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arXiv2016

Quantum nonlocality in the excitation energy transfer in the Fenna-Matthews-Olson complex

The Fenna-Matthews-Olson (FMO) complex - a pigment protein complex involved in photosynthesis in green sulfur bacteria - is remarkably efficient in transferring excitation energy from light harvesting antenna molecules to a reaction center. Recent experimental and theoretical studies suggest that quantum coherence and entanglement may play a role in this excitation energy transfer (EET). We examine whether bipartite quantum nonlocality, a property that expresses a stronger-than-entanglement form of correlation, exists between different pairs of chromophores in the FMO complex when modeling the EET by the hierarchically coupled equations of motion method. We compare the results for nonlocality with the amount of bipartite entanglement in the system. In particular, we analyze in what way these correlation properties are affected by different initial conditions. It is found that bipartite nonlocality only exists when the initial conditions are chosen in an unphysiological manner and probably is absent when considering the EET in the FMO complex in its natural habitat. It is also seen that nonlocality and entanglement behave quite differently in this system. In particular, for localized initial states, nonlocality only exists on a very short time scale and then drops to zero in an abrupt manner. As already known from previous studies, quantum entanglement between chromophore pairs on the other hand is oscillating and exponentially decaying and follow thereby a pattern more similar to the chromophore population dynamics. The abrupt disappearance of nonlocality in the presence of nonvanishing entanglement is a phenomenon we call nonlocality sudden death; a striking manifestation of the difference between these two types of correlations in quantum systems.

quant-ph↗

arXiv2016

Dose and dose-rate dependence of mutation frequency under long-term exposure - A new look at DDREF from WAM model -

We investigate the dose and dose-rate dependence of the mutation frequency caused by artificial radiations with Whack-A-Mole (WAM) model which we have recently proposed. In particular, we pay special attention to the case of long-term and low dose-rate exposure. The results indicate that the dose-rate dependence is successfully described with WAM model and it may replace the so-called DDREF, the concept of which has long been adopted to take account of the difference between the high dose-rate data and the low dose-rate ones. Basic properties of WAM model are discussed emphasizing the dose-rate dependence to demonstrate how the explicit dose-rate dependence built in the model plays a key role. By adopting the parameters that are determined to fit the mega mouse experiments, biological effects of long-term exposure to extremely low dose-rate radiation are discussed. In WAM model, the effects of the long-term exposure show a saturation property, which makes a clear distinction from the LNT hypothesis which predicts a linear increase of the effects with time.

physics.bio-ph↗

arXiv2015

A model of calcium-mediated coupling between membrane activity and clock gene expression in neurons of the suprachiasmatic nucleus

Rhythms in electrical activity in the membrane of cells in the suprachiasmatic nucleus (SCN) are crucial for the function of the circadian timing system, which is characterized by the expression of the so-called clock genes. Intracellular Ca$^{2+}$ ions seem to connect, at least in part, the electrical activity of SCN neurons with the expression of clock genes. In this paper, we introduce a simple mathematical model describing the linking of membrane activity to the transcription of one gene by means of a feedback mechanism based on the dynamics of intracellular calcium ions.

physics.bio-ph↗

arXiv2018

Phase-space analysis of large ODE systems using a low-dimensional conservation law

Simultaneous deterministic and weakly stochastic dynamics of multiple populations described by a large system of ODE's is considered in the phase space of population sizes and ODE's parameters. We show that many practically interesting problems can be formulated as a low-dimensional phase-space conservation law and solved either explicitly or with simple iterative methods. In particular, we consider: non-interacting populations with unbounded and logistic growth, populations with randomized and biased migration, populations competing for a resource, coexisting species, and populations with phase-space interactions. The method provides an alternative to Monte Carlo simulations and may be useful in the fast analysis of biological data and/or removal of deterministic trends.

math.DS↗

arXiv2015

Single-cell protein dynamics reproduce universal fluctuations in cell populations

