Connecting protein and mRNA burst distributions for stochastic models of gene expression

The intrinsic stochasticity of gene expression can lead to large variability in protein levels for genetically identical cells. Such variability in protein levels can arise from infrequent synthesis of mRNAs which in turn give rise to bursts of protein expression. Protein expression occurring in bursts has indeed been observed experimentally and recent studies have also found evidence for transcriptional bursting, i.e. production of mRNAs in bursts. Given that there are distinct experimental techniques for quantifying the noise at different stages of gene expression, it is of interest to derive analytical results connecting experimental observations at different levels. In this work, we consider stochastic models of gene expression for which mRNA and protein production occurs in independent bursts. For such models, we derive analytical expressions connecting protein and mRNA burst distributions which show how the functional form of the mRNA burst distribution can be inferred from the protein burst distribution. Additionally, if gene expression is repressed such that observed protein bursts arise only from single mRNAs, we show how observations of protein burst distributions (repressed and unrepressed) can be used to completely determine the mRNA burst distribution. Assuming independent contributions from individual bursts, we derive analytical expressions connecting means and variances for burst and steady-state protein distributions. Finally, we validate our general analytical results by considering a specific reaction scheme involving regulation of protein bursts by small RNAs. For a range of parameters, we derive analytical expressions for regulated protein distributions that are validated using stochastic simulations. The analytical results obtained in this work can thus serve as useful inputs for a broad range of studies focusing on stochasticity in gene expression

A Persistent Kuroshio in the Glacial East China Sea and Implications for Coral Paleobiogeography

The Kuroshio Current is a major hydrographical feature of the modern East China Sea, but it has been suggested that its flow was diverted to the east of the Ryukyu Arc at the Last Glacial Maximum. Shoaling of the Yonaguni Depression has also been proposed as a cause of Kuroshio Current diversion which, while unlikely to have been significant at the Last Glacial Maximum, may have been an important consideration further back in time. Using an ensemble of high‐resolution ocean simulations with climatic boundary conditions emulating those of the Last Glacial Maximum, we present the first regional state estimates of the glacial East China Sea which are both physically consistent and compatible with sea surface temperature proxy compilations. We find that while the Kuroshio Current transport in the East China Sea is slightly reduced at the Last Glacial Maximum, its path is relatively unchanged, with limited sensitivity to glacioeustatic sea level change, glacial‐interglacial changes in climate, and tectonic shoaling of the Yonaguni Depression. Simulations with the best model‐proxy agreement predict only limited contraction of the reef front at the Last Glacial Maximum, and strong surface currents associated with the glacial Kuroshio may have maintained or even improved long‐distance coral larval dispersal along the Ryukyu Arc, suggesting that conditions may have enabled coral reefs in this region to remain widespread throughout the last glacial. Further field studies investigating whether this is genuinely the case will provide insights into how the coral reef front responds to long‐term environmental change

Steady state solutions of hydrodynamic traffic models

We investigate steady state solutions of hydrodynamic traffic models in the absence of any intrinsic inhomogeneity on roads such as on-ramps. It is shown that typical hydrodynamic models possess seven different types of inhomogeneous steady state solutions. The seven solutions include those that have been reported previously only for microscopic models. The characteristic properties of wide jam such as moving velocity of its spatiotemporal pattern and/or out-flux from wide jam are shown to be uniquely determined and thus independent of initial conditions of dynamic evolution. Topological considerations suggest that all of the solutions should be common to a wide class of traffic models. The results are discussed in connection with the universality conjecture for traffic models. Also the prevalence of the limit-cycle solution in a recent study of a microscopic model is explained in this approach.Comment: 9 pages, 6 figure

Instability of dilute granular flow on rough slope

We study numerically the stability of granular flow on a rough slope in collisional flow regime in the two-dimension. We examine the density dependence of the flowing behavior in low density region, and demonstrate that the particle collisions stabilize the flow above a certain density in the parameter region where a single particle shows an accelerated behavior. Within this parameter regime, however, the uniform flow is only metastable and is shown to be unstable against clustering when the particle density is not high enough.Comment: 4 pages, 6 figures, submitted to J. Phys. Soc. Jpn.; Fig. 2 replaced; references added; comments added; misprints correcte