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arXiv2021

Elementary Intracellular Ca Signals are Initiated by a Transition of Release Channel System from a Metastable State

Cardiac muscle contraction is initiated by an elementary Ca signal (called Ca spark) which is achieved by collective action of Ca release channels in a cluster. The mechanism of this synchronization remains uncertain. This paper approaches Ca spark activation as an emergent phenomenon of an interactive system of release channels. We construct a Markov chain that applies an Ising model formalism to such release channel clusters and realistic open channel configurations to demonstrate that spark activation is described as a system transition from a metastable to an absorbing state, analogous to the pressure required to overcome surface tension in bubble formation. This yields quantitative estimates of the spark generation probability as a function of various system parameters. Our model of the release channel system yields similar results for the sarcoplasmic reticulum Ca concentration threshold for spark activation as previous experimental results, providing a mechanistic explanation of the spark initiation. Additionally, we perform numerical simulations to find spark probabilities as a function of sarcoplasmic reticulum Ca concentration obtaining similar values for spark activation threshold as our analytic model, as well as those reported in experimental studies.

q-bio.SC↗

arXiv2021

Real-Time Interactive Modeling and Simulation in Biological Physics and Active Matter with Mechanica

Modeling and simulation (M&S) has revolutionized the way modern engineered products are designed, tested and evaluated. Yet modeling and simulation is much less frequently applied in the study of natural biological and active matter systems. Two of the greatest challenges in applying M\&S approaches to natural biological systems are (1) difficulty in specifying a model, and developing a simulation from it, and (2) tuning and optimizing parameters. Here we address the first challenge directly, and develop a software library that can lead to progress in the second.

q-bio.SC↗

arXiv2022

Geometry adaptation of protrusion and polarity dynamics in confined cell migration

Cell migration in confining physiological environments relies on the concerted dynamics of several cellular components, including protrusions, adhesions with the environment, and the cell nucleus. However, it remains poorly understood how the dynamic interplay of these components and the cell polarity determine the emergent migration behavior at the cellular scale. Here, we combine data-driven inference with a mechanistic bottom-up approach to develop a model for protrusion and polarity dynamics in confined cell migration, revealing how the cellular dynamics adapt to confining geometries. Specifically, we use experimental data of joint protrusion-nucleus migration trajectories of cells on confining micropatterns to systematically determine a mechanistic model linking the stochastic dynamics of cell polarity, protrusions, and nucleus. This model indicates that the cellular dynamics adapt to confining constrictions through a switch in the polarity dynamics from a negative to a positive, self-reinforcing feedback loop. Our model further reveals how this feedback loop leads to stereotypical cycles of protrusion-nucleus dynamics that drive the migration of the cell through constrictions. These cycles are disrupted upon perturbation of cytoskeletal components, indicating that the positive feedback is controlled by cellular migration mechanisms. Our data-driven theoretical approach therefore identifies polarity feedback adaptation as a key mechanism in confined cell migration.

physics.bio-ph↗

arXiv2021

Flagellar length fluctuations: quantitative dependence on length control mechanism

Organelles of optimum size are crucial for proper functioning of a living cell. The cell employs various mechanisms for actively sensing and controlling the size of its organelles. Recently Bauer et al have opened a new research frontier in the field of subcellular size control by shedding light on the noise and fluctuations of organelles of controlled size. Taking eukaryotic flagellum as a model organelle, which is quite popular for such studies because of its linear geometry and dynamic nature, Bauer et al have analysed the nature of fluctuations of its length. Here we summarize the key questions and the fundamental importance of the recent developments. Although our attention is focussed here mainly on the experimental and theoretical works on eukaryotic flagellum, the ideas are general and applicable to wide varieties of cell organelle.

physics.bio-ph↗

arXiv2021

Dynamics and Sensitivity of Signaling Pathways

Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.

q-bio.MN↗

arXiv2021

Real time large scale $\textit{in vivo}$ observations by light-sheet microscopy reveal intrinsic synchrony, plasticity and growth cone dynamics of midline crossing axons at the ventral floor plate of the zebrafish spinal cord

