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arXiv2016

Asymptotic Solution to the Rayleigh Problem of Dynamic Soaring

Albatrosses can travel a thousand kilometers daily over the oceans. This feat is achieved through dynamic soaring, a non-flapping flight strategy where propulsive energy is extracted from horizontal wind shears. Dynamic soaring has been described as a sequence of half-turns connecting upwind climbs and downwind dives through the surface shear layer. We analytically and numerically investigate the aerodynamically optimal flight trajectory for varying shear thicknesses. Contrary to current thinking, but consistent with GPS recordings of flying albatrosses, in thin shears the optimal trajectory is composed of small angle arcs. Essentially, the albatross is a flying sailboat, sequentially acting as sail and keel, and most efficient when remaining crosswind. Our analysis constitutes a general framework for dynamic soaring, and more broadly energy extraction in complex winds.

physics.bio-ph↗

arXiv2015

Steady state thermodynamics in population dynamics

We report that population dynamics in fluctuating environment accompanies mathematically equivalent structure to steady state thermodynamics. By employing the structure, population growth in fluctuating environment is decomposed into housekeeping and excess parts. The housekeeping part represents the integral of stationary growth rate for each condition during a history of the environmental change. The excess part accounts for the excess growth generated when environment is switched. Focusing on the excess growth, we obtain Clausius inequality, which gives the upper bound of the excess growth. The equality is shown to be achieved in quasistatic environmental changes. We also clarify that this bound can be evaluated by "lineage fitness" that is an experimentally observable quantity.

cond-mat.stat-mech↗

arXiv2018

A homotopic mapping between current-based and conductance-based synapses in a mesoscopic neural model of epilepsy

Changes in brain states, as found in many neurological diseases such as epilepsy, are often described as bifurcations in mesoscopic neural models. Nearly all of these models rely on a mathematically convenient, but biophysically inaccurate, description of the synaptic input to neurons called current-based synapses. We develop a novel analytical framework to analyze the effects of a more biophysically realistic description, known as conductance-based synapses. These are implemented in a mesoscopic neural model and compared to the standard approximation via a single parameter homotopic mapping. A bifurcation analysis using the homotopy parameter demonstrates that if a more realistic synaptic coupling mechanism is used in this class of models, then a bifurcation or transition to an abnormal brain state does not occur in the same parameter space. We show that the more realistic coupling has additional mathematical parameters that require a fundamentally different biophysical mechanism to undergo a state transition. These results demonstrate the importance of incorporating more realistic synapses in mesoscopic neural models and challenge the accuracy of previous models, especially those describing brain state transitions such as epilepsy.

q-bio.NC↗

arXiv2018

Dipolar interactions between domains in lipid monolayers at the air-water interface

A great variety of biologically relevant monolayers present phase coexistence characterized by domains formed by lipids in an ordered phase state dispersed in a continuous, disordered phase. The difference in surface densities between these phases originates inter-domain dipolar interactions, which are relevant for the determination of the spacial distribution of domains, as well as their dynamics. In this work, we propose a novel manner of estimating the dipolar repulsion using a passive method that involves the analysis of images of the monolayer with phase coexistence. The method is based on the comparison of the pair correlation function obtained from experiments with that obtained from Brownian dynamics simulations of a model system. As an example, we determined the difference in dipolar density of a binary monolayer of DSPC/DMPC at the air-water interface from the analysis of the radial distribution of domains, and the results are compared with those obtained by surface potential determinations. A systematic analysis for experimentally relevant parameter range is given, which may be used as a working curve for obtaining the dipolar repulsion in different systems.

physics.bio-ph↗

arXiv2016

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.

q-bio.MN↗

arXiv2015

Stochastic robustness and relative stability of multiple pathways in biological networks

