Calcium storage in multivesicular endo-lysosome.

It is now established that endo-lysosomes, also referred to as late endosomes, serve as intracellular calcium store, in addition to the endoplasmic reticulum. While abundant calcium-binding proteins provide the latter compartment with its calcium storage capacity, essentially nothing is known about the mechanism responsible for calcium storage in endo-lysosomes. In this paper, we propose that the structural organization of endo-lysosomal membranes drives the calcium storage capacity of the compartment. Indeed, endo-lysosomes exhibit a characteristic multivesicular ultrastructure, with intralumenal membranes providing a large amount of additional bilayer surface. We used a theoretical approach to investigate the calcium storage capacity of endosomes, using known calcium binding affinities for bilayers and morphological data on endo-lysosome membrane organization. Finally, we tested our predictions experimentally after Sorting Nexin 3 depletion to decrease the intralumenal membrane content. We conclude that the major negatively-charge lipids and proteins of endo-lysosomes serve as calcium-binding molecules in the acidic calcium stores of mammalian cells, while the large surface area of intralumenal membranes provide the necessary storage capacity.

Accuracy in readout of glutamate concentrations by neuronal cells.

Glutamate and glycine are important neurotransmitters in the brain. An action potential propagating in the terminal of a presynaptic neuron causes the release of glutamate and glycine in the synapse by vesicles fusing with the cell membrane, which then activate various receptors on the cell membrane of the post-synaptic neuron. Entry of Ca[Formula: see text] through the activated NMDA receptors leads to a host of cellular processes of which long-term potentiation is of crucial importance because it is widely considered to be one of the major mechanisms behind learning and memory. By analysing the readout of glutamate concentration by the post-synaptic neurons during Ca[Formula: see text] signaling, we find that the average receptor density in hippocampal neurons has evolved to allow for accurate measurement of the glutamate concentration in the synaptic cleft.

Limitations on concentration measurements and gradient discerning times in cellular systems.

This work reports on two results. At first we revisit the Berg and Purcell calculation that provides a lower bound to the error in concentration measurement by cells by considering the realistic case when the cell starts measuring the moment it comes in contact with the chemoattractants, instead of measuring after equilibrating with the chemotactic concentration as done in the classic Berg and Purcell paper. We find that the error in concentration measurement is still the same as evaluated by Berg and Purcell. We next derive a lower bound on measurement time below which it is not possible for the cell to discern extracellular chemotactic gradients through spatial sensing mechanisms. This bound is independent of diffusion rate and concentration of the chemoattracts and is instead set by detachment rate of ligands from the cell receptors. The result could help explain experimental observations.

Average search time bounds in cue-based searches.

In this work we consider search problems that evaluate the probability distribution of finding the source at each step in the search. We start with a sample strategy where the movement at each time step is in the immediate neighborhood. The jump probability is taken to be proportional to the normalized difference between the probability of finding the source at the jump location with the probability of finding the source at the present location. We evaluate a lower bound on the average search time for a searcher using this strategy. We next consider the problem of evaluating the lower bound on the search time for a generic strategy which would utilize the source probability distribution to figure out the position of the source. We derive an expression for the lower bound on the search time. We present an analytic expression for this lower bound in a case in which the particles emitted by the source diffuse in a homogeneous manner. For a general probability distribution with entropy E, we find that the lower bound goes as e^{E/2}.

Accuracy of position determination in Ca

A living cell senses its environment and responds to external signals. In this paper, we study theoretically the precision at which cells can determine the position of a spatially localized transient extracellular signal. To this end, we focus on the case where the stimulus is converted into the release of a small molecule that acts as a second messenger, for example, Ca^{2+}, and activates kinases that change the activity of enzymes by phosphorylating them. We analyze the spatial distribution of phosphorylation events using stochastic simulations as well as a mean-field approach. Kinases that need to bind to the cell membrane for getting activated provide more accurate estimates than cytosolic kinases. Our results could explain why the rate of Ca^{2+} detachment from the membrane-binding conventional protein kinase Cα is larger than its phosphorylation rate.

Positional Information Readout in Ca

Living cells respond to spatially confined signals. Intracellular signal transmission often involves the release of second messengers like Ca^{2+}. They eventually trigger a physiological response, for example, by activating kinases that in turn activate target proteins through phosphorylation. Here, we investigate theoretically how positional information can be accurately read out by protein phosphorylation in spite of rapid second messenger diffusion. We find that accuracy is increased by binding of kinases to the cell membrane prior to phosphorylation and by increasing the rate of Ca^{2+} loss from the cell interior. These findings could explain some salient features of the conventional protein kinase Cα.