Axonal growth and guidance at the ventral floor plate is here followed $\textit{in vivo}$ in real time at high resolution by light-sheet microscopy along several hundred micrometers of the zebrafish spinal cord. The recordings show the strikingly stereotyped spatio-temporal control that governs midline crossing. Commissural axons are observed crossing the ventral floor plate midline perpendicularly at about 20 microns/h, in a manner dependent on the Robo3 receptor and with a growth rate minimum around the midline, confirming previous observations. At guidance points, commissural axons are seen to decrease their growth rate and growth cones increase in size. Commissural filopodia appear to interact with the nascent neural network, and thereby trigger immediate plastic and reversible sinusoidal-shaped bending movements of neighboring commissural shafts. Ipsilateral axons extend concurrently, but straight and without bends, at three to six times higher growth rates than commissurals, indicating they project their path on a substrate-bound surface rather than relying on diffusible guidance cues. Growing axons appeared to be under stretch, an observation that is of relevance for tension-based models of cortical morphogenesis. The \textit{in vivo} observations provide for a discussion of the current distinction between substrate-bound and diffusible guidance cues. The study applies the transparent zebrafish model that provides an experimental model system to explore further the cellular, molecular and physical mechanisms involved during axonal growth, guidance and midline crossing through a combination of $\textit{in vitro}$ and $\textit{in vivo}$ approaches.

q-bio.NC↗

arXiv2021

Aging Maxwell fluids

Many experiments show that protein condensates formed by liquid-liquid phase separation exhibit aging rheological properties. Quantitatively, recent experiments by Jawerth et al. (Science 370, 1317, 2020) show that protein condensates behave as aging Maxwell fluids with an increasing relaxation time as the condensates age. Despite the universality of this aging phenomenon, a theoretical understanding of this aging behavior is lacking. In this work, we propose a mesoscopic model of protein condensates in which a phase transition from aging phase to non-aging phase occurs as the control parameter changes, such as temperature. The model predicts that protein condensates behave as viscoelastic Maxwell fluids at all ages, with the macroscopic viscosity increasing over time. The model also predicts that protein condensates are non-Newtonian fluids under a constant shear rate with the shear stress increasing over time. Our model successfully explains multiple existing experimental observations and also makes general predictions that are experimentally testable.

cond-mat.soft↗

arXiv2021

Unravelling Heterogeneous Transport of Endosomes

A major open problem in biophysics is to understand the highly heterogeneous transport of many structures inside living cells, such as endosomes. We find that mathematically it is described by spatio-temporal heterogeneous fractional Brownian motion (hFBM) which is defined as FBM with a randomly switching anomalous exponent and random generalized diffusion coefficient. Using a comprehensive local analysis of a large ensemble of experimental endosome trajectories (> 10^5), we show that their motion is characterized by power-law probability distributions of displacements and displacement increments, exponential probability distributions of local anomalous exponents and power-law probability distributions of local generalized diffusion coefficients of endosomes which are crucial ingredients of spatio-temporal hFBM. The increased sensitivity of deep learning neural networks for FBM characterisation corroborates the development of this multi-fractal analysis. Our findings are an important step in understanding endosome transport. We also provide a powerful tool for studying other heterogeneous cellular processes.

q-bio.SC↗

arXiv2021

Encounter networks from collective mitochondrial dynamics support the emergence of effective mtDNA genomes in plant cells

Mitochondria in plant cells form strikingly dynamic populations of largely individual organelles. Each mitochondrion contains on average less than a full copy of the mitochondrial DNA (mtDNA) genome. Here, we asked whether mitochondrial dynamics may allow individual mitochondria to `collect' a full copy of the mtDNA genome over time, by facilitating exchange between individuals. Akin to trade on a social network, exchange of mtDNA fragments across organelles may lead to the emergence of full `effective' genomes in individuals over time. We characterise the collective dynamics of mitochondria in \emph{Arabidopsis thaliana} hypocotyl cells using a recent approach combining single-cell timelapse microscopy, video analysis, and network science. We then use a quantitative model to predict the capacity for the sharing and accumulation of genetic information through the networks of encounters between mitochondria. We find that biological encounter networks are strikingly well predisposed to support the collection of full genomes over time, outperforming a range of other networks generated from theory and simulation. Using results from the coupon collector's problem, we show that the upper tail of the degree distribution is a key determinant of an encounter network's performance at this task and discuss how features of mitochondrial dynamics observed in biology facilitate the emergence of full effective genomes.