Protein variability in single cells has been studied extensively in populations, but little is known about temporal protein fluctuations in a single cell over extended times. We present here traces of protein copy number measured in individual bacteria over multiple generations and investigate their statistical properties, comparing them to previously measured population snapshots. We find that temporal fluctuations in individual traces exhibit the same universal features as those previously observed in populations. Scaled fluctuations around the mean of each trace exhibit the same universal distribution shape as found in populations measured under a wide range of conditions and in two distinct microorganisms. Additionally, the mean and variance of the traces over time obey the same quadratic relation. Analyzing the temporal features of the protein traces in individual cells, reveals that within a cell cycle protein content increases as an exponential function with a rate that varies from cycle to cycle. This leads to a compact description of the protein trace as a 3-variable stochastic process - the exponential rate, the cell-cycle duration and the value at the cycle start - sampled once each cell cycle. This compact description is sufficient to preserve the universal statistical properties of the protein fluctuations, namely, the protein distribution shape and the quadratic relationship between variance and mean. Our results show that the protein distribution shape is insensitive to sub-cycle intracellular microscopic details and reflects global cellular properties that fluctuate between generations.

physics.bio-ph↗

arXiv2015

Voltage dependence of rate functions for Na+ channel inactivation within a membrane

The inactivation of a Na+ channel occurs when the activation of the charged S4 segment of domain DIV is followed by the binding of an intracellular hydrophobic motif which blocks conduction through the ion pore. The voltage dependence of Na+ channel inactivation is, in general, dependent on the rate functions of the S4 sensors of each of the domains DI to DIV. If the activation of a single voltage sensor that regulates the Na+ channel conductance is coupled to a two-stage inactivation process, the rate functions for inactivation and recovery from inactivation, as well as the time dependence of the Na+ current in terms of the variables m(t) and h(t), may be derived from a solution to the master equation for interdependent activation and inactivation. The rate functions have a voltage dependence that is consistent with the Hodgkin-Huxley empirically determined expressions, and exhibit saturation for both depolarized and hyperpolarized clamp potentials.

physics.bio-ph↗

arXiv2015

Formation of adhesion domains in stressed and confined membranes

The adhesion bonds connecting a lipid bilayer to an underlying surface may undergo a condensation transition resulting from an interplay between a short range attractive potential between them, and a long range fluctuation-induced potential of mean force. Here, we use computer simulations of a coarse-grained molecular model of supported lipid bilayers to study this transition in confined membranes, and in membranes subjected to a non-vanishing surface tension. Our results show that confinement may alter significantly the condensation transition of the adhesion bonds, whereas the application of surface tension has a very minor effect on it. We also investigate domain formation in membranes under negative tension which, in free membranes, causes enhancement of the amplitude of the membrane thermal undulations. Our results indicate that in supported membranes, this effect of a negative surface tension on the fluctuation spectrum is largely eliminated by the pressure resulting from the mixing entropy of the adhesion bonds.

cond-mat.soft↗

arXiv2015

Liquids that form due to dynamics of the molecules that depend on the local density

RNA molecules in living cells form what look like liquid droplets formed by liquid/liquid phase separation. But unlike the molecules in conventional phase separating mixtures, RNA molecules are transported by molecular motors that consume energy and so are out of equilibrium. Motivated by this we consider what sort of simple rules for the dynamics of model mRNA molecules lead to liquid/liquid phase separation. We find that dynamics that slow as the local density of molecules increases, drive the formation of liquids. We also look at the analogous separation of the two blocks of a block copolymer, in which the monomers of one block have dynamics that depend on the local density of monomers of that block. We find that this block condenses and separates from the monomers of the other block. This is a simple model of the out-of-equilibrium domain formation found in the chromatin in the nucleus of cells.

cond-mat.soft↗

arXiv2015

Transition State Theory Approach to Polymer Escape from a One Dimensional Potential Well

The rate of escape of an ideal bead-spring polymer in a symmetric double-well potential is calculated using transition state theory (TST) and the results compared with direct dynamical simulations. The minimum energy path of the transitions becomes flat and the dynamics diffusive for long polymers making the Kramers-Langer estimate poor. However, TST with dynamical corrections based on short time trajectories started at the transition state gives rate constant estimates that agree within a factor of two with the molecular dynamics simulations over a wide range of bead coupling constants and polymer lengths. The computational effort required by the TST approach does not depend on the escape rate and is much smaller than that required by molecular dynamics simulations.

