Quantitative Biology

The aim of this paper is to contribute to the basic understanding of neuronal polarization mechanisms by developing and studying a reaction-diffusion model for protein activation and inactivation. In particular we focus on a feedback loop between PI3 kinase and certain GTPases, and study its behaviour in dependence of neurite lengths. We find that if an ultrasensitive activation is included, the model can produce polarization at a critical length as observed in experiments. Symmetry breaking to polarization in the longer neurite is found only if active transport of a substance, in our case active PI3 kinase, is included into the model.

Biological cells are able to accurately sense chemicals with receptors at their surfaces, allowing cells to move towards sources of attractant and away from sources of repellent. The accuracy of sensing chemical concentration is ultimately limited by the random arrival of particles at the receptors by diffusion. This fundamental physical limit is generally considered to be the Berg & Purcell limit [H.C. Berg and E.M. Purcell, Biophys. J. {\bf 20}, 193 (1977)]. Here we derive a lower limit by applying maximum likelihood to the time series of receptor occupancy. The increased accuracy stems from solely considering the unoccupied time intervals - disregarding the occupied time intervals as these do not contain any information about the external particle concentration, and only decrease the accuracy of the concentration estimate. Receptors which minimize the bound time intervals achieve the highest possible accuracy. We discuss how a cell could implement such an optimal sensing strategy by absorbing or degrading bound particles.

In the recent paper (2011) Faas and co-workers claimed that calmodulin could directly detect Ca2+ signals by acting as extremely fast calcium buffer. However the results and their interpretation raise serious doubts about this conclusion.

In cells, most of cargos are transported by motor proteins along microtubule. Biophysically, unidirectional motion of large number of motor proteins along a single track can be described by totally asymmetric simple exclusion process (TASEP). From which many meaningful properties, such as the appearance of domain wall (defined as the borderline of high density and low density of motor protein along motion track) and boundary layers, can be obtained. However, it is biologically obvious that a single track may be occupied by different motor species. So previous studies based on TASEP of one particle species are not reasonable enough to find more detailed properties of the motion of motors along a single track. To address this problem, TASEP with two particle species is discussed in this study. Theoretical methods to get densities of each particle species are provided. Using these methods, phase transition related properties of particle densities are obtained. Our analysis show that domain wall and boundary layer of single species densities always appear simultaneously with those of the total particle density. The height of domain wall of total particle density is equal to the summation of those of single species. Phase diagrams for typical model parameters are also presented. The methods presented in this study can be generalized to analyze TASEP with more particle species.

Spindles are self-organized microtubule-based structures that segregate chromosomes during cell division. The mass of the spindle is controlled by the balance between microtubule turnover and nucleation. The mechanisms that control the spatial regulation of microtubule nucleation remain poorly understood. Previous work has found that microtubule nucleators bind to microtubules in the spindle, but it is unclear if this binding regulates the activity of those nucleators. Here we use a combination of experiments and mathematical modeling to investigate this issue. We measure the concentration of tubulin and microtubules in and around the spindle. We found a very sharp decay in microtubules at the spindle interface, which is inconsistent with the activity of microtubule nucleators being independent of their association with microtubules and consistent with a model in which microtubule nucleators are only active when bound to a microtubule. This strongly argues that the activity of microtubule nucleators is greatly enhanced when bound to microtubules. Thus, microtubule nucleators are both localized and activated by the microtubules they generate.

Over the last several decades it has been increasingly recognized that stochastic processes play a central role in transcription. Though many stochastic effects have been explained, the source of transcriptional bursting (one of the most well-known sources of stochasticity) has continued to evade understanding. Recent results have pointed to mechanical feedback as the source of transcriptional bursting but a reconciliation of this perspective with preexisting views of transcriptional regulation is lacking. In this letter we present a simple phenomenological model which is able to incorporate the traditional view of gene expression within a framework with mechanical limits to transcription. Our model explains the emergence of universal properties of gene expression, wherein the lower limit of intrinsic noise necessarily rises with mean expression level.

