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arXiv2011

A Stochastic Compartmental Model for Fast Axonal Transport

In this paper we develop a probabilistic micro-scale compartmental model and use it to study macro-scale properties of axonal transport, the process by which intracellular cargo is moved in the axons of neurons. By directly modeling the smallest scale interactions, we can use recent microscopic experimental observations to infer all the parameters of the model. Then, using techniques from probability theory, we compute asymptotic limits of the stochastic behavior of individual motor-cargo complexes, while also characterizing both equilibrium and non-equilibrium ensemble behavior. We use these results in order to investigate three important biological questions: (1) How homogeneous are axons at stochastic equilibrium? (2) How quickly can axons return to stochastic equilibrium after large local perturbations? (3) How is our understanding of delivery time to a depleted target region changed by taking the whole cell point-of-view?

physics.bio-ph↗

arXiv2010

Fluctuation relations for molecular motors

This review is focused on the application of specific fluctuation relations, such as the Gallavotti-Cohen relation, to ratchet models of a molecular motor. A special emphasis is placed on two-states models such as the flashing ratchet model. We derive the Gallavotti-Cohen fluctuation relation for these models and we discuss some of its implications.

cond-mat.stat-mech↗

arXiv2009

Anomalous Light Absorption by Small Particles

A new type of resonant light absorption by a small particle (nanocluster) is reported. The problem cannot be described within the commonly used dipole scattering approximation and should be studied with methods based upon the exact Mie solution. It is shown that the absorption cross-section has giant maxima realized at small values of the imaginary part of the complex dielectric permittivity of the particle. The maxima are situated in the vicinity of the plasmon (polariton) resonances and correspond to the regions where the dissipative damping equals the radiative one. The case is similar to the recently introduced anomalous scattering [PRL vol. 97, 263902 (2006)] and exhibits similar peculiarities.

physics.optics↗

arXiv2010

Interactions between Intrinsic and Stimulus-Evoked Activity in Recurrent Neural Networks

Trial-to-trial variability is an essential feature of neural responses, but its source is a subject of active debate. Response variability (Mast and Victor, 1991; Arieli et al., 1995 & 1996; Anderson et al., 2000 & 2001; Kenet et al., 2003; Petersen et al., 2003a & b; Fiser, Chiu and Weliky, 2004; MacLean et al., 2005; Yuste et al., 2005; Vincent et al., 2007) is often treated as random noise, generated either by other brain areas, or by stochastic processes within the circuitry being studied. We call such sources of variability external to stress the independence of this form of noise from activity driven by the stimulus. Variability can also be generated internally by the same network dynamics that generates responses to a stimulus. How can we distinguish between external and internal sources of response variability? Here we show that internal sources of variability interact nonlinearly with stimulus-induced activity, and this interaction yields a suppression of noise in the evoked state. This provides a theoretical basis and potential mechanism for the experimental observation that, in many brain areas, stimuli cause significant suppression of neuronal variability (Werner and Mountcastle, 1963; Fortier, Smith and Kalaska, 1993; Anderson et al., 2000; Friedrich and Laurent, 2004; Churchland et al., 2006; Finn, Priebe and Ferster, 2007; Mitchell, Sundberg and Reynolds, 2007; Churchland et al., 2009). The combined theoretical and experimental results suggest that internally generated activity is a significant contributor to response variability in neural circuits.

q-bio.NC↗

arXiv2010

Enzymatic Logic Gates with Noise-Reducing Sigmoid Response

Biochemical computing is an emerging field of unconventional computing that attempts to process information with biomolecules and biological objects using digital logic. In this work we survey filtering in general, in biochemical computing, and summarize the experimental realization of an AND logic gate with sigmoid response in one of the inputs. The logic gate is realized with electrode-immobilized glucose-6-phosphate dehydrogenase enzyme that catalyzes a reaction corresponding to the Boolean AND functions. A kinetic model is also developed and used to evaluate the extent to which the performance of the experimentally realized logic gate is close to optimal.

cond-mat.soft↗

arXiv2010

3D Corporate Tourism: A Concept for Innovation in Nanomaterials Engineering

Nature's materials are complex, multifunctional, hierarchical and responsive and in most instances functionality on the nanoscale is combined with performance on the macroscale. Materials engineers have just started to produce complex nanomaterials. Biomimicry and biomimetics deal with knowledge transfer from nature to technology. Inspired by the 'Biomimicry and Design Workshops' and the 'Biomimicry Innovation Method' by the US based Biomimicry Guild, '3D Corporate Tourism', a solution based approach to innovation in nanomaterials research, is proposed. The three main pillars of this integrated concept are discover, develop and design. Biologists, research and development engineers as well as designers jointly work in an environment with high inspirational potential and construct first prototypes and designs on site. This joint approach yields new links, networks and collaborations between communities of thinkers in different countries in order to stimulate and enhance creative and application oriented problem solving for society.

