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arXiv2014

Analytic stability analysis of three-component self-regulatory genetic circuit

A self-regulatory genetic circuit, where a protein acts as a positive regulator of its own production, is known to be a simplest form of biological network with a positive feedback loop. Although at least three components, DNA, RNA, and the protein, are required to form such a circuit, the stability analysis of fixed points of the self-regulatory circuit has been performed only after reducing the system into to a two-component system consisting of RNA and protein only, assuming a fast equilibration of the DNA component. Here, the stability of fixed points of the three-component positive feedback loop is analyzed by obtaining eigenvalues of full three dimensional Hessian matrix. In addition to rigorously identifying the stable fixed points and the saddle points, detailed information can be obtained, such as the number of positive eigenvalues near a saddle point. In particular, complex eigenvalues is shown to exist for sufficiently slow binding and unbinding of the auto-regulatory transcription factor to DNA, leading to oscillatory convergence to the steady states, a novel feature unseen in the two-dimensional analysis.

physics.bio-ph↗

arXiv2015

State Transitions and Decoherence in the Avian Compass

The radical pair model has been successful in explaining behavioral characteristics of the geomagnetic compass believed to underlie the navigation capability of certain avian species. In this study, the spin dynamics of the radical pair model and decoherence therein are interpreted from a microscopic state transition point of view. This helps to elucidate the interplay between the hyperfine and Zeeman interactions that enables the avian compass, and the distinctive effects of nuclear and environmental decoherence on it. Using a quantum information theoretic quantifier of coherence, we find that nuclear decoherence induces new structure in the spin dynamics without materially affecting the compass action; environmental decoherence, on the other hand, completely disrupts it.

physics.bio-ph↗

arXiv2014

Analytical models of icosahedral shells for 3D optical imaging of viruses

A modulated icosahedral shell with an inclusion is a concise description of many viruses, including recently-discovered large double-stranded DNA ones. Many X-ray scattering patterns of such viruses show major polygonal fringes, which can be reproduced in image reconstruction with a homogeneous icosahedral shell. A key question regarding a low-resolution reconstruction is how to introduce further changes to the 3D profile in an efficient way with only a few parameters. Here, we derive and compile different analytical models of such an object with consideration of practical optical setups and typical structures of such viruses. The benefits of such models include 1) inherent filtering and suppressing different numerical errors of a discrete grid, 2) providing a concise and meaningful set of descriptors for feature extraction in high-throughput classification/sorting and higher-resolution cumulative reconstructions, 3) disentangling (physical) resolution from (numerical) discretization step and having a vector graphics format for visualization or further analysis at arbitrary scales, 4) eliminating the phase-retrieval step and enforcing transparent, relevant, and controlled type/level of a-priori information in a real-space formulation, and 5) evaluating the reflections and surface resonances of an icosahedral object, and hence corrections for the common scattering model.

physics.bio-ph↗

arXiv2014

Coherent band pathways between knots and links

We categorise coherent band (aka nullification) pathways between knots and 2-component links. Additionally, we characterise the minimal coherent band pathways (with intermediates) between any two knots or 2-component links with small crossing number. We demonstrate these band surgeries for knots and links with small crossing number. We apply these results to place lower bounds on the minimum number of recombinant events separating DNA configurations, restrict the recombination pathways and determine chirality and/or orientation of the resulting recombinant DNA molecules.

math.GT↗

arXiv2014

A fluid dynamics multidimensional model of biofilm growth: stability, influence of environment and sensitivity

In this article, we study in details the fluid dynamics system proposed in Clarelli et al (2013) to model the formation of cyanobacteria biofilms. After analyzing the linear stability of the unique non trivial equilibrium of the system, we introduce in the model the influence of light and temperature, which are two important factors for the development of cyanobacteria biofilm. Since the values of the coefficients we use for our simulations are estimated through information found in the literature, some sensitivity and robustness analyses on these parameters are performed. All these elements enable us to control and to validate the model we have already derived and to present some numerical simulations in the 2D and the 3D cases.

physics.flu-dyn↗

arXiv2014

Combined collapse by bridging and self-adhesion in a prototypical polymer model inspired by the bacterial nucleoid

