Phosphatidylserine (PS) is a negatively-charged glycerophospholipid found mainly in the plasma membrane (PM) and in the late secretory/endocytic compartments, where it regulates cellular activity and can mediate apoptosis. Export of PS from the endoplasmic reticulum, its site of synthesis, to other compartments, and its transbilayer asymmetry must therefore be precisely regulated. We review recent findings on non-vesicular transport of PS by lipid transfer proteins (LTPs) at membrane contact sites, on PS flip-flop between membrane leaflets by flippases and scramblases, and on PS nano-clustering at the PM. We also discuss emerging data on cooperation between scramblases and LTPs, how perturbation of PS distribution can lead to disease, and the specific role of PS in viral infection.
The rheology of biological cells is not only determined by their cytoskeletal networks, but also by the molecular motors that crosslink and contract them. Recently it has been found that the assemblies of myosin II molecular motors in non-muscle cells are mixtures of fast and slow motor variants. Using computer simulations and an analytical mean field theory of a crossbridge model for myosin II motors, here we show that such motor ensembles effectively behave as active Maxwell elements. We calculate storage and loss moduli as a function of the model parameters and show that the rheological properties cross over from viscous to elastic as one increases the ratio of slow to fast motors. This suggests that cells tune their mechanical properties by regulating the composition of their myosin assemblies.
The validity of a complex reaction pathway proposed to treat Inflammatory Bowel Disease (IBD) was verified by a comprehensive time and frequency domain analysis. The model was taken to the frequency domain to study the effect and the significance of the negative feedback loop introduced by the reaction pathways. It could be shown that such proposed probiotics have very interesting potentials that could be used extensively in the near future.
Kevin Y. Chen, Daniel M. Zuckerman, Philip C. Nelson
Stochastic simulation can make the molecular processes of cellular control more vivid than the traditional differential-equation approach by generating typical system histories instead of just statistical measures such as the mean and variance of a population. Simple simulations are now easy for students to construct from scratch, that is, without recourse to black-box packages. In some cases, their results can also be compared directly to single-molecule experimental data. After introducing the stochastic simulation algorithm, this article gives two case studies, involving gene expression and error correction, respectively. Code samples and resulting animations showing results are given in the online supplements.
Diffusion in cell biology is important and complicated. Diffusing particles must contend with a complex environment as they make their way through the cell. We analyze a particular type of complexity that arises when diffusing particles reversibly bind to elastically tethered binding partners. Using asymptotic analysis, we derive effective equations for the transport of both single and multiple particles in the presence of such elastic tethers. We show that for the case of linear elasticity and simple binding kinetics, the elastic tethers have a weak hindering effect on particle motion when only one particle is present, while, remarkably, strongly enhancing particle motion when multiple particles are present. We give a physical interpretation of this result that suggests a similar effect may be present in other biological settings.
As a cheap and safe antimalarial agent, chloroquine (CQ) has been used in the battle against malaria for more than half century. However, the mechanism of CQ action and resistance in Plasmodium falciparum remains elusive. Based on further analysis of our published experimental results, we propose that the mechanism of CQ action and resistance might be closely linked with cell-cycle-associated amplified genomic-DNA fragments (CAGFs, singular form = CAGF) as CQ induces CAGF production in P. falciparum, which could affect multiple biological processes of the parasite, and thus might contribute to parasite death and CQ resistance. Recently, we found that CQ induced one of CAGFs, UB1- CAGF, might downregulate a probable P. falciparum cystine transporter (Pfct) gene expression, which could be used to understand the mechanism of CQ action and resistance in P. falciparum.
Kanishka Basnayake, Claire Guerrier, Zeev Schuss
et al.
The first of $N$ identical independently distributed (i.i.d.) Brownian trajectories that arrives to a small target, sets the time scale of activation, which in general is much faster than the arrival to the target of only a single trajectory. Analytical asymptotic expressions for the minimal time is notoriously difficult to compute in general geometries. We derive here asymptotic laws for the probability density function of the first and second arrival times of a large number of i.i.d. Brownian trajectories to a small target in 1,2, and 3 dimensions and study their range of validity by stochastic simulations. The results are applied to activation of biochemical pathways in cellular transduction.