q-bio.SC↗

arXiv2022

Accumulation time of diffusion in a 2D singularly perturbed domain

A general problem of current interest is the analysis of diffusion problems in singularly perturbed domains, within which small subdomains are removed from the domain interior and boundary conditions imposed on the resulting holes. One major application is to intracellular diffusion, where the holes could represent organelles or biochemical substrates. In this paper we use a combination of matched asymptotic analysis and Green's function methods to calculate the so-called accumulation time for relaxation to steady state in 2D domains. The standard measure of the relaxation rate is in terms of the principal nonzero eigenvalue of the negative Laplacian. However, this global measure does not account for possible differences in the relaxation rate at different spatial locations, is independent of the initial conditions, and relies on the assumption that the eigenvalues have sufficiently large spectral gaps. As previously established for diffusion-based morphogen gradient formation, the accumulation time provides a better measure of the relaxation process.

math.AP↗

arXiv2021

Dynamics of unfolded protein aggregation

Unfolded protein aggregation in cellular system is a problem causing various types of diseases depending on which type unfolded proteins aggregate. This phenomenon of aggregation may take place during production, storage, shipment or delivery in the cellular medium. In the present work, we studied a simplified and extended version of unfolded protein aggregation model by Lumry and Eyring using stochastic approach. We solved analytically the Master equation of the model for the probability distribution $P(x,t)$ of the unfolded protein population and the solution was found to be time dependent complex binomial distribution. In the large population limit $P(x,t)\sim Λ(x,t)\times Pois(x,t)$. Further, the distribution became Normal distribution at large population and mean of the distribution limit: $P(x,t)\simΛ(x,t)\times N(\langle qx\rangle,\langle qx\rangle)$. The fluctuations inherent in the dynamics measured by Fano factor can have sub-Poisson, Poisson and super-Poisson at different situations.

q-bio.SC↗

arXiv2021

Predicting the Directional Transport of Multivalent Cargo from Position Dependent Binding and Unbinding Rates

Multivalent cargo that can interact with substrates via multiple interaction sites exhibit shared characteristics despite being found in different systems at different length-scales. Here, a general analytical model has been developed that can describe the motion of multivalent cargo as a response to position dependence in the binding and unbinding rates of their interaction sites. Cargo exhibit both an effective diffusivity and velocity, which acts in the direction of increasing cargo-substrate binding rate and decreasing cargo-substrate unbinding rate. This model can reproduce previously published experimental findings using only the binding and unbinding rate distributions of cargo interaction sites, and without any further parameter fitting. Extension of the cargo binding model to two dimensions reveals an effective velocity with the same properties as that derived for the $1$D case.

q-bio.SC↗

arXiv2022

Unraveling Single-Particle Trajectories Confined in Tubular Networks

The analysis of single particle trajectories plays an important role in elucidating dynamics within complex environments such as those found in living cells. However, the characterization of intracellular particle motion is often confounded by confinement of the particles within non-trivial subcellular geometries. Here, we focus specifically on the case of particles undergoing Brownian motion within a tubular network, as found in some cellular organelles. An unraveling algorithm is developed to uncouple particle motion from the confining network structure, allowing for an accurate extraction of the diffusion coefficient, as well as differentiating between Brownian and fractional Brownian dynamics. We validate the algorithm with simulated trajectories and then highlight its application to an example system: analyzing the motion of membrane proteins confined in the tubules of the peripheral endoplasmic reticulum in mammalian cells. We show that these proteins undergo diffusive motion with a well-characterized diffusivity. Our algorithm provides a generally applicable approach for disentangling geometric morphology and particle dynamics in networked architectures.