Recent experimental results suggest that the E. coli chromosome feels a self-attracting interaction of osmotic origin, and is condensed in foci by bridging interactions. Motivated by these findings, we explore a generic modeling framework combining solely these two ingredients, in order to characterize their joint effects. Specifically, we study a simple polymer physics computational model with weak ubiquitous short-ranged self attraction and stronger sparse bridging interactions. Combining theoretical arguments and simulations, we study the general phenomenology of polymer collapse induced by these dual contributions, in the case of regularly-spaced bridging. Our results distinguish a regime of classical Flory-like coil-globule collapse dictated by the interplay of excluded volume and attractive energy and a switch-like collapse where bridging interaction compete with entropy loss terms from the looped arms of a star-like rosette. Additionally, we show that bridging can induce stable compartmentalized domains. In these configurations, different "cores" of bridging proteins are kept separated by star-like polymer loops in an entropically favorable multi-domain configuration, with a mechanism that parallels micellar polysoaps. Such compartmentalized domains are stable, and do not need any intra-specific interactions driving their segregation. Domains can be stable also in presence of uniform attraction, as long as the uniform collapse is above its theta point.

cond-mat.soft↗

arXiv2014

A Transform Method of a Force Curve Obtained by Surface Force Apparatus to the Density Distribution of a Liquid on a Surface: An Improved Version

We propose a transform method from a force curve obtained by a surface force apparatus (SFA) to a density distribution of a liquid on a surface of the SFA probe. (We emphasize that the transform method is a theory for the experiment.) In the method, two-body potential between the SFA probe and the solvent sphere is modeled as the soft attractive potential with rigid wall. The model potential is more realistic compared with the rigid potential applied in our earlier work. The introduction of the model potential is the improved point of the present transform method. The transform method is derived based on the statistical mechanics of a simple liquid where the simple liquid is an ensemble of small spheres. To derive the transform method, Kirkwood superposition approximation is used. It is found that the transformation can be done by a sequential computation. It is considered that the solvation structure can be obtained more precisely by using the improved transform method.

physics.chem-ph↗

arXiv2014

Slightly broken icosahedral symmetry advances Thomson problem

To advance Thomson problem we generalize physical principles suggested by Caspar and Klug (CK) to model icosahedral capsids. Proposed simplest distortions of the CK spherical arrangements yield new-type trial structures very close to the lowest energy ones. In the region 600<N<1000, where N is the number of particles in the structure, we found 40 new spherical crystals with the lowest ever seen energies and curvature-induced topological defects being not the well-known elongated scars but flatten pentagons. These crystals have N values prohibited in the CK model and demonstrate a new way to combine the local hexagonal order and spherical geometry.

cond-mat.soft↗

arXiv2014

Topology Regulation during Replication of the Kinetoplast DNA

We study theoretically the replication of Kinetoplast DNA consisting of several thousands separate mini-circles found in organisms of the class Kinetoplastida. When the cell is not actively dividing these are topologically connected in a marginally linked network of rings with only one connected component. During cell division each mini-circle is removed from the network, duplicated and then re-attached, along with its progeny. We study this process under the hypothesis that there is a coupling between the topological state of the mini-circles and the expression of genetic information encoded on them, leading to the production of Topoisomerase. This model describes a self-regulating system capable of full replication that reproduces several previous experimental findings. We find that the fixed point of the system depends on a primary free parameter of the model: the ratio between the rate of removal of mini-circles from the network (R) and their (re)attachment rate (A). The final topological state is found to be that of a marginally linked network structure in which the fraction of mini-circles linked to the largest connected component approaches unity as R/A decreases. Finally we discuss how this may suggest an evolutionary trade-off between the speed of replication and the accuracy with which a fully topologically linked state is produced.

cond-mat.soft↗

arXiv2014

A Tandem Cell for Nanopore-based DNA Sequencing with Exonuclease

A tandem cell is proposed for DNA sequencing in which an exonuclease enzyme cleaves bases (mononucleotides) from a strand of DNA for identification inside a nanopore. It has two nanopores and three compartments with the structure [cis1, upstream nanopore (UNP), trans1=cis2, downstream nanopore (DNP), trans2]. The exonuclease is attached to the exit side of UNP in trans1/cis2. A cleaved base cannot regress into cis1 because of the remaining DNA strand in UNP. A profiled electric field over DNP with positive and negative components slows down base translocation through DNP. The proposed structure is modeled with a Fokker-Planck equation and a piecewise solution presented. Results from the model indicate that with probability approaching 1 bases enter DNP in their natural order, are detected without any loss, and do not regress into DNP after progressing into trans2. Sequencing efficiency with a tandem cell would then be determined solely by the level of discrimination among the base types inside DNP.

