37 research outputs found
Spatio-temporal correlations can drastically change the response of a MAPK pathway
Multisite covalent modification of proteins is omnipresent in eukaryotic
cells. A well-known example is the mitogen-activated protein kinase (MAPK)
cascade, where in each layer of the cascade a protein is phosphorylated at two
sites. It has long been known that the response of a MAPK pathway strongly
depends on whether the enzymes that modify the protein act processively or
distributively: distributive mechanism, in which the enzyme molecules have to
release the substrate molecules in between the modification of the two sites,
can generate an ultrasensitive response and lead to hysteresis and bistability.
We study by Green's Function Reaction Dynamics, a stochastic scheme that makes
it possible to simulate biochemical networks at the particle level and in time
and space, a dual phosphorylation cycle in which the enzymes act according to a
distributive mechanism. We find that the response of this network can differ
dramatically from that predicted by a mean-field analysis based on the chemical
rate equations. In particular, rapid rebindings of the enzyme molecules to the
substrate molecules after modification of the first site can markedly speed up
the response, and lead to loss of ultrasensitivity and bistability. In essence,
rapid enzyme-substrate rebindings can turn a distributive mechanism into a
processive mechanism. We argue that slow ADP release by the enzymes can protect
the system against these rapid rebindings, thus enabling ultrasensitivity and
bistability
Reaction coordinates for the flipping of genetic switches
We present a detailed analysis, based on the Forward Flux Sampling (FFS)
simulation method, of the switching dynamics and stability of two models of
genetic toggle switches, consisting of two mutually-repressing genes encoding
transcription factors (TFs); in one model (the exclusive switch), they mutually
exclude each other's binding, while in the other model (general switch) the two
transcription factors can bind simultaneously to the shared operator region. We
assess the role of two pairs of reactions that influence the stability of these
switches: TF-TF homodimerisation and TF-DNA association/dissociation. We
factorise the flipping rate k into the product of the probability rho(q*) of
finding the system at the dividing surface (separatrix) between the two stable
states, and a kinetic prefactor R. In the case of the exclusive switch, the
rate of TF-operator binding affects both rho(q*) and R, while the rate of TF
dimerisation affects only R. In the case of the general switch both TF-operator
binding and TF dimerisation affect k, R and rho(q*). To elucidate this, we
analyse the transition state ensemble (TSE). For the exclusive switch, varying
the rate of TF-operator binding can drastically change the pathway of
switching, while changing the rate of dimerisation changes the switching rate
without altering the mechanism. The switching pathways of the general switch
are highly robust to changes in the rate constants of both TF-operator and
TF-TF binding, even though these rate constants do affect the flipping rate;
this feature is unique for non-equilibrium systems.Comment: 24 pages, 7 figure
Diffusion of transcription factors can drastically enhance the noise in gene expression
We study by simulation the effect of the diffusive motion of repressor
molecules on the noise in mRNA and protein levels in the case of a repressed
gene. We find that spatial fluctuations due to diffusion can drastically
enhance the noise in gene expression. For a fixed repressor strength, the noise
due to diffusion can be minimized by increasing the number of repressors or by
decreasing the rate of the open complex formation. We also show that the effect
of spatial fluctuations can be well described by a two-step kinetic scheme,
where formation of an encounter complex by diffusion and the subsequent
association reaction are treated separately. Our results also emphasize that
power spectra are a highly useful tool for studying the propagation of noise
through the different stages of gene expression.Comment: 15 pages, 6 figures, REVTeX
Dynamics and geometric properties of the k-Trigonometric model
We analyze the dynamics and the geometric properties of the Potential Energy
Surfaces (PES) of the k-Trigonometric Model (kTM), defined by a fully-connected
k-body interaction. This model has no thermodynamic transition for k=1, a
second order one for k=2, and a first order one for k>2. In this paper we i)
show that the single particle dynamics can be traced back to an effective
dynamical system (with only one degree of freedom); ii) compute the diffusion
constant analytically; iii) determine analytically several properties of the
self correlation functions apart from the relaxation times which we calculate
numerically; iv) relate the collective correlation functions to the ones of the
effective degree of freedom using an exact Dyson-like equation; v) using two
analytical methods, calculate the saddles of the PES that are visited by the
system evolving at fixed temperature. On the one hand we minimize |grad V|^2,
as usually done in the numerical study of supercooled liquids and, on the other
hand, we compute the saddles with minimum distance (in configuration space)
from initial equilibrium configurations. We find the same result from the two
calculations and we speculate that the coincidence might go beyond the specific
model investigated here.Comment: 36 pages, 13 figure
DNA looping provides stability and robustness to the bacteriophage lambda switch
The bistable gene regulatory switch controlling the transition from lysogeny
to lysis in bacteriophage lambda presents a unique challenge to quantitative
modeling. Despite extensive characterization of this regulatory network, the
origin of the extreme stability of the lysogenic state remains unclear. We have
constructed a stochastic model for this switch. Using Forward Flux Sampling
simulations, we show that this model predicts an extremely low rate of
spontaneous prophage induction in a recA mutant, in agreement with experimental
observations. In our model, the DNA loop formed by octamerization of CI bound
to the O_L and O_R operator regions is crucial for stability, allowing the
lysogenic state to remain stable even when a large fraction of the total CI is
depleted by nonspecific binding to genomic DNA. DNA looping also ensures that
the switch is robust to mutations in the order of the O_R binding sites. Our
results suggest that DNA looping can provide a mechanism to maintain a stable
lysogenic state in the face of a range of challenges including noisy gene
expression, nonspecific DNA binding and operator site mutations.Comment: In press on PNAS. Single file contains supplementary inf
