Quantitative Biology

Epigenetics has captured the attention of scientists in the past decades, yet its scope has been continuously changing. In this paper, we give an overview on how and why its definition has evolved and suggest several clarification on the concepts used in this field, in particular, on the notions of epigenetic information, epigenetic stability and epigenetic templating. Another issue that we address is the role of epigenetic information. Not only it is important in allowing alternative interpretations of genetic information, but it appears to be important in protecting the genetic information, moreover, we suggest that this function appeared first in evolution and only later on the epigenetic mechanisms were recruited to play a role in cell differentiation.

Synthesis of biopolymers such as DNA, RNA, and proteins are biophysical processes aided by enzymes. Performance of these enzymes is usually characterized in terms of their average error rate and speed. However, because of thermal fluctuations in these single-molecule processes, both error and speed are inherently stochastic quantities. In this paper, we study fluctuations of error and speed in biopolymer synthesis and show that they are in general correlated. This means that, under equal conditions, polymers that are synthesized faster due to a fluctuation tend to have either better or worse errors than the average. The error-correction mechanism implemented by the enzyme determines which of the two cases holds. For example, discrimination in the forward reaction rates tends to grant smaller errors to polymers with faster synthesis. The opposite occurs for discrimination in monomer rejection rates. Our results provide an experimentally feasible way to identify error-correction mechanisms by measuring the error-speed correlations.

The early steps of light response occur in the outer segment of rod and cone photoreceptor. They involve the hydrolysis of cGMP, a soluble cyclic nucleotide, that gates ionic channels located in the outer segment membrane. We shall study here the rate by which cGMP is hydrolyzed by activated phosphodiesterase (PDE). This process has been characterized experimentally by two different rate constants β d and β sub : β d accounts for the effect of all spontaneously active PDE in the outer segment, and β sub characterizes cGMP hydrolysis induced by a single light-activated PDE. So far, no attempt has been made to derive the experimental values of β d and β sub from a theoretical model, which is the goal of this work. Using a model of diffusion in the confined rod geometry, we derive analytical expressions for β d and β sub by calculating the flux of cGMP molecules to an activated PDE site. We obtain the dependency of these rate constants as a function of the outer segment geometry, the PDE activation and deactivation rates and the aqueous cGMP diffusion constant. Our formulas show good agreement with experimental measurements. Finally, we use our derivation to model the time course of the cGMP concentration in a transversally well stirred outer segment.

The movement of a particle described by Brownian motion is quantified by a single parameter, D , the diffusion constant. The estimation of D from a discrete sequence of noisy observations is a fundamental problem in biological single particle tracking experiments since it can report on the environment and/or the state of the particle itself via hydrodynamic radius. Here we present a method to estimate D that takes into account several effects that occur in practice, that are important for correct estimation of D , and that have hitherto not been combined together for estimation of D . These effects are motion blur from finite integration time of the camera, intermittent trajectories, and time-dependent localization uncertainty. Our estimation procedure, a maximum likelihood estimation, follows directly from the likelihood expression for a discretely observed Brownian trajectory that explicitly includes these effects. The manuscript begins with the formulation of the likelihood expression and then presents three methods to find the exact solution. Each method has its own advantages in either computational robustness, theoretical insight, or the estimation of hidden variables. We then compare our estimator to previously published estimators using a squared log loss function to demonstrate the benefit of including these effects.

The bulk of stochastic gene expression models in the literature do not have an explicit description of the age of a cell within a generation and hence they cannot capture events such as cell division and DNA replication. Instead, many models incorporate cell cycle implicitly by assuming that dilution due to cell division can be described by an effective decay reaction with first-order kinetics. If it is further assumed that protein production occurs in bursts then the stationary protein distribution is a negative binomial. Here we seek to understand how accurate these implicit models are when compared with more detailed models of stochastic gene expression. We derive the exact stationary solution of the chemical master equation describing bursty protein dynamics, binomial partitioning at mitosis, age-dependent transcription dynamics including replication, and random interdivision times sampled from Erlang or more general distributions; the solution is different for single lineage and population snapshot settings. We show that protein distributions are well approximated by the solution of implicit models (a negative binomial) when the mean number of mRNAs produced per cycle is low and the cell cycle length variability is large. When these conditions are not met, the distributions are either almost bimodal or else display very flat regions near the mode and cannot be described by implicit models. We also show that for genes with low transcription rates, the size of protein noise has a strong dependence on the replication time, it is almost independent of cell cycle variability for lineage measurements and increases with cell cycle variability for population snapshot measurements. In contrast for large transcription rates, the size of protein noise is independent of replication time and increases with cell cycle variability for both lineage and population measurements.

Extremely low frequency electromagnetic fields aren't considered as a real carcinogenic agent despite the fact that some studies have showed impairment of the DNA integrity in different cells lines. The aim of this study was evaluation of the late effects of a 100 Hz and 5.6 mT electromagnetic field, applied continuously or discontinuously, on the DNA integrity of Vero cells assessed by alkaline Comet assay and by cell cycle analysis. Normal Vero cells were exposed to extremely low frequency electromagnetic fields (100 Hz, 5.6 mT) for 45 minutes. The Comet assay and cell cycle analysis were performed 48 hours after the treatment. Exposed samples presented an increase of the number of cells with high damaged DNA as compared with non-exposed cells. Quantitative evaluation of the comet assay showed a significantly ( < 0.001) increase of the tail lengths, of the quantity of DNA in tail and of Olive tail moments, respectively. The analysis of the registered comet indices showed that an extremely low frequency electromagnetic field of 100 Hz and 5.6 mT had a genotoxic impact on Vero cells. Cell cycle analysis showed an increase of the frequency of the cells in S phase, proving the occurrence of single strand breaks. The most probable mechanism of induction of the registered effects is the production of different types of reactive oxygen species.