q-bio.BM↗

arXiv2014

Model for bidirectional movement of cytoplasmic dynein

Cytoplasmic dynein exhibits a directional processive movement on microtubule filaments and is known to move in steps of varying length based on the number of ATP molecules bound to it and the load that it carries. It is experimentally observed that dynein takes occasional backward steps and the frequency of such backward steps increases as the load approaches the stall force. Using a stochastic process model, we investigate the bidirectional movement of single head of a dynein motor. The probability for backward step is implemented based on Crook's fluctuation theorem of non-equilibrium statistical mechanics. We find that the movement of dynein motor is characterized with negative velocity implying backward motion beyond stall force. We observe that the motor moves backward for super stall forces by hydrolyzing the ATP exactly the same way as it does while moving forward for sub stall forces.

physics.bio-ph↗

arXiv2014

Can Natural Sunlight Induce Coherent Exciton Dynamics?

Excitation of a model photosynthetic molecular aggregate by incoherent sunlight is systematically examined. For a closed system, the excited state coherence induced by the sunlight oscillates with an average amplitude that is inversely proportional to the excitonic gap, and reaches a stationary amplitude that depends on the temperature and coherence time of the radiation field. For an open system, the light-induced dynamical coherence relaxes to a static coherence determined by the non-canonical thermal distribution resulting from the entanglement with the phonon bath. The decay of the excited state population to the common ground state establishes a non-equilibrium steady-state flux driven by the sunlight, and it defines a time window to observe the transition from dynamical to static coherence. For the parameters relevant to photosynthetic systems, the exciton dynamics initiated by the sunlight exhibits a non-negligible amount of dynamical coherence (quantum beats) on the sub-picosecond timescale; however, this sub-picosecond time-scale is long enough for light-harvesting systems to establish static coherence, which plays a crucial role in efficient energy transfer. Further, a relationship is established between the non-equilibrium steady-state induced by the sunlight and the coherent dynamics initiated from the ground state by a laser $δ$-pulse, thereby making a direct connection between incoherent sunlight excitation and ultrafast spectroscopy.

physics.chem-ph↗

arXiv2014

Theory of the Transmission of Infection in the Spread of Epidemics: Interacting Random Walkers with and without Confinement

A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a Smoluchowski equation in 2n-dimensional space that combines diffusion with confinement of each animal to its particular home range. An additional (reaction) term that comes into play when the animals are in close proximity describes the process of infection. Analytic solutions are obtained, confirmed by numerical procedures, and shown to predict a surprising effect of confinement. The effect is that infection spread has a non-monotonic dependence on the diffusion constant and/or the extent of the attachment of the animals to the home ranges. Optimum values of these parameters exist for any given distance between the attractive centers. Any change from those values, involving faster/slower diffusion or shallower/steeper confinement, hinders the transmission of infection. A physical explanation is provided by the theory. Reduction to the simpler case of no home ranges is demonstrated. Effective infection rates are calculated and it is shown how to use them in complex systems consisting of dense populations.

physics.bio-ph↗

arXiv2014

Noise Assisted Excitation Energy Transfer in a Linear Toy Model of a Selectivity Filter Backbone Strand

In this paper, we investigate the effect of noise and disorder on the efficiency of excitation energy transfer (EET) in a $N=5$ sites linear chain with "static" dipole-dipole couplings. In fact, here, the disordered chain is a toy model for one strand of the selectivity filter backbone in ion channels. It is recently discussed that the presence of quantum coherence in the selectivity filter is possible and can play a role in mediating ion-conduction and ion-selectivity in the selectivity filter. The question is "how a quantum coherence can be effective in such structures while the environment of the channel is dephasing (i.e. noisy)?" Basically, we expect that the presence of the noise should have a destructive effect in the quantum transport. In fact, we show that such expectation is valid for ordered chains. However, our results indicate that introducing the dephasing in the disordered chains leads to the weakening of the localization effects, arising from the randomness, and then increases the efficiency of quantum energy transfer. Thus, the presence of noise is crucial for the enhancement of EET efficiency in disordered chains. We also show that the contribution of both classical and quantum mechanical effects are required to improve the speed of energy transfer along the chain. Our analysis may help for better understanding of fast and efficient functioning of the selectivity filters in ion channels.