The Goldbeter-Koshland switch in the first-order region and its response to dynamic disorder
In their classical work (Proc. Natl. Acad. Sci. USA, 1981, 78:6840-6844),
Goldbeter and Koshland mathematically analyzed a reversible covalent
modification system which is highly sensitive to the concentration of
effectors. Its signal-response curve appears sigmoidal, constituting a
biochemical switch. However, the switch behavior only emerges in the
"zero-order region", i.e. when the signal molecule concentration is much lower
than that of the substrate it modifies. In this work we showed that the
switching behavior can also occur under comparable concentrations of signals
and substrates, provided that the signal molecules catalyze the modification
reaction in cooperation. We also studied the effect of dynamic disorders on the
proposed biochemical switch, in which the enzymatic reaction rates, instead of
constant, appear as stochastic functions of time. We showed that the system is
robust to dynamic disorder at bulk concentration. But if the dynamic disorder
is quasi-static, large fluctuations of the switch response behavior may be
observed at low concentrations. Such fluctuation is relevant to many biological
functions. It can be reduced by either increasing the conformation
interconversion rate of the protein, or correlating the enzymatic reaction
rates in the network.Comment: 23 pages, 4 figures, accepted by PLOS ON
Random walks and polymers in the presence of quenched disorder
After a general introduction to the field, we describe some recent results
concerning disorder effects on both `random walk models', where the random walk
is a dynamical process generated by local transition rules, and on `polymer
models', where each random walk trajectory representing the configuration of a
polymer chain is associated to a global Boltzmann weight. For random walk
models, we explain, on the specific examples of the Sinai model and of the trap
model, how disorder induces anomalous diffusion, aging behaviours and Golosov
localization, and how these properties can be understood via a strong disorder
renormalization approach. For polymer models, we discuss the critical
properties of various delocalization transitions involving random polymers. We
first summarize some recent progresses in the general theory of random critical
points : thermodynamic observables are not self-averaging at criticality
whenever disorder is relevant, and this lack of self-averaging is directly
related to the probability distribution of pseudo-critical temperatures
over the ensemble of samples of size . We describe the
results of this analysis for the bidimensional wetting and for the
Poland-Scheraga model of DNA denaturation.Comment: 17 pages, Conference Proceedings "Mathematics and Physics", I.H.E.S.,
France, November 200
Noise Filtering Strategies of Adaptive Signaling Networks: The Case of E. Coli Chemotaxis
Two distinct mechanisms for filtering noise in an input signal are identified
in a class of adaptive sensory networks. We find that the high frequency noise
is filtered by the output degradation process through time-averaging; while the
low frequency noise is damped by adaptation through negative feedback. Both
filtering processes themselves introduce intrinsic noises, which are found to
be unfiltered and can thus amount to a significant internal noise floor even
without signaling. These results are applied to E. coli chemotaxis. We show
unambiguously that the molecular mechanism for the Berg-Purcell time-averaging
scheme is the dephosphorylation of the response regulator CheY-P, not the
receptor adaptation process as previously suggested. The high frequency noise
due to the stochastic ligand binding-unbinding events and the random ligand
molecule diffusion is averaged by the CheY-P dephosphorylation process to a
negligible level in E.coli. We identify a previously unstudied noise source
caused by the random motion of the cell in a ligand gradient. We show that this
random walk induced signal noise has a divergent low frequency component, which
is only rendered finite by the receptor adaptation process. For gradients
within the E. coli sensing range, this dominant external noise can be
comparable to the significant intrinsic noise in the system. The dependence of
the response and its fluctuations on the key time scales of the system are
studied systematically. We show that the chemotaxis pathway may have evolved to
optimize gradient sensing, strong response, and noise control in different time
scalesComment: 15 pages, 4 figure
Regulation of signal duration and the statistical dynamics of kinase activation by scaffold proteins
Scaffolding proteins that direct the assembly of multiple kinases into a
spatially localized signaling complex are often essential for the maintenance
of an appropriate biological response. Although scaffolds are widely believed
to have dramatic effects on the dynamics of signal propagation, the mechanisms
that underlie these consequences are not well understood. Here, Monte Carlo
simulations of a model kinase cascade are used to investigate how the temporal
characteristics of signaling cascades can be influenced by the presence of
scaffold proteins. Specifically, we examine the effects of spatially localizing
kinase components on a scaffold on signaling dynamics. The simulations indicate
that a major effect that scaffolds exert on the dynamics of cell signaling is
to control how the activation of protein kinases is distributed over time.
Scaffolds can influence the timing of kinase activation by allowing for kinases
to become activated over a broad range of times, thus allowing for signaling at
both early and late times. Scaffold concentrations that result in optimal
signal amplitude also result in the broadest distributions of times over which
kinases are activated. These calculations provide insights into one mechanism
that describes how the duration of a signal can potentially be regulated in a
scaffold mediated protein kinase cascade. Our results illustrate another
complexity in the broad array of control properties that emerge from the
physical effects of spatially localizing components of kinase cascades on
scaffold proteins.Comment: 12 pages, 6 figure
Noise Amplification in Human Tumor Suppression following Gamma Irradiation
The influence of noise on oscillatory motion is a subject of permanent interest, both for fundamental and practical reasons. Cells respond properly to external stimuli by using noisy systems. We have clarified the effect of intrinsic noise on the dynamics in the human cancer cells following gamma irradiation. It is shown that the large amplification and increasing mutual information with delay are due to coherence resonance. Furthermore, frequency domain analysis is used to study the mechanisms