Multiple dynamic pathways always exist in biological networks, but their robustness against internal fluctuations and relative stability have not been well recognized and carefully analyzed yet. Here we try to address these issues through an illustrative example, namely the Siah-1/beta-catenin/p14/19 ARF loop of protein p53 dynamics. Its deterministic Boolean network model predicts that two parallel pathways with comparable magnitudes of attractive basins should exist after the protein p53 is activated when a cell becomes harmfully disturbed. Once the low but non-neglectable intrinsic fluctuations are incorporated into the model, we show that a phase transition phenomenon is emerged: in one parameter region the probability weights of the normal pathway, reported in experimental literature, are comparable with the other pathway which is seemingly abnormal with the unknown functions, whereas, in some other parameter regions, the probability weight of the abnormal pathway can even dominate and become globally attractive. The theory of exponentially perturbed Markov chains is applied and further generalized in order to quantitatively explain such a phase transition phenomenon, in which the nonequilibrium "activation energy barriers" along each transiting trajectory between the parallel pathways and the number of "optimal transition paths" play a central part. Our theory can also determine how the transition time and the number of optimal transition paths between the parallel pathways depend on each interaction's strength, and help to identify those possibly more crucial interactions in the biological network.

q-bio.MN↗

arXiv2015

A physical description of the adhesion and aggregation of platelets

The early stages of clot formation in blood vessels involve platelets adhesion-aggregation. Although these mechanisms have been extensively studied, gaps in their understanding still persist. We have performed detailed in-vitro experiments and developed a numerical model to better describe and understand this phenomenon. Unlike previous studies, we took into account both activated and non-activated platelets, as well as the 3D nature of the aggregation process. Our investigation reveals that blood albumin is a major parameter limiting platelet adhesion and aggregation. Our results also show that the well accepted Zydney-Colton shear-induced diffusivity is much too low to explain the observed deposition rate. Simulations are in very good agreement with observations and provide quantitative estimates of the adhesion and aggregation rates that are hard to measure experimentally.

physics.bio-ph↗

arXiv2016

Sequence-structure relations of biopolymers

Motivation: DNA data is transcribed into single-stranded RNA, which folds into specific molecular structures. In this paper we pose the question to what extent sequence- and structure-information correlate. We view this correlation as structural semantics of sequence data that allows for a different interpretation than conventional sequence alignment. Structural semantics could enable us to identify more general embedded "patterns" in DNA and RNA sequences. Results: We compute the partition function of sequences with respect to a fixed structure and connect this computation to the mutual information of a sequence-structure pair for RNA secondary structures. We present a Boltzmann sampler and obtain the a priori probability of specific sequence patterns. We present a detailed analysis for the three PDB-structures, 2JXV (hairpin), 2N3R (3-branch multi-loop) and 1EHZ (tRNA). We localize specific sequence patterns, contrast the energy spectrum of the Boltzmann sampled sequences versus those sequences that refold into the same structure and derive a criterion to identify native structures. We illustrate that there are multiple sequences in the partition function of a fixed structure, each having nearly the same mutual information, that are nevertheless poorly aligned. This indicates the possibility of the existence of relevant patterns embedded in the sequences that are not discoverable using alignments.

math.CO↗

arXiv2015

Discontinuous transitions: Multiphasic profiles for channels, binding, pH, folding and chain length

A wide variety of biological as well as non-biological processes and phenomena involving ion channels, binding, pH, folding/unfolding and effects of chain length are well represented by multiphasic profiles, a series of straight lines separated by discontinuous transitions, often in the form of noncontiguities (jumps). The lines appear to be perfectly straight, with no indication of any curvilinearity. Adjacent lines are quite often parallel or nearly so and are then necessarily separated by jumps. If the data are sufficiently detailed and precise, the conventional curvilinear profiles must be rejected for a variety of reasons, whereas sudden changes of state occur in many physical systems (see Conclusions).

physics.bio-ph↗

arXiv2016

Aquaporin-1 can work as a Maxwell's Demon in the Body

Aquaporin-1 (AQP1) is a membrane protein which is selectively permeable to water. Due to its dumbbell shape, AQP1 can sense the size information of solute molecules in osmosis. At the cost of consuming this information, AQP1 can move water against its chemical potential gradient: it is able to work as one kind of Maxwell's Demon. This effect was detected quantitatively by measuring the water osmosis of mice red blood cells. This ability may protect the red blood cells from the eryptosis elicited by osmotic shock when they move in the kidney, where a large gradient of urea is required for the urine concentrating mechanism. This finding anticipates a new beginning of inquiries into the complicated relationships among mass, energy and information in bio-systems.

