540 research outputs found
The interplay between discrete noise and nonlinear chemical kinetics in a signal amplification cascade
We used various analytical and numerical techniques to elucidate signal
propagation in a small enzymatic cascade which is subjected to external and
internal noise. The nonlinear character of catalytic reactions, which underlie
protein signal transduction cascades, renders stochastic signaling dynamics in
cytosol biochemical networks distinct from the usual description of stochastic
dynamics in gene regulatory networks. For a simple 2-step enzymatic cascade
which underlies many important protein signaling pathways, we demonstrated that
the commonly used techniques such as the linear noise approximation and the
Langevin equation become inadequate when the number of proteins becomes too
low. Consequently, we developed a new analytical approximation, based on mixing
the generating function and distribution function approaches, to the solution
of the master equation that describes nonlinear chemical signaling kinetics for
this important class of biochemical reactions. Our techniques work in a much
wider range of protein number fluctuations than the methods used previously. We
found that under certain conditions the burst-phase noise may be injected into
the downstream signaling network dynamics, resulting possibly in unusually
large macroscopic fluctuations. In addition to computing first and second
moments, which is the goal of commonly used analytical techniques, our new
approach provides the full time-dependent probability distributions of the
colored non-Gaussian processes in a nonlinear signal transduction cascade.Comment: 16 pages, 9 figure
Stochastic Ratcheting on a Funneled Energy Landscape is Necessary for Highly Efficient Contractility of Actomyosin Force Dipoles
Current understanding of how contractility emerges in disordered actomyosin
networks of non-muscle cells is still largely based on the intuition derived
from earlier works on muscle contractility. This view, however, largely
overlooks the free energy gain following passive cross-linker binding, which,
even in the absence of active fluctuations, provides a thermodynamic drive
towards highly overlapping filamentous states. In this work, we shed light on
this phenomenon, showing that passive cross-linkers, when considered in the
context of two anti-parallel filaments, generate noticeable contractile forces.
However, as binding free energy of cross-linkers is increased, a sharp onset of
kinetic arrest follows, greatly diminishing effectiveness of this contractility
mechanism, allowing the network to contract only with weakly resisting tensions
at its boundary. We have carried out stochastic simulations elucidating this
mechanism, followed by a mean-field treatment that predicts how contractile
forces asymptotically scale at small and large binding energies, respectively.
Furthermore, when considering an active contractile filament pair, based on
non-muscle myosin II, we found that the non-processive nature of these motors
leads to highly inefficient force generation, due to recoil slippage of the
overlap during periods when the motor is dissociated. However, we discovered
that passive cross-linkers can serve as a structural ratchet during these
unbound motor time spans, resulting in vast force amplification. Our results
shed light on the non-equilibrium effects of transiently binding proteins in
biological active matter, as observed in the non-muscle actin cytoskeleton,
showing that highly efficient contractile force dipoles result from synergy of
passive cross-linker and active motor dynamics, via a ratcheting mechanism on a
funneled energy landscape.Comment: 13 pages, 6 figure
Multiscale stochastic reaction-diffusion modelling: application to actin dynamics in filopodia
Two multiscale (hybrid) stochastic reaction-diffusion models of actin dynamics in a filopodium are investigated. Both hybrid algorithms combine compartment-based and molecular-based stochastic reaction-diffusion models. The first hybrid model is based on the models previously\ud
developed in the literature. The second hybrid model is based on the application of recently developed two-regime method (TRM) to a fully molecular-based model which is also developed in this paper. The results of hybrid models are compared with the results of the molecular-based model. It is shown that both approaches give comparable results, although the TRM model better agrees quantitatively with the molecular-based model
Noncommutativity Effects in FRW Scalar Field Cosmology
We study effects of noncommutativity on the phase space generated by a
non-minimal scalar field which is conformally coupled to the background
curvature in an isotropic and homogeneous FRW cosmology. These effects are
considered in two cases, when the potential of scalar field has zero and
nonzero constant values. The investigation is carried out by means of a
comparative detailed analysis of mathematical features of the evolution of
universe and the most probable universe wave functions in classically
