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arXiv2015

The role of membrane curvature for the wrapping of nanoparticles

Cellular internalization of nanoparticles requires the full wrapping of the nanoparticles by the cell membrane. This wrapping process can occur spontaneously if the adhesive interactions between the nanoparticles and the membranes are sufficiently strong to compensate for the cost of membrane bending. In this article, we show that the membrane curvature prior to wrapping plays a key role for the wrapping process, besides the size and shape of the nanoparticles that have been investigated in recent years. For membrane segments that initially bulge away from nanoparticles by having a mean curvature of the same sign as the mean curvature of the particle surface, we find strongly stable partially wrapped states that can prevent full wrapping. For membrane segments that initially bulge towards the nanoparticles, in contrast, partially wrapped states can constitute a significant energetic barrier for the wrapping process.

q-bio.SC↗
arXiv2015

Wavelet-Based Compression and Peak Detection Method for the Experimentally Estimation of Microtubules Dynamic Instability Parameters Identified in Three States

Recent studies has revealed that Microtubules (MTs) exhibit three transition states of growth, shrinkage and pause. In this paper, we first introduce a three states random evolution model as a framework for studying MTs dynamics in three transition states of growth, pause and shrinkage. Then, we introduce a non-traditional stack run encoding scheme with 5 symbols for detecting transition states as well as to encode MT experimental data. The peak detection is carried out in the wavelet domain to effectively detect these three transition states. One of the added advantages of including peak information while encoding being that it enables to detect the peaks efficiently and encodes them simultaneously in the wavelet domain without having the need to do further processing after the decoding stage. Experimental results show that using this form of non-traditional stack run encoding has better compression and reconstruction performance as opposed to traditional stack run encoding and run length encoding schemes. Parameters for MTs modeled in the three states are estimated and is shown to closely approximate original MT data for lower compression rates. As the compression rate increases, we may end up throwing away details that are required to detect transition states of MTs. Thus, choosing the right compression rate is a trade-off between admissible level of error in signal reconstruction, its parameter estimation and considerable rate of compression of MT data.

q-bio.SC↗
arXiv2015

Actin Remodeling and Polymerization Forces Control Dendritic Spine Morphology

Dendritic spines are small membranous structures that protrude from the neuronal dendrite. Each spine contains a synaptic contact site that may connect its parent dendrite to the axons of neighboring neurons. Dendritic spines are markedly distinct in shape and size, and certain types of stimulation prompt spines to evolve, in fairly predictable fashion, from thin nascent morphologies to the mushroom-like shapes associated with mature spines. This striking progression is coincident with the (re)configuration of the neuronal network during early development, learning and memory formation, and has been conjectured to be part of the machinery that encodes these processes at the scale of individual neuronal connections. It is well established that the structural plasticity of spines is strongly dependent upon the actin cytoskeleton inside the spine. A general framework that details the precise role of actin in directing the transitions between the various spine shapes is lacking. We address this issue, and present a quantitative, model-based scenario for spine plasticity validated using realistic and physiologically relevant parameters. Our model points to a crucial role for the actin cytoskeleton. In the early stages of spine formation, the interplay between the elastic properties of the spine membrane and the protrusive forces generated in the actin cytoskeleton propels the incipient spine. In the maturation stage, actin remodeling in the form of the combined dynamics of branched and bundled actin is required to form mature, mushroom-like spines. Our model identifies additional factors that plausibly aid the stabilization and maintenance of spine morphology. Taken together, our model provides unique insights into the fundamental role of actin remodeling and polymerization forces during spine formation and maturation.

physics.bio-ph↗
arXiv2018

Formalized Quantum Stochastic Processes and Hidden Quantum Models with Applications to Neuron Ion Channel Kinetics

A new class of formal latent-variable stochastic processes called hidden quantum models (HQM's) is defined in order to clarify the theoretical foundations of ion channel signal processing. HQM's are based on quantum stochastic processes which formalize time-dependent observation. They allow the calculation of autocovariance functions which are essential for frequency-domain signal processing. HQM's based on a particular type of observation protocol called independent activated measurements are shown to to be distributionally equivalent to hidden Markov models yet without an underlying physical Markov process. Since the formal Markov processes are non-physical, the theory of activated measurement allows merging energy-based Eyring rate theories of ion channel behavior with the more common phenomenological Markov kinetic schemes to form energy-modulated quantum channels. Using the simplest quantum channel model consistent with neuronal membrane voltage-clamp experiments, activation eigenenergies are calculated for the Hodgkin-Huxley K+ and Na+ ion channels. It is also shown that maximizing entropy under constrained activation energy yields noise spectral densities approximating $S(f) \sim 1/f^α$, thus offering a biophysical explanation for the ubiquitous $1/f$-type in neurological signals.