physics.bio-ph↗

arXiv2010

Ferroelectric hydration shells around proteins: Electrostatics of the protein/water interface

Numerical simulations of hydrated proteins show that protein hydration shells are polarized into a ferroelectric cluster with a large magnitude of its average dipole moment. The emergence of this new mesophase dramatically alters the statistics of electrostatic fluctuations at the protein/water interface. The linear-response relation between the average electrostatic potential and its variance breaks down, with the breadth of the electrostatic noise far exceeding the expectations of the linear response theories. The dynamics of these non-Gaussian electrostatic fluctuations are dominated by a slow (~ 1 ns) component which freezes in at the temperature of dynamical transition of proteins.

physics.bio-ph↗

arXiv2011

The mechanical creep compliance of tissue cells is gamma distributed

Investigations of natural variation among cells within a population are essential for understanding the stochastic nature of tissue cell deformation under applied load. In the existing literature, the population variation of single-cell creep compliance has so far been modeled universally by using a log-normal distribution. Here we use optical stretching, a non-contact and relatively high-throughput technique for probing cell mechanics, to accumulate a sufficient data set that demonstrates robustly that cell compliance varies according to the similar but distinct gamma distribution. Additionally, we re-examine existing simulations that were originally proposed to justify a log-normal fit, and show that in fact these simulation data also correspond to the gamma distribution. Finally, we propose a general stochastic differential equation that analytically predicts a gamma distribution of creep compliance during cell stretching, as well as the Gaussian distribution of cell recovery that we observe experimentally upon removal of applied load. The population variation is well characterized by just a single parameter in each of the creep and recovery regimes. We expect our correction of a phenomenological distribution fit, enabled by an expansive data set for mesenchymal stem cells, to enable the development of more accurate constitutive laws to describe cytoskeletal deformation. These findings thus serve to replace an empirical distribution with a better-fitting model that rests on a more solid experimental and theoretical foundation, and also provides a basis to predict and understand the stochastic nature of the mechanical response of individual cells within populations.

q-bio.CB↗

arXiv2010

Protein Folding: A Perspective From Statistical Physics

In this paper, we introduce an approach to the protein folding problem from the point of view of statistical physics. Protein folding is a stochastic process by which a polypeptide folds into its characteristic and functional 3D structure from random coil. The process involves an intricate interplay between global geometry and local structure, and each protein seems to present special problems. We introduce CSAW (conditioned self-avoiding walk), a model of protein folding that combines the features of self-avoiding walk (SAW) and the Monte Carlo method. In this model, the unfolded protein chain is treated as a random coil described by SAW. Folding is induced by hydrophobic forces and other interactions, such as hydrogen bonding, which can be taken into account by imposing conditions on SAW. Conceptually, the mathematical basis is a generalized Langevin equation. To illustrate the flexibility and capabilities of the model, we consider several examples, including helix formation, elastic properties, and the transition in the folding of myoglobin. From the CSAW simulation and physical arguments, we find a universal elastic energy for proteins, which depends only on the radius of gyration $R_{g}$ and the residue number $N$. The elastic energy gives rise to scaling laws $R_{g}\sim N^ν$ in different regions with exponents $ν=3/5,3/7,2/5$, consistent with the observed unfolded stage, pre-globule, and molten globule, respectively. These results indicate that CSAW can serve as a theoretical laboratory to study universal principles in protein folding.

cond-mat.stat-mech↗

arXiv2010

Maximal Sensitive Dependence and the Optimal Path to Epidemic Extinction

Extinction of an epidemic or a species is a rare event that occurs due to a large, rare stochastic fluctuation. Although the extinction process is dynamically unstable, it follows an optimal path that maximizes the probability of extinction. We show that the optimal path is also directly related to the finite-time Lyapunov exponents of the underlying dynamical system in that the optimal path displays maximum sensitivity to initial conditions. We consider several stochastic epidemic models, and examine the extinction process in a dynamical systems framework. Using the dynamics of the finite-time Lyapunov exponents as a constructive tool, we demonstrate that the dynamical systems viewpoint of extinction evolves naturally toward the optimal path.

physics.bio-ph↗

arXiv2010

Entropy Considerations in Spin-Selective Radical-Ion-Pair Reactions

Radical-ion-pair reactions were recently shown to manifest a host of non-trivial quantum effects accounted for by quantum measurement theory. An alternative approach purporting to describe the fundamental quantum dynamics of spin-selective radical-ion pair reactions was introduced most recently, bringing to three the competing theories, including the one traditionally used in spin chemistry. We here consider entropy as a fundamental concept enabling a comparison of the predictions of these theories against what is physically acceptable on quite general grounds.