Michele Castellana, Sophia Hsin-Jung Li, Ned S. Wingreen
In bacteria such as $\textit{Escherichia coli}$, DNA is compacted into a nucleoid near the cell center, while ribosomes$-$molecular complexes that translate messenger RNAs (mRNAs) into proteins$-$are mainly localized at the poles. We study the impact of this spatial organization using a minimal reaction-diffusion model for the cellular transcriptional-translational machinery. Our model predicts that $\sim 90\%$ of mRNAs are segregated to the poles and reveals a "circulation" of ribosomes driven by the flux of mRNAs, from synthesis in the nucleoid to degradation at the poles. To address the existence of non-specific, transient interactions between ribosomes and mRNAs, we developed a novel method to efficiently incorporate such transient interactions into reaction-diffusion equations, which allowed us to quantify the biological implications of such non-specific interactions, e.g. for ribosome efficiency.
We study the response of an autoregulated gene to a range of concentrations of signal molecules. We show that transcriptional leakage and noise due to translational bursting have the opposite effects. In a positively autoregulated gene, increasing the noise converts the response from graded to binary, while increasing the leakage converts the response from binary to graded. Our findings support the hypothesis that, being a common phenomenon, leaky expression may be a relatively easy way for evolutionary tuning of the type of gene response without changing the type of regulation from positive to negative.
Guilherme C. P. Innocentini, Michael Forger, Ovidiu Radulescu
et al.
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.
Modeling of ion transport via plasma membrane needs identification and quantitative understanding of the involved processes. Brief characterization of main ion transport systems of a yeast cell (Pma1, Ena1, TOK1, Nha1, Trk1, Trk2, non-selective cation conductance) and determining the exact number of molecules of each transporter per a typical cell allow us to predict the corresponding ion flows. In this review a comparison of ion transport in small yeast cell and several animal cell types is provided. The importance of cell volume to surface ratio is emphasized. The role of cell wall and lipid rafts is discussed in respect to required increase in spatial and temporal resolution of measurements. Conclusions are formulated to describe specific features of ion transport in a yeast cell. Potential directions of future research are outlined based on the assumptions.
Compartmentalization into biochemically distinct organelles constantly exchanging material is one of the hallmarks of eukaryotic cells. In the most naive picture of inter-organelle transport driven by concentration gradients, concentration differences between organelles should relax. We determine the conditions under which cooperative transport, i.e. based on molecular recognition, allows for the existence and maintenance of distinct organelle identities. Cooperative transport is also shown to control the flux of material transiting through a compartmentalized system, dramatically increasing the transit time under high incoming flux. By including chemical processing of the transported species, we show that this property provides a strong functional advantage to a system responsible for protein maturation and sorting.
Eric Smith, Supriya Krishnamurthy, Walter Fontana
et al.
We study a mechanism for reliable switching in biomolecular signal-transduction cascades. Steady bistable states are created by system-size cooperative effects in populations of proteins, in spite of the fact that the phosphorylation-state transitions of any molecule, by means of which the switch is implemented, are highly stochastic. The emergence of switching is a nonequilibrium phase transition in an energetically driven, dissipative system described by a master equation. We use operator and functional integral methods from reaction-diffusion theory to solve for the phase structure, noise spectrum, and escape trajectories and first-passage times of a class of minimal models of switches, showing how all critical properties for switch behavior can be computed within a unified framework.
