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arXiv2013

Analysis of the two-regime method on square meshes

The two-regime method (TRM) has been recently developed for optimizing stochastic reaction-diffusion simulations. It is a multiscale (hybrid) algorithm which uses stochastic reaction-diffusion models with different levels of detail in different parts of the computational domain. The coupling condition on the interface between different modelling regimes of the TRM was previously derived for one-dimensional models. In this paper, the TRM is generalized to higher dimensional reaction-diffusion systems. Coupling Brownian dynamics models with compartment-based models on regular (square) two-dimensional lattices is studied in detail. In this case, the interface between different modelling regimes contain either flat parts or right-angled corners. Both cases are studied in the paper. For flat interfaces, it is shown that the one-dimensional theory can be used along the line perpendicular to the TRM interface. In the direction tangential to the interface, two choices of the TRM parameters are presented. Their applicability depends on the compartment size and the time step used in the molecular-based regime. The two-dimensional generalization of the TRM is also discussed in the case of corners.

q-bio.QM↗

arXiv2013

Convergence of methods for coupling of microscopic and mesoscopic reaction-diffusion simulations

In this paper, three multiscale methods for coupling of mesoscopic (compartment-based) and microscopic (molecular-based) stochastic reaction-diffusion simulations are investigated. Two of the three methods that will be discussed in detail have been previously reported in the literature; the two-regime method (TRM) and the compartment-placement method (CPM). The third method that is introduced and analysed in this paper is the ghost cell method (GCM). Presented is a comparison of sources of error. The convergent properties of this error are studied as the time step $Δt$ (for updating the molecular-based part of the model) approaches zero. It is found that the error behaviour depends on another fundamental computational parameter $h$, the compartment size in the mesoscopic part of the model. Two important limiting cases, which appear in applications, are considered: (i) Δt approaches 0 and h is fixed; and (ii) Δt approaches 0 and h approaches 0 such that Δt/h^2 is fixed. The error for previously developed approaches (the TRM and CPM) converges to zero only in the limiting case (ii), but not in case (i). It is shown that the error of the GCM converges in the limiting case (i). Thus the GCM is superior to previous coupling techniques if the mesoscopic description is much coarser than the microscopic part of the model.

q-bio.SC↗

arXiv2013

Theory and experiment reveal unexpected calcium profiles in one-dimensional systems

Calcium is an ubiquitous second messenger that triggers a plethora of key physiological responses. The events are initiated in micro- or nano-sized compartments and determined by the complex interactions with calcium-binding proteins and mechanisms of calcium clearance. Local calcium increases in the vicinity of single channels represent an essentially non-linear reaction-diffusion problem that have been analysed previously using various linearized approximations. I revisited the problem of stationary patterns that can be generated by the point calcium source in the presence of buffer and obtained new explicit solutions. Main results of the analysis of the calcium buffering are supplemented with pertinent derivations and discussion of respective mathematical problems in Appendices. I show that for small calcium influx the calcium gradients around established around channel lumen have quasi-exponential form. For bigger fluxes, when the buffer is saturated, the model predicts periodic patterns. The transition between the two regimes depend on the capacity of buffer and its mobility. Theoretical predictions were examined using a model one-dimensional system. For sufficiently big fluxes the oscillatory calcium patterns were observed. Theoretical and experimental results are discussed in terms of their possible physiological implications.

q-bio.SC↗

arXiv2013

A Model for the Dynamics of Gene Networks

In this work we propose a model for gene expression based on the theory of random dynamical systems (RDS) and show that it has a "modularity property" in the following sense: given any collection of genes that are linked in a transcriptional network, if each of them is individually described by a certain class of RDS then there is a natural, and essentially unique, prescription for coupling them together, respecting the network topology, in such a way that the collective system formed by all genes is a RDS as well. Moreover, the class of RDS used to describe the individual genes is flexible enough to account for a wide range of stochastic behaviors within the realm of stationary processes.

q-bio.MN↗

arXiv2013

Maxwell's demon for calcium binding to calmodulin?

In the recent paper (2011) Faas and co-workers claimed that calmodulin could directly detect Ca2+ signals by acting as extremely fast calcium buffer. However the results and their interpretation raise serious doubts about this conclusion.

q-bio.SC↗

arXiv2013

Does Plasmodium falciparum have an Achilles' heel?