q-bio.SC↗
arXiv2015

Common basis for cellular motility

Motility is characteristic of life, but a common basis for movement has remained to be identified. Diverse systems in motion shift between two states depending on interactions that turnover at the rate of an applied cycle of force. Although one phase of the force cycle terminates the decay of the most recent state, continuation of the cycle of force regenerates the original decay process in a recursive cycle. By completing a cycle, kinetic energy is transformed into probability of sustaining the most recent state and the system gains a frame of reference for discrete transitions having static rather than time-dependent probability. The probability of completing a recursive cycle is computed with a Markov chain comprised of two equilibrium states and a kinetic intermediate. Given rate constants for the reactions, a random walk reproduces bias and recurrence times of walking motor molecules and bacterial flagellar switching with unrivaled fidelity.

q-bio.SC↗
arXiv2015

Cytoplasmic flows as signatures for the mechanics of mitotic positioning

The proper positioning of the mitotic spindle is crucial for asymmetric cell division and generating cell diversity during development. Proper position in the single-cell embryo of Caenorhabditis elegans is achieved initially by the migration and rotation of the pronuclear complex (PNC) and its two associated centrosomal arrays of microtubules (MTs). We present here the first systematic theoretical study of how these $O(1000)$ centrosomal microtubules (MTs) interact through the immersing cytoplasm, the cell periphery and PNC, and with each other, to achieve proper position. This study is made possible through our development of a highly efficient and parallelized computational framework that accounts explicitly for long-ranged hydrodynamic interactions (HIs) between the MTs, while also capturing their flexibility, dynamic instability, and interactions with molecular motors and boundaries. First, we show through direct simulation that previous estimates of the PNC drag coefficient, based on either ignoring or partially including HIs, lead to misprediction of the active forces and time-scales of migration. We then directly study the dynamics of PNC migration under various force-transduction models, including the pushing or pulling of MTs at the cortex, and the pulling of MTs by cytoplasmically-bound force generators. While achieving proper position and orientation on physiologically reasonable time-scales does not uniquely choose a model, we find that each model produces a different signature in its induced cytoplasmic flow and MT conformations. We suggest then that cytoplasmic flows and MT conformations can be used to differentiate between mechanisms and to determine their contribution to the migration process.

physics.bio-ph↗
arXiv2016

Ultrasensitivity and sharp threshold theorems for multisite systems

We study the ultrasensitivity of multisite binding processes where ligand molecules can bind to several binding sites, considering more particularly recent models involving complex chemical reactions in phosphorylation systems such as allosteric phosphorylation processes, or substrate-catalyst chain reactions and nucleosome mediated cooperativity. New statistics based formulas for the Hill coefficient and the effective Hill coefficient are provided and necessary conditions for a system to be ultrasensitive are exhibited. We then assume that the binding process is described by a density dependent birth and death process. We provide precise large deviation results for the steady state distribution of the process, and show that switch-like ultrasensitive responses are strongly related to the multi-stability of the associated dynamical system. Ultrasensitivity occurs if and only if the entropy of the dynamical system has more than one global minimum for some critical ligand concentration. In this case, the Hill coefficient is proportional to the number of binding sites, and the systems is highly ultrasensitive. We also discuss the interpretation of an extension $I_q$ of the effective Hill coefficient $I_{0.9}$ for which we recommend the computation of a broad range of values of $q$ instead of just the standard one corresponding to the 10% to 90% variation in the dose-response. It is shown that this single choice can sometimes mislead the conclusion by not detecting ultrasensitivity. This new approach allows a better understanding of multisite ultrasensitive systems and provides new tools for the design of such systems.

