Chk1 inhibits replication factory activation but allows dormant origin firing in existing factories

Replication origins are licensed by loading MCM2-7 hexamers before entry into S phase. However, only ∼10% of licensed origins are normally used in S phase, with the others remaining dormant. When fork progression is inhibited, dormant origins initiate nearby to ensure that all of the DNA is eventually replicated. In apparent contrast, replicative stress activates ataxia telangiectasia and rad-3–related (ATR) and Chk1 checkpoint kinases that inhibit origin firing. In this study, we show that at low levels of replication stress, ATR/Chk1 predominantly suppresses origin initiation by inhibiting the activation of new replication factories, thereby reducing the number of active factories. At the same time, inhibition of replication fork progression allows dormant origins to initiate within existing replication factories. The inhibition of new factory activation by ATR/Chk1 therefore redirects replication toward active factories where forks are inhibited and away from regions that have yet to start replication. This minimizes the deleterious consequences of fork stalling and prevents similar problems from arising in unreplicated regions of the genome

Markovian Dynamics on Complex Reaction Networks

Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm

Circular Stochastic Fluctuations in SIS Epidemics with Heterogeneous Contacts Among Sub-populations

The conceptual difference between equilibrium and non-equilibrium steady state (NESS) is well established in physics and chemistry. This distinction, however, is not widely appreciated in dynamical descriptions of biological populations in terms of differential equations in which fixed point, steady state, and equilibrium are all synonymous. We study NESS in a stochastic SIS (susceptible-infectious-susceptible) system with heterogeneous individuals in their contact behavior represented in terms of subgroups. In the infinite population limit, the stochastic dynamics yields a system of deterministic evolution equations for population densities; and for very large but finite system a diffusion process is obtained. We report the emergence of a circular dynamics in the diffusion process, with an intrinsic frequency, near the endemic steady state. The endemic steady state is represented by a stable node in the deterministic dynamics; As a NESS phenomenon, the circular motion is caused by the intrinsic heterogeneity within the subgroups, leading to a broken symmetry and time irreversibility.Comment: 29 pages, 5 figure

One-Dimensional Birth-Death Process and Delbr\"{u}ck-Gillespie Theory of Mesoscopic Nonlinear Chemical Reactions

As a mathematical theory for the stochasstic, nonlinear dynamics of individuals within a population, Delbr\"{u}ck-Gillespie process (DGP) $n(t)\in\mathbb{Z}^N$, is a birth-death system with state-dependent rates which contain the system size $V$ as a natural parameter. For large $V$, it is intimately related to an autonomous, nonlinear ordinary differential equation as well as a diffusion process. For nonlinear dynamical systems with multiple attractors, the quasi-stationary and stationary behavior of such a birth-death process can be underestood in terms of a separation of time scales by a $T^*\sim e^{\alpha V}$ $(\alpha>0)$: a relatively fast, intra-basin diffusion for $t\ll T^*$ and a much slower inter-basin Markov jump process for $t\gg T^*$. In the present paper for one-dimensional systems, we study both stationary behavior ($t=\infty$) in terms of invariant distribution $p_n^{ss}(V)$, and finite time dynamics in terms of the mean first passsage time (MFPT) $T_{n_1\rightarrow n_2}(V)$. We obtain an asymptotic expression of MFPT in terms of the "stochastic potential" $\Phi(x,V)=-(1/V)\ln p^{ss}_{xV}(V)$. We show in general no continuous diffusion process can provide asymptotically accurate representations for both the MFPT and the $p_n^{ss}(V)$ for a DGP. When $n_1$ and $n_2$ belong to two different basins of attraction, the MFPT yields the $T^*(V)$ in terms of $\Phi(x,V)\approx \phi_0(x)+(1/V)\phi_1(x)$. For systems with a saddle-node bifurcation and catastrophe, discontinuous "phase transition" emerges, which can be characterized by $\Phi(x,V)$ in the limit of $V\rightarrow\infty$. In terms of time scale separation, the relation between deterministic, local nonlinear bifurcations and stochastic global phase transition is discussed. The one-dimensional theory is a pedagogic first step toward a general theory of DGP.Comment: 32 pages, 3 figure