commutative and noncommutative frames and quantum counterparts. The influence
of noncommutativity is explored by the two noncommutative parameters of space
and momentum sectors with a relative focus on the role of the noncommutative
parameter of momentum sector. The solutions are presented with some of their
numerical diagrams, in the commutative and noncommutative scenarios, and their
properties are compared. We find that impose of noncommutativity in the
momentum sector causes more ability in tuning time solutions of variables in
classical level, and has more probable states of universe in quantum level. We
also demonstrate that special solutions in classical and allowed wave functions
in quantum models impose bounds on the values of noncommutative parameters.Comment: 13 pages, 5 figure
The Stochastic Dynamics of Filopodial Growth
AbstractA filopodium is a cytoplasmic projection, exquisitely built and regulated, which extends from the leading edge of the migrating cell, exploring the cell's neighborhood. Commonly, filopodia grow and retract after their initiation, exhibiting rich dynamical behaviors. We model the growth of a filopodium based on a stochastic description which incorporates mechanical, physical, and biochemical components. Our model provides a full stochastic treatment of the actin monomer diffusion and polymerization of each individual actin filament under stress of the fluctuating membrane. We investigated the length distribution of individual filaments in a growing filopodium and studied how it depends on various physical parameters. The distribution of filament lengths turned out to be narrow, which we explained by the negative feedback created by the membrane load and monomeric G-actin gradient. We also discovered that filopodial growth is strongly diminished upon increasing retrograde flow, suggesting that regulating the retrograde flow rate would be a highly efficient way to control filopodial extension dynamics. The filopodial length increases as the membrane fluctuations decrease, which we attributed to the unequal loading of the membrane force among individual filaments, which, in turn, results in larger average polymerization rates. We also observed significant diffusional noise of G-actin monomers, which leads to smaller G-actin flux along the filopodial tube compared with the prediction using the diffusion equation. Overall, partial cancellation of these two fluctuation effects allows a simple mean field model to rationalize most of our simulation results. However, fast fluctuations significantly renormalize the mean field model parameters. The biological significance of our filopodial model and avenues for future development are also discussed
Steric Effects Induce Geometric Remodeling of Actin Bundles in Filopodia.
Filopodia are ubiquitous fingerlike protrusions, spawned by many eukaryotic cells, to probe and interact with their environments. Polymerization dynamics of actin filaments, comprising the structural core of filopodia, largely determine their instantaneous lengths and overall lifetimes. The polymerization reactions at the filopodial tip require transport of G-actin, which enter the filopodial tube from the filopodial base and diffuse toward the filament barbed ends near the tip. Actin filaments are mechanically coupled into a tight bundle by cross-linker proteins. Interestingly, many of these proteins are relatively short, restricting the free diffusion of cytosolic G-actin throughout the bundle and, in particular, its penetration into the bundle core. To investigate the effect of steric restrictions on G-actin diffusion by the porous structure of filopodial actin filament bundle, we used a particle-based stochastic simulation approach. We discovered that excluded volume interactions result in partial and then full collapse of central filaments in the bundle, leading to a hollowed-out structure. The latter may further collapse radially due to the activity of cross-linking proteins, hence producing conical-shaped filament bundles. Interestingly, electron microscopy experiments on mature filopodia indeed frequently reveal actin bundles that are narrow at the tip and wider at the base. Overall, our work demonstrates that excluded volume effects in the context of reaction-diffusion processes in porous networks may lead to unexpected geometric growth patterns and complicated, history-dependent dynamics of intermediate metastable configurations.he research leading to these results received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 239870. R.E. thanks the Royal Society for a University Research Fellowship, and the Leverhulme Trust for a Philip Leverhulme Prize (this prize money was used to support research visits of G.A.P. in Oxford). G.A.P. was supported by National Science Foundation grant No. CHE-1363081. U.D. was supported by a Junior Interdisciplinary Fellowship via Wellcome Trust grant No. 105602/Z/14/Z. This work was partially carried out during a visit by R.E. and U.D. to the Isaac Newton Institute. This work was partially supported by a grant from the Simons Foundation
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