physics.bio-ph↗

arXiv2021

How enzymatic activity is involved in chromatin organization

Spatial organization of chromatin plays a critical role in genome regulation. Various types of affinity mediators and enzymes have been attributed to regulate spatial organization of chromatin from a thermodynamics perspective. However, at the mechanistic level, enzymes act in their unique ways. Here, we construct a polymer physics model following the mechanistic scheme of Topoisomerase-II, an enzyme resolving topological constraints of chromatin, and investigate its role on interphase chromatin organization. Our computer simulations demonstrate Topoisomerase-II's ability to phase separate chromatin into eu- and heterochromatic regions with a characteristic wall-like organization of the euchromatic regions. Exploiting a mean-field framework, we argue that the ability of the euchromatic regions crossing each other due to enzymatic activity of Topoisomerase-II induces this phase separation. Motivated from a recent experimental observation on different structural states of the eu- and the heterochromatic units, we further extend our model to a bidisperse setting and show that the characteristic features of the enzymatic activity driven phase separation survives there. The existence of these characteristic features, even under the non-localized action of the enzyme, highlights the critical role of enzymatic activity in chromatin organization, and points out the importance of further experiments along this line.

physics.bio-ph↗

arXiv2022

Reaction Network Motifs for Static and Dynamic Absolute Concentration Robustness

Networks with absolute concentration robustness (ACR) have the property that a translation of a coordinate hyperplane either contains all steady states (static ACR) or attracts all trajectories (dynamic ACR). The implication for the underlying biological system is robustness in the concentration of one of the species independent of the initial conditions as well as independent of the concentration of all other species. Identifying network conditions for dynamic ACR is a challenging problem. We lay the groundwork in this paper by studying small reaction networks, those with 2 reactions and 2 species. We give a complete classification by ACR properties of these minimal reaction networks. The dynamics is rich even within this simple setting. Insights obtained from this work will help illuminate the properties of more complex networks with dynamic ACR.

math.DS↗

arXiv2022

Evolutionary timeline of a modeled cell

A theoretical study of cell evolution is presented here. By using a toolbox containing an intracellular catalytic reaction network model and a mutation-selection process, four distinct phases of self-organization were unveiled. First, the nutrients prevail as the central substrate of the chemical reactions. Second, the cell becomes a small-world. Third, a highly connected core component emerges, concurrently with the nutrient carriers becoming the central product of reactions. Finally, the cell reaches a steady configuration where the concentrations of the core chemical species are described by Zipf's law.

physics.bio-ph↗

arXiv2022

Non-reciprocal multifarious self-organization

A hallmark of living systems is the ability to employ a common set of versatile building blocks that can self-organize into a multitude of different structures, in a way that can be controlled with minimal cost. This capability can only be afforded in non-equilibrium conditions, as evident from the energy-consuming nature of the plethora of such dynamical processes. In the last three decades, synthetic self-assembly has experienced a significant boost with the development of tools to design specific interactions at different scales, from nucleic acids and peptides to proteins and colloids. To achieve automated dynamical control of such self-assembled structures and transitions between them, we need to identify the relevant fundamental aspects of non-equilibrium dynamics that can enable such processes. Here, we identify programmable non-reciprocal interactions as a potential paradigm using which such functionalities can be achieved. In particular, we propose a model that enables a system to learn and retrieve predetermined desired structures and transition between them, thus behaving as a shape-shifter. The learning rule is composed of reciprocal interactions that lead to the equilibrium assembly of the structures, and non-reciprocal interactions that give rise to non-equilibrium dynamical transitions between the structures.

cond-mat.stat-mech↗

arXiv2022

Focal cortical dysplasia as a cause of epilepsy: the current evidence of associated genes and future therapeutic treatments

Focal cortical dysplasias (FCDs) are the most common cause of treatment resistant epilepsy affecting the pediatric population. Most individuals with FCD have seizure onset during the first five years of life and the majority will have seizures by the age of sixteen. Many cases of FCD are postulated to be the result of abnormal brain development in utero by germline or somatic gene mutations regulating neuronal growth and migration during corticogenesis. Other cases of FCD are thought to be related to infections during brain development, or even other causes still unable to be fully determined. Typical anti-seizure medications are oftentimes ineffective in FCD as well as surgery is unable to be successfully performed due to the involvement of eloquent areas of the brain or insufficient resection of the epileptogenic focus, posing a challenge for physicians. The genetic nature of FCD provides an avenue for drug development with several genetic and molecular targets undergoing study over the last two decades.

q-bio.NC↗