Neural networks impedance control of robots interacting with environments

In this paper, neural networks impedance control is proposed for robot-environment interaction. Iterative learning control is developed to make the robot dynamics follow a given target impedance model. To cope with the problem of unknown robot dynamics, neural networks are employed such that neither the robot structure nor the physical parameters are required for the control design. The stability and performance of the resulted closed-loop system are discussed through rigorous analysis and extensive remarks. The validity and feasibility of the proposed method are verified through simulation studies

Replication factory activation can be decoupled from the replication timing program by modulating Cdk levels

In the metazoan replication timing program, clusters of replication origins located in different subchromosomal domains fire at different times during S phase. We have used Xenopus laevis egg extracts to drive an accelerated replication timing program in mammalian nuclei. Although replicative stress caused checkpoint-induced slowing of the timing program, inhibition of checkpoint kinases in an unperturbed S phase did not accelerate it. Lowering cyclin-dependent kinase (Cdk) activity slowed both replication rate and progression through the timing program, whereas raising Cdk activity increased them. Surprisingly, modest alteration of Cdk activity changed the amount of DNA synthesized during different stages of the timing program. This was associated with a change in the number of active replication factories, whereas the distribution of origins within active factories remained relatively normal. The ability of Cdks to differentially effect replication initiation, factory activation, and progression through the timing program provides new insights into the way that chromosomal DNA replication is organized during S phase

Stochastic association of neighboring replicons creates replication factories in budding yeast

Peer reviewedPublisher PD

Interaction of HTLV-1 Tax with minichromosome maintenance proteins accelerates the replication timing program

The Tax oncoprotein encoded by the Human T-cell leukemia virus type 1 (HTLV-1) plays a pivotal role in viral persistence and pathogenesis. HTLV-1 infected cells proliferate faster than normal lymphocytes, expand through mitotic division and accumulate genomic lesions. Here, we show that Tax associates with the minichromosome maintenance MCM2-7 helicase complex and localizes to origins of replication. Tax modulates the spatiotemporal program of origin activation and fires supplementary origins at the onset of S phase. Thereby, Tax increases the DNA replication rate, accelerates S phase progression but also generates a replicative stress characterized by the presence of genomic lesions. Mechanistically, Tax favors p300 recruitment and histone hyperacetylation at late replication domains advancing their replication timing in early S phase

The Chemical Master Equation Approach to Nonequilibrium Steady-State of Open Biochemical Systems: Linear Single-Molecule Enzyme Kinetics and Nonlinear Biochemical Reaction Networks

We develop the stochastic, chemical master equation as a unifying approach to the dynamics of biochemical reaction systems in a mesoscopic volume under a living environment. A living environment provides a continuous chemical energy input that sustains the reaction system in a nonequilibrium steady state with concentration fluctuations. We discuss the linear, unimolecular single-molecule enzyme kinetics, phosphorylation-dephosphorylation cycle (PdPC) with bistability, and network exhibiting oscillations. Emphasis is paid to the comparison between the stochastic dynamics and the prediction based on the traditional approach based on the Law of Mass Action. We introduce the difference between nonlinear bistability and stochastic bistability, the latter has no deterministic counterpart. For systems with nonlinear bistability, there are three different time scales: (a) individual biochemical reactions, (b) nonlinear network dynamics approaching to attractors, and (c) cellular evolution. For mesoscopic systems with size of a living cell, dynamics in (a) and (c) are stochastic while that with (b) is dominantly deterministic. Both (b) and (c) are emergent properties of a dynamic biochemical network; We suggest that the (c) is most relevant to major cellular biochemical processes such as epi-genetic regulation, apoptosis, and cancer immunoediting. The cellular evolution proceeds with transitions among the attractors of (b) in a “punctuated equilibrium” manner