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

How does a protein search for the specific site on DNA: the role of disorder

Proteins can locate their specific targets on DNA up to two orders of magnitude faster than the Smoluchowski three-dimensional diffusion rate. This happens due to non-specific adsorption of proteins to DNA and subsequent one-dimensional sliding along DNA. We call such one-dimensional route towards the target "antenna". We studied the role of the dispersion of nonspecific binding energies within the antenna due to quasi random sequence of natural DNA. Random energy profile for sliding proteins slows the searching rate for the target. We show that this slowdown is different for the macroscopic and mesoscopic antennas.Comment: 4 pages, 4 figure

Effects of Sequence Disorder on DNA Looping and Cyclization

Effects of sequence disorder on looping and cyclization of the double-stranded DNA are studied theoretically. Both random intrinsic curvature and inhomogeneous bending rigidity are found to result in a remarkably wide distribution of cyclization probabilities. For short DNA segments, the range of the distribution reaches several orders of magnitude for even completely random sequences. The ensemble averaged values of the cyclization probability are also calculated, and the connection to the recent experiments is discussed.Comment: 8 pages, 4 figures, LaTeX; accepted to Physical Review E; v2: a substantially revised version; v3: references added, conclusions expanded, minor editorial corrections to the text; v4: a substantially revised and expanded version (total number of pages doubled); v5: new Figure 4, captions expanded, minor editorial improvements to the tex

Effects of Kinks on DNA Elasticity

We study the elastic response of a worm-like polymer chain with reversible kink-like structural defects. This is a generic model for (a) the double-stranded DNA with sharp bends induced by binding of certain proteins, and (b) effects of trans-gauche rotations in the backbone of the single-stranded DNA. The problem is solved both analytically and numerically by generalizing the well-known analogy to the Quantum Rotator. In the small stretching force regime, we find that the persistence length is renormalized due to the presence of the kinks. In the opposite regime, the response to the strong stretching is determined solely by the bare persistence length with exponential corrections due to the ``ideal gas of kinks''. This high-force behavior changes significantly in the limit of high bending rigidity of the chain. In that case, the leading corrections to the mechanical response are likely to be due to the formation of multi-kink structures, such as kink pairs.Comment: v1: 16 pages, 7 figures, LaTeX; submitted to Physical Review E; v2: a new subsection on soft kinks added to section Theory, sections Introduction and Conclusions expanded, references added, other minor changes; v3: a reference adde

A quantitative comparison of sRNA-based and protein-based gene regulation

Small, non-coding RNAs (sRNAs) play important roles as genetic regulators in prokaryotes. sRNAs act post-transcriptionally via complementary pairing with target mRNAs to regulate protein expression. We use a quantitative approach to compare and contrast sRNAs with conventional transcription factors (TFs) to better understand the advantages of each form of regulation. In particular, we calculate the steady-state behavior, noise properties, frequency-dependent gain (amplification), and dynamical response to large input signals of both forms of regulation. While the mean steady-state behavior of sRNA-regulated proteins exhibits a distinctive tunable threshold-linear behavior, our analysis shows that transcriptional bursting leads to significantly higher intrinsic noise in sRNA-based regulation than in TF-based regulation in a large range of expression levels and limits the ability of sRNAs to perform quantitative signaling. Nonetheless, we find that sRNAs are better than TFs at filtering noise in input signals. Additionally, we find that sRNAs allow cells to respond rapidly to large changes in input signals. These features suggest a niche for sRNAs in allowing cells to transition quickly yet reliably between distinct states. This functional niche is consistent with the widespread appearance of sRNAs in stress-response and quasi-developmental networks in prokaryotes.Comment: 26 pages, 8 figures; accepted for publication in Molecular Systems Biolog

Facilitated diffusion of DNA-binding proteins: Simulation of large systems

The recently introduced method of excess collisions (MEC) is modified to estimate diffusion-controlled reaction times inside systems of arbitrary size. The resulting MEC-E equations contain a set of empirical parameters, which have to be calibrated in numerical simulations inside a test system of moderate size. Once this is done, reaction times of systems of arbitrary dimensions are derived by extrapolation, with an accuracy of 10 to 15 percent. The achieved speed up, when compared to explicit simulations of the reaction process, is increasing proportional to the extrapolated volume of the cell.Comment: 8 pages, 4 figures, submitted to J. Chem. Phy

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

Fixed points and limit cycles in the population dynamics of lysogenic viruses and their hosts

Starting with stochastic rate equations for the fundamental interactions between microbes and their viruses, we derive a mean field theory for the population dynamics of microbe-virus systems, including the effects of lysogeny. In the absence of lysogeny, our model is a generalization of that proposed phenomenologically by Weitz and Dushoff. In the presence of lysogeny, we analyze the possible states of the system, identifying a novel limit cycle, which we interpret physically. To test the robustness of our mean field calculations to demographic fluctuations, we have compared our results with stochastic simulations using the Gillespie algorithm. Finally, we estimate the range of parameters that delineate the various steady states of our model.Comment: 20 pages, 16 figures, 4 table

Facilitated diffusion of DNA-binding proteins

The diffusion-controlled limit of reaction times for site-specific DNA-binding proteins is derived from first principles. We follow the generally accepted concept that a protein propagates via two competitive modes, a three-dimensional diffusion in space and a one-dimensional sliding along the DNA. However, our theoretical treatment of the problem is new. The accuracy of our analytical model is verified by numerical simulations. The results confirm that the unspecific binding of protein to DNA, combined with sliding, is capable to reduce the reaction times significantly.Comment: 4 pages, 2 figures Nov 22 2005 - accepted for PR