q-bio.SC↗
arXiv2015

Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella

Axonemal dyneins are the molecular motors responsible for the beating of cilia and flagella. These motors generate sliding forces between adjacent microtubule doublets within the axoneme, the motile cytoskeletal structure inside the flagellum. To create regular, oscillatory beating patterns, the activities of the axonemal dyneins must be coordinated both spatially and temporally. It is thought that coordination is mediated by stresses or strains that build up within the moving axoneme, but it is not known which components of stress or strain are involved, nor how they feed back on the dyneins. To answer this question, we used isolated, reactivate axonemes of the unicellular alga Chlamydomonas as a model system. We derived a theory for beat regulation in a two-dimensional model of the axoneme. We then tested the theory by measuring the beat waveforms of wild type axonemes, which have asymmetric beats, and mutant axonemes, in which the beat is nearly symmetric, using high-precision spatial and temporal imaging. We found that regulation by sliding forces fails to account for the measured beat, due to the short lengths of Chlamydomonas cilia. We found that regulation by normal forces (which tend to separate adjacent doublets) cannot satisfactorily account for the symmetric waveforms of the mbo2 mutants. This is due to the model's failure to produce reciprocal inhibition across the axes of the symmetrically beating axonemes. Finally, we show that regulation by curvature accords with the measurements. Unexpectedly, we found that the phase of the curvature feedback indicates that the dyneins are regulated by the dynamic (i.e. time-varying) component of axonemal curvature, but not by the static one. We conclude that a high-pass filtered curvature signal is a good candidate for the signal that feeds back to coordinate motor activity in the axoneme.

physics.bio-ph↗
arXiv2015

Statistical Thermodynamic Foundation for the Origin and Evolution of Life

In this paper we review and extend our earlier recent work on thermostated systems. A description of nano-biological systems by Markov chains in coordinate space in the strongly overdamped limit is presented. Characterization of the most probable path is given and a new formula for the probability of this special path is provided from recursion formulae. The deterministic limit is derived and the significance of Lagrange multipliers introduced when constructing the most probable path is elucidated. The characterization of the generation of path entropy by the most probable path is given an equivalent interpretation relating to the rate of entropy production by the most probable path. The paper concludes with an account of the biological implications. Here we address why the origin of life and its subsequent evolution took place, not the particular chemical details of how it happened.

q-bio.SC↗
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↗
arXiv2015

Modelling the Role of Nitric Oxide in Cerebral Autoregulation

Malfunction of the system which regulates the bloodflow in the brain is a major cause of stroke and dementia, costing many lives and many billions of pounds each year in the UK alone. This regulatory system, known as cerebral autoregulation, has been the subject of much experimental and mathematical investigation yet our understanding of it is still quite limited. One area in which our understanding is particularly lacking is that of the role of nitric oxide, understood to be a potent vasodilator. The interactions of nitric oxide with the better understood myogenic response remain un-modelled and poorly understood. In this thesis we present a novel model of the arteriolar control mechanism, comprising a mixture of well-established and new models of individual processes, brought together for the first time. We show that this model is capable of reproducing experimentally observed behaviour very closely and go on to investigate its stability in the context of the vasculature of the whole brain. In conclusion we find that nitric oxide, although it plays a central role in determining equilibrium vessel radius, is unimportant to the dynamics of the system and its responses to variation in arterial blood pressure. We also find that the stability of the system is very sensitive to the dynamics of Ca$^{2+}$ within the muscle cell, and that self-sustaining Ca$^{2+}$ waves are not necessary to cause whole-vessel radius oscillations consistent with vasomotion.

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arXiv2016

Reaction Diffusion patterns in Pseudoplatystoma fishes

This paper studies how patterns derived from a system of reaction-diffusion equations may vary significantly depending upon boundary and initial conditions, as well as in the spatial dependence of the coefficients involved. From an extensive numerical study of the BVAM model, we demonstrate that the geometric pattern of a reaction-diffusion system is not uniquely determined by the value of the parameters in the equation. From this result, we suggest that the variability of patterns among individuals of the same species may have its roots in this sensitivity. Furthermore, this study analyzes briefly how the inclusion of the advection and the space dependency in the parameters of the model influences the forms of a specific pattern. The results of this study are compared to the skin patterns that appear in Pseudoplatystom} fishes.

