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arXiv2012

On the photosynthetic potential in the very Early Archean oceans

In this work we apply a mathematical model of photosynthesis to quantify the potential for photosynthetic life in the very Early Archean oceans. We assume the presence of oceanic blockers of ultraviolet radiation, specifically ferrous ions. For this scenario, our results suggest a potential for photosynthetic life greater than or similar to that in later eras/eons, such as the Late Archean and the current Phanerozoic eon.

q-bio.PE↗

arXiv2016

Mitochondrial Ca2+ uptake in skeletal muscle health and disease

Muscle uses Ca2+ as a messenger to control contraction and relies on ATP to maintain the intracellular Ca2+ homeostasis. Mitochondria are the major sub-cellular organelle of ATP production. With a negative inner membrane potential, mitochondria take up Ca2+ from their surroundings, a process called mitochondrial Ca2+ uptake. Under physiological conditions, Ca2+ uptake into mitochondria promotes ATP production. Excessive uptake causes mitochondrial Ca2+ overload, which activates downstream adverse responses leading to cell dysfunction. Moreover, mitochondrial Ca2+ uptake could shape spatio-temporal patterns of intracellular Ca2+ signaling. Malfunction of mitochondrial Ca2+ uptake is implicated in muscle degeneration. Unlike non-excitable cells, mitochondria in muscle cells experience dramatic changes of intracellular Ca2+ levels. Besides the sudden elevation of Ca2+ level induced by action potentials, Ca2+ transients in muscle cells can be as short as a few milliseconds during a single twitch or as long as minutes during tetanic contraction, which raises the question whether mitochondrial Ca2+ uptake is fast and big enough to shape intracellular Ca2+ signaling during excitation-contraction coupling and creates technical challenges for quantification of the dynamic changes of Ca2+ inside mitochondria. This review focuses on characterization of mitochondrial Ca2+ uptake in skeletal muscle and its role in muscle physiology and diseases.

q-bio.BM↗

arXiv2006

Integrin activation - the importance of a positive feedback

Integrins mediate cell adhesion and are essential receptors for the development and functioning of multicellular organisms. Integrin activation is known to require both ligand and talin binding and to correlate with cluster formation but the activation mechanism and precise roles of these processes are not yet resolved. Here mathematical modeling, with known experimental parameters, is used to show that the binding of a stabilizing factor, such as talin, is alone insufficient to enable ligand-dependent integrin activation for all observed conditions; an additional positive feedback is required.

q-bio.MN↗

arXiv2010

An Evolutionary Reduction Principle for Mutation Rates at Multiple Loci

A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models. A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface - a generalization of the hyperplane found by Zhivotovsky et al. (1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance. Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.

q-bio.PE↗

arXiv2013

The Influence of Spatial Variation in Chromatin Density Determined by X-ray Tomograms on the Time to Find DNA Binding Sites

In this work we examine how volume exclusion caused by regions of high chromatin density might influence the time required for proteins to find specific DNA binding sites. The spatial variation of chromatin density within mouse olfactory sensory neurons is determined from soft X-ray tomography reconstructions of five nuclei. We show that there is a division of the nuclear space into regions of low-density euchromatin and high-density heterochromatin. Volume exclusion experienced by a diffusing protein caused by this varying density of chromatin is modeled by a repulsive potential. The value of the potential at a given point in space is chosen to be proportional to the density of chromatin at that location. The constant of proportionality, called the volume exclusivity, provides a model parameter that determines the strength of volume exclusion. Numerical simulations demonstrate that the mean time for a protein to locate a binding site localized in euchromatin is minimized for a finite, non-zero volume exclusivity. For binding sites in heterochromatin, the mean time is minimized when the volume exclusivity is zero (the protein experiences no volume exclusion). An analytical theory is developed to explain these results. The theory suggests that for binding sites in euchromatin there is an optimal level of volume exclusivity that balances a reduction in the volume searched in finding the binding site, with the height of effective potential barriers the protein must cross during the search process.