cond-mat.dis-nn↗

arXiv2014

Fluorescence Resonance Energy Transfer (FRET) sensor

The applications of Fluorescence resonance energy transfer (FRET) have expanded tremendously in the last 25 years, and the technique has become a staple technique in many biological and biophysical fields. FRET can be used as spectroscopic ruler in various areas such as structural elucidation of biological molecules and their interactions, in vitro assays, in vivo monitoring in cellular research, nucleic acid analysis, signal transduction, light harvesting, and metallic nanomaterials etc. Based on the mechanism of FRET a variety of novel chemical sensors and Biosensors have been developed. This review highlights the recent applications of sensitive and selective ratiometric FRET based sensors.

physics.bio-ph↗

arXiv2014

Neural computation at the thermal limit

Although several measurements and analyses support the idea that the brain is energy-optimized, there is one disturbing, contradictory observation: In theory, computation limited by thermal noise can occur as cheaply as ~$2.9\cdot 10^{-21}$ joules per bit (kTln2). Unfortunately, for a neuron the ostensible discrepancy from this minimum is startling - ignoring inhibition the discrepancy is $10^7$ times this amount and taking inhibition into account $>10^9$. Here we point out that what has been defined as neural computation is actually a combination of computation and neural communication: the communication costs, transmission from each excitatory postsynaptic activation to the S4-gating-charges of the fast Na+ channels of the initial segment (fNa's), dominate the joule-costs. Making this distinction between communication to the initial segment and computation at the initial segment (i.e., adding up of the activated fNa's) implies that the size of the average synaptic event reaching the fNa's is the size of the standard deviation of the thermal noise. Moreover, defining computation as the addition of activated fNa's, yields a biophysically plausible mechanism for approaching the desired minimum. This mechanism, requiring something like the electrical engineer's equalizer (not much more than the action potential generating conductances), only operates at threshold. This active filter modifies the last few synaptic excitations, providing barely enough energy to allow the last sub-threshold gating charge to transport. That is, the last, threshold-achieving S4-subunit activation requires an energy that matches the information being provided by the last few synaptic events, a ratio that is near kTln2 joules per bit.

q-bio.NC↗

arXiv2014

Travelling wave solutions of the reaction-diffusion mathematical model of glioblastoma growth: An Abel equation based approach

We consider quasi-stationary (travelling wave type) solutions to a nonlinear reaction-diffusion equation with arbitrary, autonomous coefficients, describing the evolution of glioblastomas, aggressive primary brain tumors that are characterized by extensive infiltration into the brain and are highly resistant to treatment. The second order nonlinear equation describing the glioblastoma growth through travelling waves can be reduced to a first order Abel type equation. By using the integrability conditions for the Abel equation several classes of exact travelling wave solutions of the general reaction-diffusion equation that describes glioblastoma growth are obtained, corresponding to different forms of the product of the diffusion and reaction functions. The solutions are obtained by using the Chiellini lemma and the Lemke transformation, respectively, and the corresponding equations represent generalizations of the classical Fisher--Kolmogorov equation. The biological implications of two classes of solutions are also investigated by using both numerical and semi-analytical methods for realistic values of the biological parameters.

q-bio.TO↗

arXiv2014

Hydration of Kr(aq) in dilute and concentrated solutions

Molecular dynamics simulations of water with both multi-Kr and single Kr atomic solutes are carried out to implement quasi-chemical theory evaluation of the hydration free energy of Kr(aq). This approach obtains free energy differences reflecting Kr-Kr interactions at higher concentrations. Those differences are negative changes in hydration free energies with increasing concentrations at constant pressure. The changes are due to a slight reduction of packing contributions in the higher concentration case. The observed Kr-Kr distributions, analyzed with the extrapolation procedure of Krüger, \emph{et al.}, yield a modestly attractive osmotic second virial coefficient, $B_2\approx -60~\mathrm{cm}^3$/mol. The thermodynamic analysis interconnecting these two approaches shows that they are closely consistent with each other, providing support for both.

physics.chem-ph↗