cond-mat.soft↗

arXiv2016

Large deviations for two scale chemical kinetic processes

We formulate the large deviations for a class of two scale chemical kinetic processes motivated from biological applications. The result is successfully applied to treat a genetic switching model with positive feedbacks. The corresponding Hamiltonian is convex with respect to the momentum variable as a by-product of the large deviation theory. This property ensures its superiority in the rare event simulations compared with the result obtained by formal WKB asymptotics. The result is of general interest to understand the large deviations for multiscale problems.

math.PR↗

arXiv2015

Entropy, Ergodicity and Stem Cell Multipotency

Populations of mammalian stem cells commonly exhibit considerable cell-cell variability. However, the functional role of this diversity is unclear. Here, we analyze expression fluctuations of the stem cell surface marker Sca1 in mouse hematopoietic progenitor cells using a simple stochastic model and find that the observed dynamics naturally lie close to a critical state, thereby producing a diverse population that is able to respond rapidly to environmental changes. We propose an information-theoretic interpretation of these results that views cellular multipotency as an instance of maximum entropy statistical inference.

q-bio.CB↗

arXiv2015

Binding of transcription factors adapts to resolve information-energy trade-off

We examine the binding of transcription factors to DNA in terms of an information transfer problem. The input of the noisy channel is the biophysical signal of a factor bound to a DNA site, and the output is a distribution of probable DNA sequences at this site. This task involves an inherent tradeoff between the information gain and the energetics of the binding interaction - high binding energies provide higher information gain but hinder the dynamics of the system as factors are bound too tightly. We show that adaptation of the binding interaction towards increasing information transfer under a general energy constraint implies that the information gain per specific binding energy at each base-pair is maximized. We analyze hundreds of prokaryote and eukaryote transcription factors from various organisms to evaluate the discrimination energies. We find that, in accordance with our theoretical argument, binding energies nearly maximize the information gain per energy. This work suggests the adaptation of information gain as a generic design principle of molecular recognition systems.

q-bio.GN↗

arXiv2015

Non-linear irreversible thermodynamics of single-molecule experiments

Irreversible thermodynamics of single-molecule experiments subject to external constraining forces of a mechanical nature is presented. Extending Onsager's formalism to the non-linear case of systems under non-equilibrium external constraints, we are able to calculate the entropy production and the general non-linear kinetic equations for the variables involved. In particular, we analyze the case of RNA stretching protocols obtaining critical oscillations between different configurational states when forced by external means to remain in the unstable region of its free-energy landscape, as observed in experiments. We also calculate the entropy produced during these hopping events, and show how resonant phenomena in stretching experiments of single RNA macromolecules may arise. We also calculate the hopping rates using Kramer's approach obtaining a good comparison with experiments.

physics.bio-ph↗

arXiv2015

General formulation of Luria-Delbr{ü}ck distribution of the number of mutants

The Luria-Delbr{ü}ck experiment is a cornerstone of evolutionary theory, demonstrating the randomness of mutations before selection. The distribution of the number of mutants in this experiment has been the subject of intense investigation during the last 70 years. Despite this considerable effort, most of the results have been obtained under the assumption of constant growth rate, which is far from the experimental condition. We derive here the properties of this distribution for arbitrary growth function, for both the deterministic and stochastic growth of the mutants. The derivation we propose uses the number of wild type bacteria as the independent variable instead of time. The derivation is surprisingly simple and versatile, allowing many generalizations to be taken easily into account.