q-bio.SC↗

arXiv2015

Protein synthesis driven by dynamical stochastic transcription

In this manuscript we propose a mathematical framework to couple transcription and translation in which mRNA production is described by a set of master equations while the dynamics of protein density is governed by a random differential equation. The coupling between the two processes is given by a stochastic perturbation whose statistics satisfies the master equations. In this approach, from the knowledge of the analytical time dependent distribution of mRNA number, we are able to calculate the dynamics of the probability density of the protein population.

q-bio.SC↗

arXiv2017

A generalized Michaelis-Menten equation in protein synthesis: effects of mis-charged cognate tRNA and mis-reading of codon

The sequence of amino acid monomers in the primary structure of a protein is decided by the corresponding sequence of codons (triplets of nucleic acid monomers) on the template messenger RNA (mRNA). The polymerization of a protein, by incorporation of the successive amino acid monomers, is carried out by a molecular machine called ribosome. We develop a stochastic kinetic model that captures the possibilities of mis-reading of mRNA codon and prior mis-charging of a tRNA. By a combination of analytical and numerical methods we obtain the distribution of the times taken for incorporation of the successive amino acids in the growing protein in this mathematical model. The corresponding exact analytical expression for the average rate of elongation of a nascent protein is a `biologically motivated' generalization of the {\it Michaelis-Menten formula} for the average rate of enzymatic reactions. This generalized Michaelis-Menten-like formula (and the exact analytical expressions for a few other quantities) that we report here display the interplay of four different branched pathways corresponding to selection of four different types of tRNA.

physics.bio-ph↗

arXiv2017

A Mathematical Framework for Kinetochore-Driven Activation Feedback in the Mitotic Checkpoint

Proliferating cells properly divide into their daughter cells through a process that is mediated by kinetochores, protein-complexes that assemble at the centromere of each sister chromatid. Each kinetochore has to establish a tight bipolar attachment to the spindle apparatus before sister-chromatid separation is initiated. The Spindle Assembly Checkpoint (SAC) links the biophysical attachment status of the kinetochores to mitotic progression, and ensures that even a single misaligned kinetochore keeps the checkpoint active. The mechanism by which this is achieved is still elusive. Current computational models of the human SAC disregard important biochemical properties by omitting any kind of feedback loop, proper kinetochore signals, and other spatial properties such as the stability of the system and diffusion effects. To allow for more realistic in silico study of the dynamics of the SAC model, a minimal mathematical framework for SAC activation and silencing is introduced. A nonlinear ordinary differential equation model successfully reproduces bifurcation signaling switches with attachment of all 92 kinetochores and activation of APC/C by kinetochore-driven feedback. A partial differential equation model and mathematical linear stability analyses indicate the influence of diffusion and system stability. The conclusion is that quantitative models of the human SAC should account for the positive feedback on APC/C activation driven by the kinetochores which is essential for SAC silencing. Experimental diffusion coefficients for MCC sub-complexes are found to be insufficient for rapid APC/C inhibition. The presented analysis allows for systems-level understanding of mitotic control and the minimal new model can function as a basis for developing further quantitative-integrative models of the cell division cycle

q-bio.SC↗

arXiv2019

Renewal reward perspective on linear switching diffusion systems

In many biological systems, the movement of individual agents is commonly characterized as having multiple qualitatively distinct behaviors that arise from various biophysical states. This is true for vesicles in intracellular transport, micro-organisms like bacteria, or animals moving within and responding to their environment. For example, in cells the movement of vesicles, organelles and other cargo are affected by their binding to and unbinding from cytoskeletal filaments such as microtubules through molecular motor proteins. A typical goal of theoretical or numerical analysis of models of such systems is to investigate the effective transport properties and their dependence on model parameters. While the effective velocity of particles undergoing switching diffusion is often easily characterized in terms of the long-time fraction of time that particles spend in each state, the calculation of the effective diffusivity is more complicated because it cannot be expressed simply in terms of a statistical average of the particle transport state at one moment of time. However, it is common that these systems are regenerative, in the sense that they can be decomposed into independent cycles marked by returns to a base state. Using decompositions of this kind, we calculate effective transport properties by computing the moments of the dynamics within each cycle and then applying renewal-reward theory. This method provides a useful alternative large-time analysis to direct homogenization for linear advection-reaction-diffusion partial differential equation models. Moreover, it applies to a general class of semi-Markov processes and certain stochastic differential equations that arise in models of intracellular transport. Applications of the proposed framework are illustrated for case studies such as mRNA transport in developing oocytes and processive cargo movement by teams of motor proteins.