Plasmodium falciparum is the parasite that causes the most severe form of malaria. Currently, science has been established about its cellular structures, its metabolic processes, and even the molecular structures of its intrinsic membrane proteins responsible for transporting water, nutrient, and waste molecules across the parasite plasma membrane (PPM). I hypothesize that Plasmodium falciparum has an Achilles' heel that can be attacked with erythritol, the well-known sweetener that is classified as generally safe. Most organisms have in their cell membrane two types of water-channel proteins: aquaporins to maintain hydro-homeostasis across the membrane and aquaglyceroporins to uptake glycerols etc. In contrast, P. falciparum has only one type of such proteins---the multi-functional aquaglyceroporin (PfAQP) expressed in the PPM---to do both jobs. Moreover, the parasite also uses PfAQP to excrete its metabolic wastes (ammonia included) produced at a very high rate in the blood stage. This extremely high efficiency of the bug using one protein for multiple essential tasks makes the parasite fatally vulnerable. Erythritol in the blood stream can kill the parasite by clogging up its PfAQP channel that needs to be open for maintaining hydro-homeostasis and for excreting toxic wastes across the bug's PPM. In vitro tests are to measure the growth/death rate of P. falciparum in blood with various erythritol concentrations. In vivo experiments are to administer groups of infected mice with various doses of erythritol and monitor the parasite growth levels from blood samples drawn from each group. Clinic trials can be performed to observe the added effects of administering to patients erythritol along with the known drugs because erythritol was classified as a safe food ingredient.

q-bio.SC↗

arXiv2013

Solving single molecules: filtering noisy discrete data made of photons and other type of observables

In numerous systems in biophysics and related fields, scientists measure (with very smart methods) individual molecules (e.g. biopolymers (proteins, DNA, RNA, etc), nano - crystals, ion channels), aiming at finding a model from the data. But the noise is not solved accurately in not so few cases and this may lead to misleading models. Here, we solve the noise. We consider two state photon trajectories from any on off kinetic scheme (KS): the process emitting photons with a rate γon when it is in the on state, and emitting with a rate γoff when it is in the off state. We develop a filter that removes the noise resulting in clean data also in cases where binning fails. The filter is a numerical algorithm with various new statistical treatments. It is based on a new general likelihood function developed here, with observable dependent form. The filter can solve the noise, in the detectable region of the rate space: that is, we also find a region where the data is "too" noisy. Consistency tests will find the region's type from the data. If the data is ruled "too noisy", binning obviously fails, and one should apply simpler methods on the raw data and realizing that the extracted information is partial. We show that not applying the filter while cleaning results in erroneous rates. This filter (with minor adjustments) can solve the noise in any discrete state trajectories, yet extensions are needed in "tackling" the noise from other data, e.g. continuous data and FRET data. The filter developed here is complementary with our previous projects in this field, where we have solved clean two state data with the development of reduced dimensions forms (RDFs): only the combined procedures enabling building the most accurate model from noisy trajectories from single molecules

q-bio.SC↗

arXiv2013

From Clarkia to Escherichia and Janus: the physics of natural and synthetic active colloids

An active colloid is a suspension of particles that transduce free energy from their environment and use the energy to engage in intrinsically non-equilibrium activities such as growth, replication and self-propelled motility. An obvious example of active colloids is a suspension of bacteria such as Escherichia coli, their physical dimensions being almost invariably in the colloidal range. Synthetic self-propelled particles have also become available recently, such as two-faced, or Janus, particles propelled by differential chemical reactions on their surfaces driving a self-phoretic motion. In these lectures, I give a pedagogical introduction to the physics of single-particle and collective properties of active colloids, focussing on self propulsion. I will compare and contrast phenomena in suspensions of `swimmers' with the behaviour of suspensions of passive particles, where only Brownian motion (discovered by Robert Brown in granules from the pollen of the wild flower {\it Clarkia pulchella}) is relevant. I will pay particular attention to issues that pertain to performing experiments using these active particle suspensions, such as how to characterise the suspension's swimming speed distribution, and include an appendix to guide physicists wanting to start culturing motile bacteria.

cond-mat.soft↗

arXiv2013

Translation by adaptor-helicase cycle in oligomer world

A mechanism of the translation in oligomer world is proposed. The translation is carried out by a minimum cycle, which is sustained by adaptors and helicases, and the first information processing in oligomer world. We expect that such a cycle actually worked in a primitive cell and can be constructed in vitro. By computer simulation we have shown that a proofreading is achieved by the fluctuation in the cell. It is rather paradoxical that the proofreading is effective for the system consisting of molecular machines with low efficiency.

q-bio.BM↗

arXiv2013

Motor function in interpolar microtubules during metaphase

We analyze experimental observations of microtubules undergoing small fluctuations about a "balance point" when mixed in solution of two different kinesin motor proteins, KLP61F and Ncd. It has been proposed that the microtubule movement is due to stochastic variations in the densities of the two species of motor proteins. We test this hypothesis here by showing how it maps onto a one-dimensional random walk in a random environment. Our estimate of the amplitude of the fluctuations agrees with experimental observations. We point out that there is an initial transient in the position of the microtubule where it will typically move of order its own length. We compare the physics of this gliding assay to a recent theory of the role of antagonistic motors on restricting interpolar microtubule sliding of a cell's mitotic spindle during prometaphase. It is concluded that randomly positioned antagonistic motors can restrict relative movement of microtubules, however they do so imperfectly. A variation in motor concentrations is also analyzed and shown to lead to greater control of spindle length.