physics.bio-ph↗

arXiv2015

Seasonal Floquet states in a game-driven evolutionary dynamics

Mating preferences of many biological species are not constant but season-dependent. Within the framework of evolutionary game theory this can be modeled with two finite opposite-sex populations playing against each other following the rules that are periodically changing. By combining Floquet theory and the concept of quasi-stationary distributions, we reveal existence of metastable time-periodic states in the evolution of finite game-driven populations. The evolutionary Floquet states correspond to time-periodic probability flows in the strategy space which cannot be resolved within the mean-field framework. The lifetime of metastable Floquet states increases with the size $N$ of populations so that they become attractors in the limit $N \rightarrow \infty$.

q-bio.PE↗

arXiv2015

Topology, Geometry, and Stability: Protein Folding and Evolution

The protein folding problem must ultimately be solved on all length scales from the atomic up through a hierarchy of complicated structures. By analyzing the stability of the folding process using physics and mathematics, this paper shows that features without length scales, i.e. topological features, are potentially of central importance. Topology is a natural mathematical tool for the study of shape and we avail ourselves of that tool to examine the relationship between the amino acid sequence and the shapes of protein molecules. We apply what we learn to conjectures about their biological evolution.

physics.bio-ph↗

arXiv2015

Efficient monitoring of blood-stage infection in a malaria rodent model by the rotating-crystal magneto-optical method

Global research efforts have been focused on the simultaneous improvement of the efficiency and sensitivity of malaria diagnosis in resource-limited settings and for the active case detection of asymptomatic infections. A recently developed magneto-optical (MO) method allows the high-sensitivity detection of malaria pigment (hemozoin) crystals in blood via their magnetically induced rotational motion. The evaluation of the method using synthetic $β$-hematin crystals and P. falciparum in vitro cultures implies its potential for in-field diagnosis. Here, we study the performance of the method in monitoring the in vivo onset and progression of the blood stage infection using a malaria mouse model. We found that the MO method can detect the first generation of intraerythrocytic parasites at the ring stage 61-66 hours after sporozoite injection demonstrating better sensitivity than light microscopy and flow cytometry. MO measurements performed after treatment of severe P. berghei infections show that the clearance period of hemozoin in mice is approx. 5 days which indicates the feasibility of the detection of later reinfections as well. Being label and reagent-free, cost-effective and rapid, together with the demonstrated sensitivity, we believe that the MO method is a suitable candidate for in-depth clinical evaluation in endemic settings.

physics.bio-ph↗

arXiv2015

Influences of quantum mechanically mixed electronic and vibrational pigment states in 2D electronic spectra of photosynthetic systems: Strong electronic coupling cases

In 2D electronic spectroscopy studies, long-lived quantum beats have recently been observed in photosynthetic systems, and it has been suggested that the beats are produced by quantum mechanically mixed electronic and vibrational states. Concerning the electronic-vibrational quantum mixtures, the impact of protein-induced fluctuations was examined by calculating the 2D electronic spectra of a weakly coupled dimer with vibrational modes in the resonant condition [J. Chem. Phys. 142, 212403 (2015)]. This analysis demonstrated that quantum mixtures of the vibronic resonance are rather robust under the influence of the fluctuations at cryogenic temperatures, whereas the mixtures are eradicated by the fluctuations at physiological temperatures. However, this conclusion cannot be generalized because the magnitude of the coupling inducing the quantum mixtures is proportional to the inter-pigment coupling. In this study, we explore the impact of the fluctuations on electronic-vibrational quantum mixtures in a strongly coupled dimer. with an off-resonant vibrational mode. Toward this end, we calculate electronic energy transfer (EET) dynamics and 2D electronic spectra of a dimer that corresponds to the most strongly coupled bacteriochlorophyll molecules in the Fenna-Matthews-Olson complex in a numerically accurate manner. The quantum mixtures are found to be robust under the exposure of protein-induced fluctuations at cryogenic temperatures, irrespective of the resonance. At 300 K, however, the quantum mixing is disturbed more strongly by the fluctuations, and therefore, the beats in the 2D spectra become obscure even in a strongly coupled dimer with a resonant vibrational mode. Further, the overall behaviors of the EET dynamics are demonstrated to be dominated by the environment and coupling between the 0-0 vibronic transitions as long as the Huang-Rhys factor of the vibrational mode is small.

physics.bio-ph↗