The spatiotemporal oscillations of the Min proteins in the bacterium Escherichia coli play an important role in cell division. A number of different models have been proposed to explain the dynamics from the underlying biochemistry. Here, we extend a previously described discrete polymer model from a deterministic to a stochastic formulation. We express the stochastic evolution of the oscillatory system as a map from the probability distribution of maximum polymer length in one period of the oscillation to the probability distribution of maximum polymer length half a period later and solve for the fixed point of the map with a combined analytical and numerical technique. This solution gives a theoretical prediction of the distributions of both lengths of the polar MinD zones and periods of oscillations -- both of which are experimentally measurable. The model provides an interesting example of a stochastic hybrid system that is, in some limits, analytically tractable.
The jasmonate (JA) signaling pathway in plants is activated as defense response to a number of stresses like attacks by pests or pathogens and wounding by animals. Some recent experiments provide significant new knowledge on the molecular detail and connectivity of the pathway. The pathway has two major components in the form of feedback loops, one negative and the other positive. We construct a minimal mathematical model, incorporating the feedback loops, to study the dynamics of the JA signaling pathway. The model exhibits transient gene expression activity in the form of JA pulses in agreement with experimental observations. The dependence of the pulse amplitude, duration and peak time on the key parameters of the model is determined computationally. The deterministic and stochastic aspects of the pathway dynamics are investigated using both the full mathematical model as well as a reduced version of it. We also compare the mechanism of pulse formation with the known mechanisms of pulse generation in some bacterial and viral systems.
Roberto Chignola, Alessio Del Fabbro, Edoardo Milotti
We study the dynamics of intracellular calcium oscillations in the presence of proteins that bind calcium on multiple sites and that are generally believed to act as passive calcium buffers in cells. We find that multisite calcium-binding proteins set a sharp threshold for calcium oscillations. Even with high concentrations of calcium-binding proteins, internal noise, which shows up spontaneously in cells in the process of calcium wave formation, can lead to self-oscillations. This produces oscillatory behaviors strikingly similar to those observed in real cells. In addition, for given intracellular concentrations of both calcium and calcium-binding proteins the regularity of these oscillations changes and reaches a maximum as a function noise variance, and the overall system dynamics displays stochastic coherence. We conclude that calcium-binding proteins may have an important and active role in cellular communication.
Masatoshi Nishikawa, Hiroaki Takagi, Atsuko H. Iwane
et al.
Mechanochemical coupling was studied for two different types of myosin motors in cells: myosin V, which carries cargo over long distances by as a single molecule; and myosin II, which generates a contracting force in cooperation with other myosin II molecules. Both mean and variance of myosin V velocity at various [ATP] obeyed Michaelis-Menten mechanics, consistent with tight mechanochemical coupling. Myosin II, working in an ensemble, however, was explained by a loose coupling mechanism, generating variable step sizes depending on the ATP concentration and realizing a much larger step (200 nm) per ATP hydrolysis than myosin V through its cooperative nature at zero load. These different mechanics are ideal for the respective myosin's physiological functions.
Trajectories of on-off events are the output of many single molecule experiments. Usually, one describes the underlying mechanism that generates the trajectory using a kinetic scheme, and by analyzing the trajectory aims at deducing this scheme. In a previous work [O. Flomenbom, J. Klafter, and A. Szabo, submitted (2004)], we showed that when successive events along a trajectory are uncorrelated, all the information in the trajectory is contained in two basic functions, which are the waiting time probability functions (PDFs) of the on state and of the off state. The kinetic schemes that lead to such uncorrelated trajectories were termed reducible. Here we discuss the reasons that lead to reducible schemes. In particular, the topology of reducible schemes is characterized and proven.
We investigate a mechanism for the polar localization of proteins in bacteria. We focus on the MinCD/DivIVA system regulating division site placement in the rod-shaped bacterium Bacillus subtilis. Our model relies on a combination of geometric effects and reaction-diffusion dynamics to direct proteins to both cell poles, where division is then blocked. We discuss similarities and differences with related division models in Escherichia coli and also develop extensions of the model to asymmetric polar protein localization. We propose that our mechanism for polar localization may be employed more widely in bacteria, especially in outgrowing spores, which do not possess any pre-existing polar division apparatus from prior division events.