physics.bio-ph↗

arXiv2016

A general framework for microscopically reversible processes with memory

Statistical Mechanics deals with ensembles of microstates that are compatible with fixed constraints and that on average define a thermodynamic macrostate. The evolution of a small system is normally subjected to changing constraints and involve a stochastic dependence on previous events. Here, we develop a theory for reversible processes with memory that comprises equilibrium statistics and that converges to the same physics in the limit of independent events. This framework is based on the characterization of single phase-space pathways and is used to derive ensemble-average dynamics in stochastic systems driven by a protocol in the limit of no friction. We show that the state of a system depends on its history to the extent of attaining a one-to-one correspondence between states and pathways when memory covers all the previous events. Equilibrium appears as the consequence of exploring all pathways that connect two states by all procedures. This theory is useful to interpret single-molecule experiments in Biophysics and other fields in Nanoscience and an adequate platform for a general theory of irreversible processes.

cond-mat.stat-mech↗

arXiv2016

Energy dissipation in flows through curved spaces

Fluid dynamics in intrinsically curved geometries is encountered in many physical systems in nature, ranging from microscopic bio-membranes all the way up to general relativity at cosmological scales. Despite the diversity of applications, all of these systems share a common feature: the free motion of particles is affected by inertial forces originating from the curvature of the embedding space. Here we reveal a fundamental process underlying fluid dynamics in curved space: the free motion of fluids, in the complete absence of solid walls or obstacles, exhibits loss of energy due exclusively to the intrinsic curvature of space. We find that local sources of curvature generate viscous stresses as a result of the inertial forces. The curvature-induced viscous forces are shown to cause hitherto unnoticed and yet appreciable energy dissipation, which might play a significant role for a variety of physical systems involving fluid dynamics in curved spaces.

physics.flu-dyn↗

arXiv2015

Single Molecule Spectroscopy of Monomeric LHCII: Experiment and Theory

We derive approximate equations of motion for excited state dynamics of a multilevel open quantum system weakly interacting with light to describe fluorescence detected single molecule spectra. Based on the Frenkel exciton theory, we construct a model for the chlorophyll part of the LHCII complex of higher plants and its interaction with previously proposed excitation quencher in the form of the lutein molecule Lut 1. The resulting description is valid over a broad range of timescales relevant for single molecule spectroscopy, i.e. from ps to minutes. Validity of these equations is demonstrated by comparing simulations of ensemble and single-molecule spectra of monomeric LHCII with experiments. Using a conformational change of the LHCII protein as a switching mechanism, the intensity and spectral time traces of individual LHCII complexes are simulated, and the experimental statistical distributions are reproduced. Based on our model, it is shown that with reasonable assumptions about its interaction with chlorophylls, Lut 1 can act as an efficient fluorescence quencher in LHCII.

physics.bio-ph↗

arXiv2015

Rate equation model of phototransduction into the membranous disks of mouse rod cells

A theoretical model was developed to investigate the rod phototransduction process in the mouse. In particular, we explored the biochemical reactions of several chemical components that contribute to the signaling process into/around the membranous disks in the outer segments of the rod cells. We constructed a rate equation model incorporating the molecular crowding effects of rhodopsin according to experimental results, which may hinder the diffusion of molecules on the disk mem- brane. The present model could effectively reproduce and explain the mechanisms of the following phenomena observed in experiments. First, the activations and relaxation of the wild-type mouse rod cell progressed more slowly than those of mutant cells containing half the amount of rhodopsin on the disk membrane. Second, the strong photoactivated state of the cell was sustained for a longer period when the light stimuli were strong. Finally, the lifetime of photoactivation exhibited a logarithmic increase with increasing light strength given exposure to strong light stimuli.

physics.bio-ph↗

arXiv2018

Optimal occlusion uniformly partitions red blood cells fluxes within a microvascular network