q-bio.SC↗
arXiv2016

Catch bond mechanism in Dynein motor driven collective transport

Recent experiments have demonstrated that dynein motor exhibits catch bonding behaviour, in which the unbinding rate of a single dynein decreases with increasing force, for a certain range of force. Motivated by these experiments, we propose a model for catch bonding in dynein using a threshold force bond deformation (TFBD) model wherein catch bonding sets in beyond a critical applied load force. We study the effect of catch bonding on unidirectional transport properties of cellular cargo carried by multiple dynein motors within the framework of this model. We find catch bonding can result in dramatic changes in the transport properties, which are in sharp contrast to kinesin driven unidirectional transport, where catch bonding is absent. We predict that, under certain conditions, the average velocity of the cellular cargo can actually increase as applied load is increased. We characterize the transport properties in terms of a velocity profile phase plot in the parameter space of the catch bond strength and the stall force of the motor. This phase plot yields predictions that may be experimentally accessed by suitable modifications of motor transport and binding properties. Our work necessitates a reexamination of existing theories of collective bidirectional transport of cellular cargo where the catch bond effect of dynein described in this paper is expected to play a crucial role.

physics.bio-ph↗
arXiv2016

A geometric invariant for the study of planar curves and its application to spiral tip meander

Planar curves with periodically varying curvature arise in the natural sciences as the result of a wide variety of periodic processes. The total curvature of a periodic arc in such curves constrains their symmetry. It is shown how the total curvature can be computed without reparameterizing the curve to unit speed. The use of the total curvature of the periodic arcs is demonstrated through a series of four examples from various branches of science. Insights gained from these examples are applied to improve the modeling of spiral wave meander.

q-bio.SC↗
arXiv2016

Automated image segmentation and division plane detection in single live Staphylococcus aureus cells

Staphylococcus aureus is a coccal bacterium, which divides by binary fission. After division the cells remain attached giving rise to small clusters, with a characteristic 'bunch of grapes' morphology. S. aureus is an important human pathogen and this, combined with the increasing prevalence of antibiotic-resistant strains, such as Methicillin Resistant S. aureus (MRSA), make it an excellent subject for studies of new methods of antimicrobial action. Many antibiotics, such as penicillin, prevent S. aureus cell division and so an understanding of this fundamental process may pave the way to the identification of novel drugs. We present here a novel image analysis framework for automated detection and segmentation of cells in S. aureus clusters, and identification of their cell division planes. We demonstrate the technique on GFP labelled EzrA, a protein that localises to a mid-cell plane during division and is involved in regulation of cell size and division. The algorithms may have wider applicability in detecting morphologically complex structures of fluorescently-labelled proteins within cells in other cell clusters.

q-bio.SC↗
arXiv2016

Allosteric control in icosahedral capsid assembly

During the lifecycle of a virus, viral proteins and other components self-assemble to form a symmetric protein shell called a capsid. This assembly process is subject to multiple competing constraints, including the need to form a thermostable shell while avoiding kinetic traps. It has been proposed that viral assembly satisfies these constraints through allosteric regulation, including the interconversion of capsid proteins among conformations with different propensities for assembly. In this article we use computational and theoretical modeling to explore how such allostery affects the assembly of icosahedral shells. We simulate assembly under a wide range of protein concentrations, protein binding affinities, and two different mechanisms of allosteric control. We find that, above a threshold strength of allosteric control, assembly becomes robust over a broad range of subunit binding affinities and concentrations, allowing the formation of highly thermostable capsids. Our results suggest that allostery can significantly shift the range of protein binding affinities that lead to successful assembly, and thus should be accounted for in models that are used to estimate interaction parameters from experimental data.

q-bio.SC↗
arXiv2016

Multiscale modeling of diffusion in a crowded environment

We present a multiscale approach to model diffusion in a crowded environment and its effect on the reaction rates. Diffusion in biological systems is often modeled by a discrete space jump process in order to capture the inherent noise of biological systems, which becomes important in the low copy number regime. To model diffusion in the crowded cell environment efficiently, we compute the jump rates in this mesoscopic model from local first exit times, which account for the microscopic positions of the crowding molecules, while the diffusing molecules jump on a coarser Cartesian grid. We then extract a macroscopic description from the resulting jump rates, where the excluded volume effect is modeled by a diffusion equation with space dependent diffusion coefficient. The crowding molecules can be of arbitrary shape and size and numerical experiments demonstrate that those factors together with the size of the diffusing molecule play a crucial role on the magnitude of the decrease in diffusive motion. When correcting the reaction rates for the altered diffusion we can show that molecular crowding either enhances or inhibits chemical reactions depending on local fluctuations of the obstacle density.

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