q-bio.CB↗

arXiv2013

A new model of filtration and macromolecules transport across capillary walls

Metabolic substrates, such as oxygen and glucose, are rapidly delivered to the cell through filtration across microvessels walls. Modelling this important process is complicated by the coupling between flow and transport equations, which are linked through the osmotic pressure induced by the colloidal plasma proteins. Microvessel wall is a composite media with the internal glycocalyx layer exerting a remarkable sieving effect on macromolecules, with respect to the external layer composed by endothelial cells. The physiological structure of microvessel is represented as the superimposition of two membranes with different properties; the inner membrane represents the glycocalyx, while the outer membrane represents the surrounding endothelial cells. Application of mass conservation principle and thermodynamic considerations lead to a model composed by two coupled second-order partial differential equations in the hydrostatic and osmotic pressures, one expressing volumetric mass conservation and the other, which is non-linear, expressing macromolecules mass conservation. Despite system complexity, the assumption that the properties of the layers are piece-wise constant allows us to obtain analytical solutions for the two pressures. This solution is in agreement with experimental observations, which contrary to common belief, show that flow reversal cannot occur in steady state unless luminal hydrostatic pressure drops below physiologically plausible values. The observed variations of volumetric and solute mass flux in case of a significant reduction of luminal hydrostatic pressure are in qualitative agreement with observed variations during experiments reported in the literature. On the other hand, homogenising microvessel wall into a single-layer membrane with equivalent properties leads to a different distribution of pressure across microvessel wall, not consistent with observations.

q-bio.SC↗

arXiv2013

A simple model of filtration and macromolecule transport through microvascular walls

Multiple Sclerosis (MS) is a disorder that usually appears in adults in their thirties. It has a prevalence that ranges between 2 and 150 per 100 000. Epidemiological studies of MS have provided hints on possible causes for the disease ranging from genetic, environmental and infectious factors to other factors of vascular origin. Despite the tremendous effort spent in the last few years, none of the hypotheses formulated so far has gained wide acceptance and the causes of the disease remain unknown. From a clinical point of view, a high correlation has been recently observed between MS and Chronic Cerebro-Spinal Venous Insufficiency (CCSVI) in a statistically significant number of patients. In this pathological situation CCSVI may induce alterations of blood pressure in brain microvessels, thereby perturbing the exchange of small hydrophilic molecules between the blood and the external cells. In the presence of large pressure alterations it cannot be excluded also the leakage of macromolecules that otherwise would not cross the vessel wall. All these disorders may trigger immune defenses with the destruction of myelin as a side effect. In the present work we investigate the role of perturbed blood pressure in brain microvessels as driving force for an altered exchange of small hydrophilic solutes and leakage of macromolecules into the interstitial fluid. With a simplified, yet realistic, model we obtain closed-form steady-state solutions for fluid flow and solute transport across the microvessel wall. Finally, we use these results (i) to interpret experimental data available in the literature and (ii) to carry out a preliminary analysis of the disorder in the exchange processes triggered by an increase of blood pressure, thereby relating our preliminary results to the hypothesised vascular connection to MS.

q-bio.SC↗

arXiv2013

Cell-cycle regulated transcription associates with DNA replication timing in yeast and human

Eukaryotic DNA replication follows a specific temporal program, with some genomic regions consistently replicating earlier than others, yet what determines this program is largely unknown. Highly transcribed regions have been observed to replicate in early S-phase in all plant and animal species studied to date, but this relationship is thought to be absent from both budding yeast and fission yeast. No association between cell-cycle regulated transcription and replication timing has been reported for any species. Here I show that in budding yeast, fission yeast, and human, the genes most highly transcribed during S-phase replicate early, whereas those repressed in S-phase replicate late. Transcription during other cell-cycle phases shows either the opposite correlation with replication timing, or no relation. The relationship is strongest near late-firing origins of replication, which is not consistent with a previously proposed model -- that replication timing may affect transcription -- and instead suggests a potential mechanism involving the recruitment of limiting replication initiation factors during S-phase. These results suggest that S-phase transcription may be an important determinant of DNA replication timing across eukaryotes, which may explain the well-established association between transcription and replication timing.