q-bio.SC↗

arXiv2020

Dynamics of Vesicles Driven Into Closed Constrictions by Molecular Motors

We study the dynamics of a model of membrane vesicle transport into dendritic spines, which are bulbous intracellular compartments in neurons driven by molecular motors. We reduce the lubrication model proposed in [Fai et al., Active elastohydrodynamics of vesicles in narrow, blind constrictions. Phys. Rev. Fluids, 2 (2017), 113601] to a fast-slow system, yielding an analytically and numerically tractable equation equivalent to the original model in the overdamped limit. The model's key parameters are the ratio of motors that prefer to push toward the head of the dendritic spine to the ratio of motors that prefer to push in the opposite direction. We perform a numerical bifurcation analysis in these parameters and find that steady-state vesicle velocities appear and disappear through several saddle-node bifurcations. This process allows us to identify the region of parameter space in which multiple stable velocities exist. We show by direct calculations that there can only be unidirectional motion for sufficiently close vesicle-to-spine diameter ratios. Our analysis predicts the critical vesicle-to-spine diameter ratio, at which there is a transition from unidirectional to bidirectional motion, consistent with experimental observations of vesicle trajectories in the literature.

q-bio.CB↗

arXiv2023

Inferring stochastic rates from heterogeneous snapshots of particle positions

Many imaging techniques for biological systems -- like fixation of cells coupled with fluorescence microscopy -- provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

q-bio.SC↗

arXiv2014

Getting into shape: how do rod-like bacteria control their geometry?

Rod-like bacteria maintain their cylindrical shapes with remarkable precision during growth. However, they are also capable to adapt their shapes to external forces and constraints, for example by growing into narrow or curved confinements. Despite being one of the simplest morphologies, we are still far from a full understanding of how shape is robustly regulated, and how bacteria obtain their near-perfect cylindrical shapes with excellent precision. However, recent experimental and theoretical findings suggest that cell-wall geometry and mechanical stress play important roles in regulating cell shape in rod-like bacteria. We review our current understanding of the cell wall architecture and the growth dynamics, and discuss possible candidates for regulatory cues of shape regulation in the absence or presence of external constraints. Finally, we suggest further future experimental and theoretical directions, which may help to shed light on this fundamental problem.

q-bio.SC↗

arXiv2008

Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction

The cytoplasm of a living cell is crowded with several macromolecules of different shapes and sizes. Molecular diffusion in such a medium becomes anomalous due to the presence of macromolecules and diffusivity is expected to decrease with increase in macromolecular crowding. Moreover, many cellular processes are dependent on molecular diffusion in the cell cytosol. The enzymatic reaction rate has been shown to be affected by the presence of such macromolecules. A simple numerical model is proposed here based on percolation and diffusion in disordered systems to study the effect of macromolecular crowding on the enzymatic reaction rates. The model explains qualitatively some of the experimental observations.

cond-mat.stat-mech↗

arXiv2019

Biochemically altered human erythrocytes as a carrier for targeted delivery of primaquine: an in vitro study

The aim of this study was to investigate human erythrocytes as a carrier for targeted drug delivery of primaquine (PQ). The process of PQ loading in human erythrocytes, as well as the effect of PQ loading on the oxidative status of erythrocytes, was also studied. At PQ concentrations of 2, 4, 6, and 8 mg/mL and an incubation time of 2 h, the ratios of the concentrations of PQ entrapped in erythrocytes to that in the incubation medium were 0.515, 0.688, 0.697 and 0.788, respectively. The maximal decline of erythrocyte reduced glutathione content was observed at 8 mg/mL of PQ compared with native erythrocytes p < 0.001. In contrast, malondialdehyde and protein carbonyl were significantly increased in cells loaded with PQ (p < 0.001). Furthermore, osmotic fragility of PQ carrier erythrocytes was increased in comparison with unloaded cells. Electron microscopy revealed spherocyte formation with PQ carrier erythrocytes. PQ-loaded cells showed sustained drug release over a 48 h period. Erythrocytes were loaded with PQ successfully, but there were some biochemical as well as physiological changes that resulted from the effect of PQ on the oxidative status of drug-loaded erythrocytes. These changes may result in favorable targeting of PQ-loaded cells to reticulo-endothelial organs. The relative impact of these changes remains to be explored in ongoing animal studies.

