1,168 research outputs found
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
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