Born continuum solvent model. Starting from its fully extended conformation, our simulation has produced a final structure resembling that of NMR native structure to within 1A main-chain root mean square deviation. Remarkably, the simulated structure stayed in the native state for most part of the simulation after it reached the state. Of greater significance is that our simulation has not only reached the correct main-chain conformation, but also a very high degree of accuracy in side-chain packing conformation. This feat has traditionally been a challenge for ab initio simulation studies. In addition to characterization of the trajectory, comparison of our results to experimental data is also presented. Analysis of the trajectory suggests that the rate-limiting step of folding of this mini-protein is the packing of the Trp side-chain.     

Exploring the effects of different immersion environments on the growth of gold nanostructures

Even though Au crystallizes only as a simple FCC structure in bulk there have been many different and fascinating structures discovered experimentally for Au on the nanoscale. Unfortunately, for Au a direct ab-initio approach in studying dynamic growth mechanisms of nanostructures is prohibitively expensive from a computational perspective, so here we use methods based on accurate semi-empirical, many-body potentials whose parameters are obtained from a combination of empirical and ab-initio data as a viable alternative. We show that this method when combined with molecular dynamics may be used to simulate the growth of Au particles in a bath of solvent atoms (either in a gaseous or liquid state) which results in structures of a range of different morphologies. An analysis of the results indicates what characteristics of the solvent and its interactions are important in determining these different morphologies.     

A Many-Body Field Theory Approach to Stochastic Models in Population Biology

Background

Many models used in theoretical ecology, or mathematical epidemiology are stochastic, and may also be spatially-explicit. Techniques from quantum field theory have been used before in reaction-diffusion systems, principally to investigate their critical behavior. Here we argue that they make many calculations easier and are a possible starting point for new approximations.

Methodology

We review the many-body field formalism for Markov processes and illustrate how to apply it to a ‘Brownian bug’ population model, and to an epidemic model. We show how the master equation and the moment hierarchy can both be written in particularly compact forms. The introduction of functional methods allows the systematic computation of the effective action, which gives the dynamics of mean quantities. We obtain the 1-loop approximation to the effective action for general (space-) translation invariant systems, and thus approximations to the non-equilibrium dynamics of the mean fields.

Conclusions

The master equations for spatial stochastic systems normally take a neater form in the many-body field formalism. One can write down the dynamics for generating functional of physically-relevant moments, equivalent to the whole moment hierarchy. The 1-loop dynamics of the mean fields are the same as those of a particular moment-closure.     

Spatio-temporal dynamics of the grey-sided vole in Hokkaido: identifying coupling using state-based Markov-chain modelling

Explaining synchronization of cyclical or fluctuating populations over geographical regions presents ecologists with novel analytical challenges. We have developed a method to measure synchrony within spatial-temporal datasets of population densities applicable to both periodic and irregularly fluctuating populations. The dynamics of each constituent population is represented by a discrete Markov model. The state of a population trajectory at each time-point is classified as one of 'increase', 'decrease', 'peak' or 'trough'. The set of populations at any time-point is characterized by the frequency distribution of these different states, and the time-evolution of this frequency distribution used to test the hypothesis that the dynamics of each population proceeds independently of the others. The analysis identifies years in which population coupling results in synchronous states and onto which states the system converges, and identifies those years in which synchrony remains high but is accounted for by coupling observed in previous years. It also enables identification of which pairs of sites show the highest levels of coupling. Applying these methods to populations of the grey-sided vole on Hokkaido reveals them to be fluctuating in greater synchrony than would be expected from independent dynamics, and that this level of synchrony is maintained through intermittent coupling acting in ca. 1 year in four or five. High synchrony occurs between sites with similar vegetation and of similar altitude indicating that coupling may be mediated through shared environmental stimuli. When coupling is indicated, convergence is equally likely to occur on a peak state as a trough, indicating that synchronization may be brought about by the response of populations to a combination of different stimuli rather than by the action of any single process.     

Mathematical modeling and simulation of seated stability

Various methods have been used to quantify the kinematic variability or stability of the human spine. However, each of these methods evaluates dynamic behavior within the stable region of state space. In contrast, our goal was to determine the extent of the stable region. A 2D mathematical model was developed for a human sitting on an unstable seat apparatus (i.e., the “wobble chair”). Forward dynamic simulations were used to compute trajectories based on the initial state. From these trajectories, a scalar field of trajectory divergence was calculated, specifically a finite time Lyapunov exponent (FTLE) field. Theoretically, ridges of local maxima within this field are expected to partition the state space into regions of qualitatively different behavior. We found that ridges formed at the boundary between regions of stability and failure (i.e., falling). The location of the basin of stability found using the FTLE field matched well with the basin of stability determined by an alternative method. In addition, an equilibrium manifold was found, which describes a set of equilibrium configurations that act as a low dimensional attractor in the controlled system. These simulations are a first step in developing a method to locate state space boundaries for torso stability. Identifying these boundaries may provide a framework for assessing factors that contribute to health risks associated with spinal injury and poor balance recovery (e.g., age, fatigue, load/weight, and distribution). Furthermore, an approach is presented that can be adapted to find state space boundaries in other biomechanical applications.     