F1F0 ATP synthase (ATPase) either facilitates the synthesis of ATP in the mitochondrial membranes and bacterial inner membranes in a process driven by the proton moving force (pmf), or uses the energy from ATP hydrolysis to pump protons against the concentration gradient across the membrane. ATPase is composed of two rotary motors, F0 and F1, which generate the opposing rotation and compete for control of their shared central gamma-shaft. Here we present a self-consistent physical model of the F1 motor as a simplified two-state Brownian ratchet based on the asymmetry of torsional elastic energy of the coiled-coil gamma-shaft. This stochastic model unifies the physical description of linear and rotary motors and explains the stepped unidirectional rotation of the γ -shaft, in agreement with the `binding-change' ideas of Boyer. Substituting the model parameters, all independently known from recent experiments, our model quantitatively reproduces the ATPase operation, e.g. the `no-load' angular velocity is ca. 400~rad/s anticlockwise at 4 mM ATP, in close agreement with experiment. Increasing the pmf torque exerted by F0 can slow, stop and overcome the torque generated by F1, switching from ATP hydrolysis to synthesis at a very low value of `stall torque'. We discuss the matters of the motor efficiency, which is very low if calculated from the useful mechanical work it produces - but is quite high when the `useful outcome' is measured in the number of H+ pushed against the chemical gradient in the F1 ATP-driven operation.

Cellular responses often require the fast activation or repression of specific genes, which depends on Transcription Factors (TFs) that have to quickly find the promoters of these genes within a large genome. Transcription Factors (TFs) search for their DNA promoter target by alternating between bulk diffusion and sliding along the DNA, a mechanism known as facilitated diffusion. We study a facilitated diffusion framework with switching between three search modes: a bulk mode and two sliding modes triggered by conformational changes between two protein conformations. In one conformation (search mode) the TF interacts unspecifically with the DNA backbone resulting in fast sliding. In the other conformation (recognition mode) it interacts specifically and strongly with DNA base pairs leading to slow displacement. From the bulk, a TF associates with the DNA at a random position that is correlated with the previous dissociation point, which implicitly is a function of the DNA structure. The target affinity depends on the conformation. We derive exact expressions for the mean first passage time (MFPT) to bind to the promoter and the conditional probability to bind before detaching when arriving at the promoter site. We systematically explore the parameter space and compare various search scenarios. We compare our results with experimental data for the dimeric Lac repressor search in E.Coli bacteria. We find that a coiled DNA conformation is absolutely necessary for a fast MFPT. With frequent spontaneous conformational changes, a fast search time is achieved even when a TF becomes immobilized in the recognition state due to the specific bindings. We find a MFPT compatible with experimental data in presence of a specific TF-DNA interaction energy that has a Gaussian distribution with a large variance.

We formulate and analyze a theoretical model for the regulation of microtubule (MT) polymerization dynamics by the signaling proteins Rac1 and stathmin. In cells, the MT growth rate is inhibited by cytosolic stathmin, which, in turn, is inactivated by Rac1. Growing MTs activate Rac1 at the cell edge, which closes a positive feedback loop. We investigate both tubulin sequestering and catastrophe promotion as mechanisms for MT growth inhibition by stathmin. For a homogeneous stathmin concentration in the absence of Rac1, we find a switch-like regulation of the MT mean length by stathmin. For constitutively active Rac1 at the cell edge, stathmin is deactivated locally, which establishes a spatial gradient of active stathmin. In this gradient, we find a stationary bimodal MT length distributions for both mechanisms of MT growth inhibition by stathmin. One subpopulation of the bimodal length distribution can be identified with fast growing and long pioneering MTs in the region near the cell edge, which have been observed experimentally. The feedback loop is closed through Rac1 activation by MTs. For tubulin sequestering by stathmin, this establishes a bistable switch with two stable states: one stable state corresponds to upregulated MT mean length and bimodal MT length distributions, i.e., pioneering MTs; the other stable state corresponds to an interrupted feedback with short MTs. Stochastic effects as well as external perturbations can trigger switching events. For catastrophe promoting stathmin we do not find bistability.

In this paper, we develop and analyze a minimal model for a 2D network of cross-linked actin filaments and myosin motors, representing the cortical cytoskeleton of eukaryotic cells. We implement coarse-grained representations of force production by myosin motors and stress dissipation through an effective cross-link friction and filament turnover. We use this model to characterize how the sustained production of active stress, and the steady dissipation of elastic stress, depend individually on motor activity, effective cross-link friction and filament turnover. Then we combine these results to gain insights into how microscopic network parameters control steady state flow produced by asymmetric distributions of motor activity. Our results provide a framework for understanding how local modulation of microscopic interactions within contractile networks control macroscopic quantities like active stress and effective viscosity to control cortical deformation and flow at cellular scales.