In animals, gas exchange between blood and tissues occurs in narrow vessels, whose diameter is comparable to that of a red blood cell. Red blood cells must deform to squeeze through these narrow vessels, transiently blocking or occluding the vessels they pass through. Although the dynamics of vessel occlusion have been studied extensively, it remains an open question why microvessels need to be so narrow. We study occlusive dynamics within a model microvascular network: the embryonic zebrafish trunk. We show that pressure feedbacks created when red blood cells enter the finest vessels of the trunk act together to uniformly partition red blood cells through the microvasculature. Using mathematical models as well as direct observation, we show that these occlusive feedbacks are tuned throughout the trunk network to prevent the vessels closest to the heart from short-circuiting the network. Thus occlusion is linked with another open question of microvascular function: how are red blood cells delivered at the same rate to each micro-vessel? Our analysis shows that tuning of occlusive feedbacks increase the total dissipation within the network by a factor of 11, showing that uniformity of flows rather than minimization of transport costs may be prioritized by the microvascular network.

q-bio.TO↗

arXiv2016

A Path Integral Approach to Age Dependent Branching Processes

Age dependent population dynamics are frequently modeled with generalizations of the classic McKendrick-von Foerster equation. These are deterministic systems, and a stochastic generalization was recently reported in [1,2]. Here we develop a fully stochastic theory for age-structured populations via quantum field theoretical Doi-Peliti techniques. This results in a path integral formulation where birth and death events correspond to cubic and quadratic interaction terms. This formalism allows us to efficiently recapitulate the results in [1,2], exemplifying the utility of Doi-Peliti methods. Furthermore, we find that the path integral formulation for age-structured moments has an exact perturbative expansion that explicitly relates to the hereditary structure between correlated individuals. These methods are then generalized with a binary fission model of cell division.

physics.bio-ph↗

arXiv2016

The Poisson Boltzmann equation and the charge separation phenomenon at the silica-water interface: A holistic approach

The Poisson Boltzmann equation is known for its success in describing the Debye layer that arises from the charge separation phenomenon at the silica/water interface. However, by treating only the mobile ionic charges in the liquid, the Poisson Boltzmann equation accounts for only half of the electrical double layer, with the other half, the surface charge layer, being beyond its computational domain. In this work, we take a holistic approach to the charge separation phenomenon at the silica/water interface by treating, within a single computational domain, the electrical double layer that comprises both the mobile ions in the liquid and the surface charge density. The Poisson Nernst Planck equations are used as the rigorous basis for our methodology. The holistic approach has the advantage of being able to predict surface charge variations that arise either from the addition of salt and acid to the liquid, or from the decrease of the liquid channel width to below twice the Debye length. As the electrical double layer must be overall neutral, we use this constraint to derive both the form of the static limit of the Poisson Nernst Planck equations, as well as a global chemical potential that replaces the classical zeta potential as the boundary value for the PB equation, which can be re-derived from our formalism. We present several predictions of our theory that are beyond the framework of the PB equation alone, e.g., the surface capacitance and the so-called pK and pL values, the isoelectronic point at which the surface charge layer is neutralized, and the appearance of a Donnan potential that arises from the formation of an electrical double layer at the inlet regions of a nano-channel connected to the bulk reservoir. All theory predictions are shown to be in good agreement with the experimental observations.

cond-mat.soft↗

arXiv2017

On the perfomance of a photosystem II reaction centre-based photocell

The photosystem II reaction centre is the photosynthetic complex responsible for oxygen production on Earth. Its water splitting function is particularly favoured by the formation of a stable charge separated state via a pathway that starts at an accessory chlorophyll. Here we envision a photovoltaic device that places one of these complexes between electrodes and investigate how the mean current and its fluctuations depend on the microscopic interactions underlying charge separation in the pathway considered. Our results indicate that coupling to well resolved vibrational modes does not necessarily offer an advantage in terms of power output but can lead to photo-currents with suppressed noise levels characterizing a multi-step ordered transport process. Besides giving insight into the suitability of these complexes for molecular-scale photovoltaics, our work suggests a new possible biological function for the vibrational environment of photosynthetic reaction centres, namely, to reduce the intrinsic current noise for regulatory processes.

physics.bio-ph↗