Applying forces to elastic network models of large biomolecules using a haptic feedback device

Elastic network models of biomolecules have proved to be relatively good at predicting global conformational changes particularly in large systems. Software that facilitates rapid and intuitive exploration of conformational change in elastic network models of large biomolecules in response to externally applied forces would therefore be of considerable use, particularly if the forces mimic those that arise in the interaction with a functional ligand. We have developed software that enables a user to apply forces to individual atoms of an elastic network model of a biomolecule through a haptic feedback device or a mouse. With a haptic feedback device the user feels the response to the applied force whilst seeing the biomolecule deform on the screen. Prior to the interactive session normal mode analysis is performed, or pre-calculated normal mode eigenvalues and eigenvectors are loaded. For large molecules this allows the memory and number of calculations to be reduced by employing the idea of the important subspace, a relatively small space of the first M lowest frequency normal mode eigenvectors within which a large proportion of the total fluctuation occurs. Using this approach it was possible to study GroEL on a standard PC as even though only 2.3% of the total number of eigenvectors could be used, they accounted for 50% of the total fluctuation. User testing has shown that the haptic version allows for much more rapid and intuitive exploration of the molecule than the mouse version

Multi-heme Cytochromes in Shewanella oneidensis MR-1:Structures, functions and opportunities

Multi-heme cytochromes are employed by a range of microorganisms to transport electrons over distances of up to tens of nanometers. Perhaps the most spectacular utilization of these proteins is in the reduction of extracellular solid substrates, including electrodes and insoluble mineral oxides of Fe(III) and Mn(III/IV), by species of Shewanella and Geobacter. However, multi-heme cytochromes are found in numerous and phylogenetically diverse prokaryotes where they participate in electron transfer and redox catalysis that contributes to biogeochemical cycling of N, S and Fe on the global scale. These properties of multi-heme cytochromes have attracted much interest and contributed to advances in bioenergy applications and bioremediation of contaminated soils. Looking forward there are opportunities to engage multi-heme cytochromes for biological photovoltaic cells, microbial electrosynthesis and developing bespoke molecular devices. As a consequence it is timely to review our present understanding of these proteins and we do this here with a focus on the multitude of functionally diverse multi-heme cytochromes in Shewanella oneidensis MR-1. We draw on findings from experimental and computational approaches which ideally complement each other in the study of these systems: computational methods can interpret experimentally determined properties in terms of molecular structure to cast light on the relation between structure and function. We show how this synergy has contributed to our understanding of multi-heme cytochromes and can be expected to continue to do so for greater insight into natural processes and their informed exploitation in biotechnologies

Causal connectivity of evolved neural networks during behavior

To show how causal interactions in neural dynamics are modulated by behavior, it is valuable to analyze these interactions without perturbing or lesioning the neural mechanism. This paper proposes a method, based on a graph-theoretic extension of vector autoregressive modeling and 'Granger causality,' for characterizing causal interactions generated within intact neural mechanisms. This method, called 'causal connectivity analysis' is illustrated via model neural networks optimized for controlling target fixation in a simulated head-eye system, in which the structure of the environment can be experimentally varied. Causal connectivity analysis of this model yields novel insights into neural mechanisms underlying sensorimotor coordination. In contrast to networks supporting comparatively simple behavior, networks supporting rich adaptive behavior show a higher density of causal interactions, as well as a stronger causal flow from sensory inputs to motor outputs. They also show different arrangements of 'causal sources' and 'causal sinks': nodes that differentially affect, or are affected by, the remainder of the network. Finally, analysis of causal connectivity can predict the functional consequences of network lesions. These results suggest that causal connectivity analysis may have useful applications in the analysis of neural dynamics

Phase resetting reveals network dynamics underlying a bacterial cell cycle

Genomic and proteomic methods yield networks of biological regulatory interactions but do not provide direct insight into how those interactions are organized into functional modules, or how information flows from one module to another. In this work we introduce an approach that provides this complementary information and apply it to the bacterium Caulobacter crescentus, a paradigm for cell-cycle control. Operationally, we use an inducible promoter to express the essential transcriptional regulatory gene ctrA in a periodic, pulsed fashion. This chemical perturbation causes the population of cells to divide synchronously, and we use the resulting advance or delay of the division times of single cells to construct a phase resetting curve. We find that delay is strongly favored over advance. This finding is surprising since it does not follow from the temporal expression profile of CtrA and, in turn, simulations of existing network models. We propose a phenomenological model that suggests that the cell-cycle network comprises two distinct functional modules that oscillate autonomously and couple in a highly asymmetric fashion. These features collectively provide a new mechanism for tight temporal control of the cell cycle in C. crescentus. We discuss how the procedure can serve as the basis for a general approach for probing network dynamics, which we term chemical perturbation spectroscopy (CPS)

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Information theoretical study of cross-talk mediated signal transduction in MAPK pathways

Biochemical networks related to similar functional pathways are often correlated due to cross-talk among the homologous proteins in the different networks. Using a stochastic framework, we address the functional significance of the cross-talk between two pathways. Our theoretical analysis on generic MAPK pathways reveals cross-talk is responsible for developing coordinated fluctuations between the pathways. The extent of correlation evaluated in terms of the information theoretic measure provides directionality to net information propagation. Stochastic time series and scattered plot suggest that the cross-talk generates synchronization within a cell as well as in a cellular population. Depending on the number of input and output, we identify signal integration and signal bifurcation motif that arise due to inter-pathway connectivity in the composite network. Analysis using partial information decomposition quantifies the net synergy in the information propagation through these branched pathways.Comment: Revised version, 17 pages, 5 figure

Protein folding tames chaos

Protein folding produces characteristic and functional three-dimensional structures from unfolded polypeptides or disordered coils. The emergence of extraordinary complexity in the protein folding process poses astonishing challenges to theoretical modeling and computer simulations. The present work introduces molecular nonlinear dynamics (MND), or molecular chaotic dynamics, as a theoretical framework for describing and analyzing protein folding. We unveil the existence of intrinsically low dimensional manifolds (ILDMs) in the chaotic dynamics of folded proteins. Additionally, we reveal that the transition from disordered to ordered conformations in protein folding increases the transverse stability of the ILDM. Stated differently, protein folding reduces the chaoticity of the nonlinear dynamical system, and a folded protein has the best ability to tame chaos. Additionally, we bring to light the connection between the ILDM stability and the thermodynamic stability, which enables us to quantify the disorderliness and relative energies of folded, misfolded and unfolded protein states. Finally, we exploit chaos for protein flexibility analysis and develop a robust chaotic algorithm for the prediction of Debye-Waller factors, or temperature factors, of protein structures