Issues in data expansion in understanding criticality in biological systems.

At the point of a second-order phase transition also termed as a critical point, systems display long-range order and their macroscopic behaviors are independent of the microscopic details making up the system. Due to these properties, it has long been speculated that biological systems that show similar behavior despite having very different microscopics, may be operating near a critical point. Recent methods in neuroscience are making it possible to explore whether criticality exists in neural networks. Despite being large in size, many datasets are only a minute sample of the neural system and methods have to be developed to expand these datasets to study criticality. In this work we develop an analytical method of expanding a dataset to the large N limit to make statements about the critical nature of the dataset. We show that different ways of expanding the dataset while keeping its variance and mean fixed yield different results regarding criticality. This hence casts doubts on the established procedures for deducing criticality of biological systems through expansion of finite-sized datasets.

Physical model of protein cluster positioning in growing bacteria.

Chemotaxic receptors in bacteria form clusters at cell poles and also laterally, and this clustering plays an important role in signal transduction. These clusters were found to be periodically arranged on the surface of the bacterium Escherichia coli, independent of any known positioning mechanism. In this work we extend a model based on diffusion and aggregation to more realistic geometries and present a means based on "bursty" protein production to distinguish spontaneous positioning from an independently existing positioning mechanism. We also consider the case of isotropic cellular growth and characterize the degree of order arising spontaneously. Our model could also be relevant for other examples of periodically positioned protein clusters in bacteria.

Bacterial motion in narrow capillaries.

Motile bacteria often have to pass through small tortuous pores in soil or tissue of higher organisms. However, their motion in this prevalent type of niche is not fully understood. Here, we modeled it with narrow glass capillaries and identified a critical radius (Rc) for bacterial motion. Near the surface of capillaries narrower than that, the swimming trajectories are helices. In larger capillaries, they swim in distorted circles. Under non-slip condition, the peritrichous Escherichia coli swam in left-handed helices with an Rc of ~10 µm near glass surface. However, slipping could occur in the fast monotrichous Pseudomonas fluorescens, when a speed threshold was exceeded, and thus both left-handed and right-handed helices were executed in glass capillaries. In the natural non-cylindrical pores, the near-surface trajectories would be spirals and twisted loops. Engaging in such motions reduces the bacterial migration rate. With a given pore size, the run length and the tumbling angle of the bacterium determine the probability and duration of their near-surface motion. Shear flow and chemotaxis potentially enhance it. Based on this observation, the puzzling previous observations on bacterial migration in porous environments can be interpreted.

Modeling curvature-dependent subcellular localization of the small sporulation protein SpoVM in Bacillus subtilis.

Recent in vivo experiments suggest that in the bacterium, Bacillus subtilis, the cue for the localization of the small sporulation protein, SpoVM, an essential factor in spore coat formation, is curvature of the bacterial plasma membrane. In vitro measurements of SpoVM adsorption to vesicles of varying sizes also find high sensitivity of adsorption to vesicle radius. This curvature-dependent adsorption is puzzling given the orders of magnitude difference in length scale between an individual protein and the radius of curvature of the cell or vesicle, suggesting protein clustering on the membrane. Here we develop a minimal model to study the relationship between curvature-dependent membrane adsorption and clustering of SpoVM. Based on our analysis, we hypothesize that the radius dependence of SpoVM adsorption observed in vitro is governed primarily by membrane tension, while for in-vivo localization of SpoVM, we propose a highly sensitive mechanism for curvature sensing based on the formation of macroscopic protein clusters on the membrane.

Modeling the dynamics of dendritic actin waves in living cells.

The actin cytoskeleton in living cells exhibits a high degree of capacity for dynamic self-organization. Recent experiments have observed propagating actin waves in Dictyostelium cells recovering from complete depolymerization of their actin cytoskeleton. The propagation of these waves appear to be dependent on a programmed recruitment of a few proteins that control actin assembly and disassembly. Such waves also arise spontaneously along the plasma membrane of the cell, and it has been suggested that actin waves enable the cell to scan a surface for particles to engulf. Based on known molecular components involved in wave propagation, we present and study a minimal reaction-diffusion model for actin wave production observed in recovering cells.