q-bio.TO↗

arXiv2018

Theoretical Model and Characteristics of Mitochondrial Thermogenesis

Mitochondria of brown adipocyte (BA) are the main intracellular sites for thermogenesis, which have been targeted for therapy to reduce obesity. However, there are long-standing critique and debates about the ability of raising cellular temperature by endogenous thermogenesis. Currently, the wrong theoretical model gave about the five orders of magnitude less than facts. Here, based on the first law of thermodynamics and thermal diffusion equation, the deduced theoretical model of mitochondrial thermogenesis satisfies Laplace equation, and is a special case for thermal diffusion equation. The model settles the long-standing questioning about the ability of raising cellular temperature by endogenous thermogenesis, and explains the thermogenic characteristics of brown adipocyte. The model and calculations also suggest that the number of free available proton is the major limiting factor for endogenous thermogenesis and its speed.

q-bio.SC↗

arXiv2016

Purification of recombinant human and Drosophila septin hexamers for TIRF assays of actin-septin filament assembly

Septins are guanine nucleotide-binding proteins that are conserved from fungi to humans. Septins assemble into heterooligomeric complexes and higher-order structures with key roles in various cellular functions including cell migration and division. The mechanisms by which septins assemble and interact with other cytoskeletal elements like actin remain elusive. A powerful approach to address this question is by cell-free reconstitution of pu- rified cytoskeletal proteins combined with fluorescence microscopy. Here, we describe procedures for the purification of recombinant Drosophila and human septin hexamers from Escherichia coli and reconstitution of actin-septin coassembly. These procedures can be used to compare assembly of Drosophila and human septins and their coassembly with the actin cytoskeleton by total internal reflection fluorescence microscopy.

q-bio.SC↗

arXiv2016

Visualizing septins in early Drosophila embryos

Functional studies in Drosophila have been key for establishing a role for the septin family of proteins in animal cell division and thus extending for the first time observations from the budding yeast to animal cells. Visualizing the distribution of specific septins in different Drosophila tissues and, in particular, in the Drosophila embryo, together with biochemical and mutant phenotype data, has contributed important advances to our understanding of animal septin biology, suggesting roles in processes other than in cytokinesis. Septin localization using immunofluorescence assays has been possible due to the generation of antibodies against different Drosophila septins. The recent availability of lines expressing fluorescent protein fusions of specific septins further promises to facilitate studies on septin dynamics. Here, we provide protocols for preparing early Drosophila embryos to visualize septins using immunofluorescence assays and live fluorescence microscopy. The genetic tractability of the Drosophila embryo together with its amenability to high-resolution fluorescence microscopy promises to provide novel insights into animal septin structure and function.

q-bio.SC↗

arXiv2021

Fluid flow in the sarcomere

A highly organized and densely packed lattice of molecular machinery within the sarcomeres of muscle cells powers contraction. Although many of the proteins that drive contraction have been studied extensively, the mechanical impact of fluid shearing within the lattice of molecular machinery has received minimal attention. It was recently proposed that fluid flow augments substrate transport in the sarcomere, however, this analysis used analytical models of fluid flow in the molecular machinery that could not capture its full complexity. By building a finite element model of the sarcomere, we estimate the explicit flow field, and contrast it with analytical models. Our results demonstrate that viscous drag forces on sliding filaments are surprisingly small in contrast to the forces generated by single myosin molecular motors. This model also indicates that the energetic cost of fluid flow through viscous shearing with lattice proteins is likely minimal. The model also highlights a steep velocity gradient between sliding filaments and demonstrates that the maximal radial fluid velocity occurs near the tips of the filaments. To our knowledge, this is the first computational analysis of fluid flow within the highly structured sarcomere.

q-bio.SC↗