Mathematical modeling of differentiation in dictyostelium discoideum

Methods for the dynamic analysis of biochemical differentiation are presented. These are demonstrated in the analysis of biochemical differentiation of the carbohydrate system in D. discoideum. Procedures for simplification which are presented are projection and contraction of the system trajectory in state space and the generation of reduced equivalent dynamic metabolic networks. The importance of the hierarchical structure of differentiating systems is discussed and the concept of a dynamic embedding diagram is introduced. It is shown that complex systems must be analyzed on an epoch by epoch basis, each epoch being a period of time characterized by a constant dynamic embedding diagram, and that widely different time scales and state space scales may be necessary in different epochs. In particular there is no a priori lower limit to the time scale which may be necessary during the analysis. Some problems in mathematically defining differentiation are discussed.     

New insights into motor cortex

An exciting new experiment on the motor cortex of monkeys, by Shenoy and colleagues, begins to elucidate how the neuronal ensemble travels in a systematic fashion through state space. This trajectory through state space may help to explain how the motor cortex sets up and then triggers arm movements.     

Governing stem cell research in California and the USA: towards a social infrastructure

Owing to the restrictive human embryonic stem cell (hESC) policies of the US government, the question of whether to pursue human embryonic stem cell experiments has dominated the ethical and political discourse concerning such research. Explicit attention must now turn to problems of implementing the research on a large scale: in the 2004 US elections, California voters approved a state initiative for stem cell research, earmarking $3 billion in direct spending over 10 years. This article explores three ethical and political problem areas emerging out of the California program, the resolution of which will help set the trajectory of hESC research in the US and abroad, and then proposes an institutional approach to help address them: a network of public stem cell banks in the US that feature transparent and shared governance.     

Inhibitor of DNA Binding 4 (ID4) Is Highly Expressed in Human Melanoma Tissues and May Function to Restrict Normal Differentiation of Melanoma Cells

Melanoma tissues and cell lines are heterogeneous, and include cells with invasive, proliferative, stem cell-like, and differentiated properties. Such heterogeneity likely contributes to the aggressiveness of the disease and resistance to therapy. One model suggests that heterogeneity arises from rare cancer stem cells (CSCs) that produce distinct cancer cell lineages. Another model suggests that heterogeneity arises through reversible cellular plasticity, or phenotype-switching. Recent work indicates that phenotype-switching may include the ability of cancer cells to dedifferentiate to a stem cell-like state. We set out to investigate the phenotype-switching capabilities of melanoma cells, and used unbiased methods to identify genes that may control such switching. We developed a system to reversibly synchronize melanoma cells between 2D-monolayer and 3D-stem cell-like growth states. Melanoma cells maintained in the stem cell-like state showed a striking upregulation of a gene set related to development and neural stem cell biology, which included SRY-box 2 (SOX2) and Inhibitor of DNA Binding 4 (ID4). A gene set related to cancer cell motility and invasiveness was concomitantly downregulated. Intense and pervasive ID4 protein expression was detected in human melanoma tissue samples, suggesting disease relevance for this protein. SiRNA knockdown of ID4 inhibited switching from monolayer to 3D-stem cell-like growth, and instead promoted switching to a highly differentiated, neuronal-like morphology. We suggest that ID4 is upregulated in melanoma as part of a stem cell-like program that facilitates further adaptive plasticity. ID4 may contribute to disease by preventing stem cell-like melanoma cells from progressing to a normal differentiated state. This interpretation is guided by the known role of ID4 as a differentiation inhibitor during normal development. The melanoma stem cell-like state may be protected by factors such as ID4, thereby potentially identifying a new therapeutic vulnerability to drive differentiation to the normal cell phenotype.     