Recently the physical characterization of a number of biological processes has proven indispensable for a full understanding of natural phenomena. One such example is the mechanical properties of transcription, which have been shown to have significant effects in gene expression. In this letter we introduce a simple description of the basic physical elements of transcription where RNA elongation, RNA polymerase rotation and DNA supercoiling are coupled. The resulting framework describes the relative amount of RNA polymerase rotation and DNA supercoiling that occurs during RNA elongation. Asymptotic behavior is derived and can be used to experimentally extract unknown mechanical parameters of transcription. Incorporation of mechanical limits to RNA polymerase is accomplished yielding an equation of motion for DNA supercoiling and RNA elongation with transcriptional stalling. Important implications for gene expression, chromatin structure and genome organization are discussed.

Heart muscle contraction is normally activated by a synchronized Ca release from sarcoplasmic reticulum (SR), a major intracellular Ca store. However, under abnormal conditions Ca leaks from the SR, decreasing heart contraction amplitude and increasing risk of life-threatening arrhythmia. The mechanisms and regimes of SR operation generating the abnormal Ca leak remain unclear. Here we employed both numerical and analytical modeling to get mechanistic insights into the emergent Ca leak phenomenon. Our numerical simulations using a detailed realistic model of Ca release unit (CRU) reveal sharp transitions resulting in Ca leak. The emergence of leak is closely mapped mathematically to the Ising model from statistical mechanics. The system steady-state behavior is determined by two aggregate parameters: the analogues of magnetic field ( h ) and the inverse temperature ( β ) in the Ising model, for which we have explicit formulas in terms of SR Ca and release channel opening/closing rates. The classification of leak regimes takes the shape of a phase β - h diagram, with the regime boundaries occurring at h =0 and a critical value of β ( β∗ ) which we estimate using a classical Ising model and mean field theory. Our theory predicts that a synchronized Ca leak will occur when h >0 and β>β∗ and a disordered leak occurs when β<β∗ and h is not too negative. The disorder leak is distinguished from synchronized leak (in long-lasting sparks) by larger Peierls contour lengths, an output parameter reflecting degree of disorder. Thus, in addition to our detailed numerical model approach we also offer an instantaneous computational tool using analytical formulas of the Ising model for respective RyR parameters and SR Ca load that describe and classify phase transitions and leak emergence.

Protein-DNA interactions are critical for the successful functioning of all natural systems. The key role in these interactions is played by processes of protein search for specific sites on DNA. Although it has been studied for many years, only recently microscopic aspects of these processes became more clear. In this work, we present a review on current theoretical understanding of the molecular mechanisms of the protein target search. A comprehensive discrete-state stochastic method to explain the dynamics of the protein search phenomena is introduced and explained. Our theoretical approach utilizes a first-passage analysis and it takes into account the most relevant physical-chemical processes. It is able to describe many fascinating features of the protein search, including unusually high effective association rates, high selectivity and specificity, and the robustness in the presence of crowders and sequence heterogeneity.

We examine the budding of a nanoscale particle through a lipid bilayer using molecular dynamics simulations, free energy calculations, and an elastic theory, with the aim of determining the extent to which equilibrium elasticity theory can describe the factors that control the mechanism and efficiency of budding. The particle is a smooth sphere which experiences attractive interactions to the lipid head groups. Depending on the parameters, we observe four classes of dynamical trajectories: particle adhesion to the membrane, stalled partially wrapped states, budding followed by scission, and membrane rupture. In most regions of parameter space we find that the elastic theory agrees nearly quantitatively with the simulated phase behavior as a function of adhesion strength, membrane bending rigidity, and particle radius. However, at parameter values near the transition between particle adhesion and budding, we observe long-lived partially wrapped states which are not captured by existing elastic theories. These states could constrain the accessible system parameters for those enveloped viruses or drug delivery vehicles which rely on exo- or endocytosis for membrane transport.