Stochastic dynamics of macromolecular-assembly networks

The formation and regulation of macromolecular complexes provides the backbone of most cellular processes, including gene regulation and signal transduction. The inherent complexity of assembling macromolecular structures makes current computational methods strongly limited for understanding how the physical interactions between cellular components give rise to systemic properties of cells. Here we present a stochastic approach to study the dynamics of networks formed by macromolecular complexes in terms of the molecular interactions of their components. Exploiting key thermodynamic concepts, this approach makes it possible to both estimate reaction rates and incorporate the resulting assembly dynamics into the stochastic kinetics of cellular networks. As prototype systems, we consider the lac operon and phage lambda induction switches, which rely on the formation of DNA loops by proteins and on the integration of these protein-DNA complexes into intracellular networks. This cross-scale approach offers an effective starting point to move forward from network diagrams, such as those of protein-protein and DNA-protein interaction networks, to the actual dynamics of cellular processes.Comment: Open Access article available at http://www.nature.com/msb/journal/v2/n1/full/msb4100061.htm

The Lazy Bureaucrat Scheduling Problem

We introduce a new class of scheduling problems in which the optimization is performed by the worker (single ``machine'') who performs the tasks. A typical worker's objective is to minimize the amount of work he does (he is ``lazy''), or more generally, to schedule as inefficiently (in some sense) as possible. The worker is subject to the constraint that he must be busy when there is work that he can do; we make this notion precise both in the preemptive and nonpreemptive settings. The resulting class of ``perverse'' scheduling problems, which we denote ``Lazy Bureaucrat Problems,'' gives rise to a rich set of new questions that explore the distinction between maximization and minimization in computing optimal schedules.Comment: 19 pages, 2 figures, Latex. To appear, Information and Computatio

Probabilistic Bounds on the Length of a Longest Edge in Delaunay Graphs of Random Points in d-Dimensions

Motivated by low energy consumption in geographic routing in wireless networks, there has been recent interest in determining bounds on the length of edges in the Delaunay graph of randomly distributed points. Asymptotic results are known for random networks in planar domains. In this paper, we obtain upper and lower bounds that hold with parametric probability in any dimension, for points distributed uniformly at random in domains with and without boundary. The results obtained are asymptotically tight for all relevant values of such probability and constant number of dimensions, and show that the overhead produced by boundary nodes in the plane holds also for higher dimensions. To our knowledge, this is the first comprehensive study on the lengths of long edges in Delaunay graphsComment: 10 pages. 2 figures. In Proceedings of the 23rd Canadian Conference on Computational Geometry (CCCG 2011). Replacement of version 1106.4927, reference [5] adde

Lambda-prophage induction modeled as a cooperative failure mode of lytic repression

We analyze a system-level model for lytic repression of lambda-phage in E. coli using reliability theory, showing that the repressor circuit comprises 4 redundant components whose failure mode is prophage induction. Our model reflects the specific biochemical mechanisms involved in regulation, including long-range cooperative binding, and its detailed predictions for prophage induction in E. coli under ultra-violet radiation are in good agreement with experimental data.Comment: added referenc

Analytical study of an exclusive genetic switch

The nonequilibrium stationary state of an exclusive genetic switch is considered. The model comprises two competing species and a single binding site which, when bound to by a protein of one species, causes the other species to be repressed. The model may be thought of as a minimal model of the power struggle between two competing parties. Exact solutions are given for the limits of vanishing binding/unbinding rates and infinite binding/unbinding rates. A mean field theory is introduced which is exact in the limit of vanishing binding/unbinding rates. The mean field theory and numerical simulations reveal that generically bistability occurs and the system is in a symmetry broken state. An exact perturbative solution which in principle allows the nonequilibrium stationary state to be computed is also developed and computed to first and second order.Comment: 28 pages, 6 figure

Enhancement of the stability of genetic switches by overlapping upstream regulatory domains

We study genetic switches formed from pairs of mutually repressing operons. The switch stability is characterised by a well defined lifetime which grows sub-exponentially with the number of copies of the most-expressed transcription factor, in the regime accessible by our numerical simulations. The stability can be markedly enhanced by a suitable choice of overlap between the upstream regulatory domains. Our results suggest that robustness against biochemical noise can provide a selection pressure that drives operons, that regulate each other, together in the course of evolution.Comment: 4 pages, 5 figures, RevTeX

Stochastic Simulations of the Repressilator Circuit

The genetic repressilator circuit consists of three transcription factors, or repressors, which negatively regulate each other in a cyclic manner. This circuit was synthetically constructed on plasmids in {\it Escherichia coli} and was found to exhibit oscillations in the concentrations of the three repressors. Since the repressors and their binding sites often appear in low copy numbers, the oscillations are noisy and irregular. Therefore, the repressilator circuit cannot be fully analyzed using deterministic methods such as rate-equations. Here we perform stochastic analysis of the repressilator circuit using the master equation and Monte Carlo simulations. It is found that fluctuations modify the range of conditions in which oscillations appear as well as their amplitude and period, compared to the deterministic equations. The deterministic and stochastic approaches coincide only in the limit in which all the relevant components, including free proteins, plasmids and bound proteins, appear in high copy numbers. We also find that subtle features such as cooperative binding and bound-repressor degradation strongly affect the existence and properties of the oscillations.Comment: Accepted to PR

Draft Genome Sequence for Desulfovibrio africanus Strain PCS.

Desulfovibrio africanus strain PCS is an anaerobic sulfate-reducing bacterium (SRB) isolated from sediment from Paleta Creek, San Diego, CA. Strain PCS is capable of reducing metals such as Fe(III) and Cr(VI), has a cell cycle, and is predicted to produce methylmercury. We present the D. africanus PCS genome sequence