quant-ph↗

arXiv2012

Modeling symbiosis by interactions through species carrying capacities

We introduce a mathematical model of symbiosis between different species by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies or to social, economic and financial societies. Our model includes three basic types: symbiosis with direct mutual interactions, symbiosis with asymmetric interactions, and symbiosis without direct interactions. In all cases, we provide a complete classification of all admissible dynamical regimes. The proposed model of symbiosis turned out to be very rich, as it exhibits four qualitatively different regimes: convergence to stationary states, unbounded exponential growth, finite-time singularity, and finite-time death or extinction of species.

physics.bio-ph↗

arXiv2010

Electrical Conductance in Biological Molecules

Nucleic acids and proteins are not only biologically important polymers: They have recently been recognized as novel functional materials surpassing in many aspects the conventional ones. Although Herculean efforts have been undertaken to unravel fine functioning mechanisms of the biopolymers in question, there is still much more to be done. This particular paper presents the topic of biomolecular charge transport, with a particular focus on charge transfer/transport in DNA and protein molecules. Here the experimentally revealed details, as well as the presently available theories, of charge transfer/transport along these biopolymers are critically reviewed and analyzed. A summary of the active research in this field is also given, along with a number of practical recommendations.

cond-mat.soft↗

arXiv2010

The geometrical origin of the strain-twist coupling in double helices

The geometrical coupling between strain and twist in double helices is investigated. Overwinding, where strain leads to further winding, is shown to be a universal property for helices, which are stretched along their longitudinal axis when the initial pitch angle is below the zero-twist angle (39.4 deg). Unwinding occurs at larger pitch angles. The zero-twist angle is the unique pitch angle at the point between overwinding and unwinding, and it is independent of the mechanical properties of the double helix. This suggests the existence of zero-twist structures, i.e. structures that display neither overwinding, nor unwinding under strain. Estimates of the overwinding of DNA, chromatin, and RNA are given.

physics.bio-ph↗

arXiv2010

Cavity-water interface is polar

We present the results of numerical simulations of the electrostatics and dynamics of water hydration shells surrounding Kihara cavities given by a Lennard-Jones (LJ) layer at the surface of a hard-sphere cavity. The local dielectric response of the hydration layer substantially exceeds that of bulk water, with the magnitude of the dielectric constant peak in the shell increasing with the growing cavity size. The polar shell propagates into bulk water to approximately the cavity radius. The statistics of the electrostatic field produced by water inside the cavity follow linear response and approach the prediction of continuum electrostatics with increasing cavity size.

physics.bio-ph↗

arXiv2010

Role of Loading Device on Single-Molecule Mechanical Manipulation of Free Energy Landscape

Single-molecule mechanical manipulation has enabled the quantitative understanding of the kinetics of bond ruptures as well as protein unfolding mechanism. Single-molecule experiments with theoretical models have allowed one to gain insight into free energy landscape for chemical bond and/or protein folding. For mechanically induced bond rupture, the bond-rupture kinetics may be governed by loading device. However, the role of loading device on the kinetics of mechanical rupture has been rarely received much attention until recently. In this work, we have theoretically and/or computationally studied the effect of loading-device stiffness on the kinetics of mechanical unfolding. Specifically, we have considered a one-dimensional model for a bond rupture whose kinetics is depicted by Kramers' theory. It is elucidated that the kinetics of bond rupture is determined by force constant of loading device. The Brownian dynamics simulation of a bond rupture is considered in order to validate our theory. It is illustrated that the mean rupture force is dependent on the force constant of a loading device, such that increase in the loading-device stiffness leads to the higher bond rupture force. Moreover, we have taken into account the computational simulation of mechanical unfolding of a small protein, i.e. β-hairpin. Our simulation shows that unfolding force is highly correlated with the stiffness of a loading device. Our numerical and theoretical studies highlight the significance of a loading device on the kinetics of mechanical unfolding of a chemical bond and/or a folded domain in the single-molecule mechanical experiments.

physics.bio-ph↗

arXiv2010

Error-Control and Digitalization Concepts for Chemical and Biomolecular Information Processing Systems

We consider approaches for controlling the buildup of noise by design of gates for chemical and biomolecular computing, in order to realize stable, scalable networks for multi-step information processing. Solvable rate-equation models are introduced and used to illustrate several recently developed concepts and methodologies. We also outline future challenges and possible research directions.

physics.bio-ph↗

arXiv2010

Statistical Mechanics Model for Protein Folding

We present a novel statistical mechanics formalism for the theoretical description of the process of protein folding$\leftrightarrow$unfolding transition in water environment. The formalism is based on the construction of the partition function of a protein obeying two-stage-like folding kinetics. Using the statistical mechanics model of solvation of hydrophobic hydrocarbons we obtain the partition function of infinitely diluted solution of proteins in water environment. The calculated dependencies of the protein heat capacities upon temperature are compared with the corresponding results of experimental measurements for staphylococcal nuclease and metmyoglobin.

physics.bio-ph↗