Forward and Backward Inference in Spatial Cognition

This paper shows that the various computations underlying spatial cognition can be implemented using statistical inference in a single probabilistic model. Inference is implemented using a common set of ‘lower-level’ computations involving forward and backward inference over time. For example, to estimate where you are in a known environment, forward inference is used to optimally combine location estimates from path integration with those from sensory input. To decide which way to turn to reach a goal, forward inference is used to compute the likelihood of reaching that goal under each option. To work out which environment you are in, forward inference is used to compute the likelihood of sensory observations under the different hypotheses. For reaching sensory goals that require a chaining together of decisions, forward inference can be used to compute a state trajectory that will lead to that goal, and backward inference to refine the route and estimate control signals that produce the required trajectory. We propose that these computations are reflected in recent findings of pattern replay in the mammalian brain. Specifically, that theta sequences reflect decision making, theta flickering reflects model selection, and remote replay reflects route and motor planning. We also propose a mapping of the above computational processes onto lateral and medial entorhinal cortex and hippocampus.     

GPU-accelerated molecular dynamics simulation of solid covalent crystals

Graphics processing unit (GPU) is becoming a powerful computational tool in science and engineering. In this paper, different from previous molecular dynamics (MD) simulation with pair potentials and many-body potentials, two MD simulation algorithms implemented on a single GPU are presented to describe a special category of many-body potentials – bond order potentials used frequently in solid covalent materials, such as the Tersoff potentials for silicon crystals. The simulation results reveal that the performance of GPU implementations is apparently superior to their CPU counterpart. Furthermore, the proposed algorithms are generalised, transferable and scalable, and can be extended to the simulations with general many-body interactions such as Stillinger–Weber potential and so on.     

Thermodynamic stability of ecosystems

The stability of ecosystems during periods of stasis in their macro-evolutionary trajectory is studied from a non-equilibrium thermodynamic perspective. Individuals of the species are considered as units of entropy production and entropy exchange in an open thermodynamic system. Within the framework of the classical theory of irreversible thermodynamics, and under the condition of constant external constraints, such a system will naturally evolve toward a globally stable thermodynamic stationary state. It is thus suggested that the ecological steady state, or stasis, is a particular case of the thermodynamic stationary state, and that the evolution of community stability through natural selection is a manifestation of non-equilibrium thermodynamic directives. Furthermore, it is argued that punctuation of stasis leading to ecosystem succession, may be a manifestation of non-equilibrium "phase transitions" brought on by a change of external constraints through a thermodynamic critical point.     

A Molecular Dynamics Investigation of Vinculin Activation

Vinculin activation plays a critical role in focal adhesion initiation and formation. In its native state, vinculin is in an autoinhibitory conformation in which domain 1 prevents interaction of the vinculin tail domain with actin by steric hindrance. Once activated, vinculin is able to interact with both actin and talin. Several hypotheses have been put forth addressing the mechanisms of vinculin activation. One set of studies suggests that vinculin interaction with talin is sufficient to cause activation, whereas another set of studies suggests that a simultaneous interaction with several binding partners is necessary to achieve vinculin activation. Using molecular-dynamics (MD) simulations, we investigate the mechanisms of vinculin activation and suggest both a trajectory of conformational changes leading to vinculin activation, and key structural features that are likely involved in stabilizing the autoinhibited conformation. Assuming that the simultaneous interaction of vinculin with both actin and talin causes a stretching force on vinculin, and that vinculin activation results from a removal of steric hindrance blocking the actin-binding sites, we simulate with MD the stretching and activation of vinculin. The MD simulations are further confirmed by normal-mode analysis and simulation after residue modification. Taken together, the results of these simulations suggest that bending of the vinculin-binding-site region in vinculin away from the vinculin tail is the likely trajectory of vinculin activation.     

On the possibility of linear modelling the human arm neuromuscular apparatus

It has been widely claimed that linear models of the neuromuscular apparatus give very inaccurate approximations of human arm reaching movements. The present paper examines this claim by quantifying the contributions of the various non-linear effects of muscle force generation on the accuracy of linear approximation. We performed computer simulations of a model of a two-joint arm with six monarticular and biarticular muscles. The global actions of individual muscles resulted in a linear dependence of the joint torques on the joint angles and angular velocities, despite the great non-linearity of the muscle properties. The effect of time delay in force generation is much more important for model accuracy than all the non-linear effects, while ignoring this time delay in linear approximation results in large errors. Thus, the viscosity coefficients are rather underestimated and some of them can even be paradoxically estimated to be negative. Similarly, our computation showed that ignoring the time delay resulted in large errors in the estimation of the hand equilibrium trajectory. This could explain why experimentally estimated hand equilibrium trajectories may be complex, even during a simple reaching movement. The hand equilibrium trajectory estimated by a linear model becomes simple when the time delay is taken into account, and it is close to that actually used in the non-linear model. The results therefore provide a theoretical basis for estimating the hand equilibrium trajectory during arm reaching movements and hence for estimating the time course of the motor control signals associated with this trajectory, as set out in the equilibrium point hypothesis. Received: 17 February 1999 / Accepted in revised form: 22 October 1999