q-bio.GN↗

arXiv2015

Ion mediated cross-shield driven mucous swelling kinetics

We present an experimentally guided, bi-phasic, multi-species ionic gel model to compare and make quantitative predictions on the viscoelastic properties of healthy mucus versus Cystic-Fibrosis infected mucus. The mixture theory consists of the mucus (polymer phase) and water (solvent phase) as well as several different ions: H$^+$, Na$^+$, Cl$^-$ and Ca$^{2+}$. The model is calibrated with the experimental data of mucus diffusivities. Numerical studies reveal that the Donnan forces are the dominating mechanism driving the mucus swelling/deswelling transition. However, these transitions could be continuous or discontinuous, depending on the complex interplay between ionic bath concentrations, pH, polymer mass in the solvent and the average charge per monomer.

q-bio.SC↗

arXiv2014

Analysis of DevR regulated genes in Mycobacterium tuberculosis

The DevRS two component system of Mycobacterium tuberculosis is responsible for its dormancy in host and becomes operative under hypoxic condition. It is experimentally known that phosphorylated DevR controls the expression of several downstream genes in a complex manner. In the present work we propose a theoretical model to show role of binding sites in DevR mediated gene expression. Individual and collective role of binding sites in regulating DevR mediated gene expression has been shown via modeling. Objective of the present work is two fold. First, to describe qualitatively the temporal dynamics of wild type genes and their known mutants. Based on these results we propose that DevR controlled gene expression follows a specific pattern which is efficient in describing other DevR mediated gene expression. Second, to analyze behavior of the system from information theoretical point of view. Using the tools of information theory we have calculated molecular efficiency of the system and have shown that it is close to the maximum limit of isothermal efficiency.

q-bio.MN↗

arXiv2013

Potential wells for AMPA receptors organized in ring nanodomains

By combining high-density super-resolution imaging with a novel stochastic analysis, we report here a peculiar nano-structure organization revealed by the density function of individual AMPA receptors moving on the surface of cultured hippocampal dendrites. High density regions of hundreds of nanometers for the trajectories are associated with local molecular assembly generated by direct molecular interactions due to physical potential wells. We found here that for some of these regions, the potential wells are organized in ring structures. We could find up to 3 wells in a single ring. Inside a ring receptors move in a small band the width of which is of hundreds of nanometers. In addition, rings are transient structures and can be observed for tens of minutes. Potential wells located in a ring are also transient and the position of their peaks can shift with time. We conclude that these rings can trap receptors in a unique geometrical structure contributing to shape receptor trafficking, a process that sustains synaptic transmission and plasticity.

q-bio.SC↗

arXiv2013

Nanoscale elucidation of Na,K-ATPase isoforms in dendritic spines

The dimensions of neuronal synapses suggest that optical super-resolution imaging methods are necessary for thorough investigation of protein distributions and interactions. Nanoscopic evaluation of neuronal samples has presented practical hurdles, but advancing methods are making synaptic protein topology and quantification measurements feasible. This work explores the application of Photoactivated Localization Microscopy (PALM) pointilistic super-resolution imaging for investigation of the membrane bound sodium pump, the Na,K-ATPase, in matured neurons. Two isoforms of the sodium pump (ATP1a1 and ATP1a3) were studied in cultured neurons using the PALM-compatible fluorescent proteins PAGFP and mEos. Nanoscopic imaging reveals a compartmentalized distribution of sodium pumps in dendritic spines. Several nanoclusters of pumps are typically found in the spine head and relatively few in the spine neck. The density of sodium pumps was estimated from a quantification of detected single molecules to 600-800 pump copies/um2 in the spine heads. We have utilized PALM for dissection of nanoscale localization in mature cultured neurons and demonstrated similar topology and quantification estimates with PAGFP and mEos. PALM topology assessments of the sodium pump appeared similar to previous STED studies, though quantification estimates varied notably, implying that sample labeling strategies and choice of nanoscopic imaging method are critical factors for correct quantification.

physics.bio-ph↗

arXiv2013

The importance of crowding in signaling, genetic, and metabolic networks

It is now well established that the cell is a highly crowded environment. Yet, the effects of crowding on the dynamics of signaling pathways, gene regulation networks and metabolic networks are still largely unknown. Crowding can alter both molecular diffusion and the equilibria of biomolecular reactions. In this review, we first discuss how diffusion can affect biochemical networks. Diffusion of transcription factors can increase noise in gene expression, while diffusion of proteins between intracellular compartments or between cells can reduce concentration fluctuations. In push-pull networks diffusion can impede information transmission, while in multi-site protein modification networks diffusion can qualitatively change the macroscopic response of the system, such as the loss or emergence of bistability. Moreover, diffusion can directly change the metabolic flux. We describe how crowding affects diffusion, and thus how all these phenomena are influenced by crowding. Yet, a potentially more important effect of crowding on biochemical networks is mediated via the shift in the equilibria of bimolecular reactions, and we provide computational evidence that supports this idea. Finally, we discuss how the effects of crowding can be incorporated in models of biochemical networks.

q-bio.MN↗