477 research outputs found
Analytical study of non Gaussian fluctuations in a stochastic scheme of autocatalytic reactions
A stochastic model of autocatalytic chemical reactions is studied both
numerically and analytically. The van Kampen perturbative scheme is
implemented, beyond the second order approximation, so to capture the non
Gaussianity traits as displayed by the simulations. The method is targeted to
the characterization of the third moments of the distribution of fluctuations,
originating from a system of four populations in mutual interaction. The theory
predictions agree well with the simulations, pointing to the validity of the
van Kampen expansion beyond the conventional Gaussian solution.Comment: 15 pages, 8 figures, submitted to Phys. Rev.
Steady-state fluctuations of a genetic feedback loop:an exact solution
Genetic feedback loops in cells break detailed balance and involve
bimolecular reactions; hence exact solutions revealing the nature of the
stochastic fluctuations in these loops are lacking. We here consider the master
equation for a gene regulatory feedback loop: a gene produces protein which
then binds to the promoter of the same gene and regulates its expression. The
protein degrades in its free and bound forms. This network breaks detailed
balance and involves a single bimolecular reaction step. We provide an exact
solution of the steady-state master equation for arbitrary values of the
parameters, and present simplified solutions for a number of special cases. The
full parametric dependence of the analytical non-equilibrium steady-state
probability distribution is verified by direct numerical solution of the master
equations. For the case where the degradation rate of bound and free protein is
the same, our solution is at variance with a previous claim of an exact
solution (Hornos et al, Phys. Rev. E {\bf 72}, 051907 (2005) and subsequent
studies). We show explicitly that this is due to an unphysical formulation of
the underlying master equation in those studies.Comment: 31 pages, 3 figures. Accepted for publication in the Journal of
Chemical Physics (2012
Directed cell migration in the presence of obstacles
BACKGROUND: Chemotactic movement is a common feature of many cells and microscopic organisms. In vivo, chemotactic cells have to follow a chemotactic gradient and simultaneously avoid the numerous obstacles present in their migratory path towards the chemotactic source. It is not clear how cells detect and avoid obstacles, in particular whether they need a specialized biological mechanism to do so. RESULTS: We propose that cells can sense the presence of obstacles and avoid them because obstacles interfere with the chemical field. We build a model to test this hypothesis and find that this naturally enables efficient at-a-distance sensing to be achieved with no need for a specific and active obstacle-sensing mechanism. We find that (i) the efficiency of obstacle avoidance depends strongly on whether the chemotactic chemical reacts or remains unabsorbed at the obstacle surface. In particular, it is found that chemotactic cells generally avoid absorbing barriers much more easily than non-absorbing ones. (ii) The typically low noise in a cell's motion hinders the ability to avoid obstacles. We also derive an expression estimating the typical distance traveled by chemotactic cells in a 3D random distribution of obstacles before capture; this is a measure of the distance over which chemotaxis is viable as a means of directing cells from one point to another in vivo. CONCLUSION: Chemotactic cells, in many cases, can avoid obstacles by simply following the spatially perturbed chemical gradients around obstacles. It is thus unlikely that they have developed specialized mechanisms to cope with environments having low to moderate concentrations of obstacles
A characteristic lengthscale causes anomalous size effects and boundary programmability in mechanical metamaterials
The architecture of mechanical metamaterialsis designed to harness geometry,
non-linearity and topology to obtain advanced functionalities such as shape
morphing, programmability and one-way propagation. While a purely geometric
framework successfully captures the physics of small systems under idealized
conditions, large systems or heterogeneous driving conditions remain
essentially unexplored. Here we uncover strong anomalies in the mechanics of a
broad class of metamaterials, such as auxetics, shape-changers or topological
insulators: a non-monotonic variation of their stiffness with system size, and
the ability of textured boundaries to completely alter their properties. These
striking features stem from the competition between rotation-based
deformations---relevant for small systems---and ordinary elasticity, and are
controlled by a characteristic length scale which is entirely tunable by the
architectural details. Our study provides new vistas for designing, controlling
and programming the mechanics of metamaterials in the thermodynamic limit.Comment: Main text has 4 pages, 4 figures + Methods and Supplementary
Informatio
Breakdown of the reaction-diffusion master equation with nonelementary rates
The chemical master equation (CME) is the exact mathematical formulation of
chemical reactions occurring in a dilute and well-mixed volume. The
reaction-diffusion master equation (RDME) is a stochastic description of
reaction-diffusion processes on a spatial lattice, assuming well-mixing only on
the length scale of the lattice. It is clear that, for the sake of consistency,
the solution of the RDME of a chemical system should converge to the solution
of the CME of the same system in the limit of fast diffusion: indeed, this has
been tacitly assumed in most literature concerning the RDME. We show that, in
the limit of fast diffusion, the RDME indeed converges to a master equation,
but not necessarily the CME. We introduce a class of propensity functions, such
that if the RDME has propensities exclusively of this class then the RDME
converges to the CME of the same system; while if the RDME has propensities not
in this class then convergence is not guaranteed. These are revealed to be
elementary and non-elementary propensities respectively. We also show that
independent of the type of propensity, the RDME converges to the CME in the
simultaneous limit of fast diffusion and large volumes. We illustrate our
results with some simple example systems, and argue that the RDME cannot be an
accurate description of systems with non-elementary rates.Comment: 8 pages, 3 figure
Mechanical Metamaterials with Negative Compressibility Transitions
When tensioned, ordinary materials expand along the direction of the applied
force. Here, we explore network concepts to design metamaterials exhibiting
negative compressibility transitions, during which a material undergoes
contraction when tensioned (or expansion when pressured). Continuous
contraction of a material in the same direction of an applied tension, and in
response to this tension, is inherently unstable. The conceptually similar
effect we demonstrate can be achieved, however, through destabilisations of
(meta)stable equilibria of the constituents. These destabilisations give rise
to a stress-induced solid-solid phase transition associated with a twisted
hysteresis curve for the stress-strain relationship. The strain-driven
counterpart of negative compressibility transitions is a force amplification
phenomenon, where an increase in deformation induces a discontinuous increase
in response force. We suggest that the proposed materials could be useful for
the design of actuators, force amplifiers, micro-mechanical controls, and
protective devices.Comment: Supplementary information available at
http://www.nature.com/nmat/journal/v11/n7/abs/nmat3331.htm
Intrinsic Noise Analyzer: A Software Package for the Exploration of Stochastic Biochemical Kinetics Using the System Size Expansion
The accepted stochastic descriptions of biochemical dynamics under well-mixed conditions are given by the Chemical Master Equation and the Stochastic Simulation Algorithm, which are equivalent. The latter is a Monte-Carlo method, which, despite enjoying broad availability in a large number of existing software packages, is computationally expensive due to the huge amounts of ensemble averaging required for obtaining accurate statistical information. The former is a set of coupled differential-difference equations for the probability of the system being in any one of the possible mesoscopic states; these equations are typically computationally intractable because of the inherently large state space. Here we introduce the software package intrinsic Noise Analyzer (iNA), which allows for systematic analysis of stochastic biochemical kinetics by means of van Kampenβs system size expansion of the Chemical Master Equation. iNA is platform independent and supports the popular SBML format natively. The present implementation is the first to adopt a complementary approach that combines state-of-the-art analysis tools using the computer algebra system Ginac with traditional methods of stochastic simulation. iNA integrates two approximation methods based on the system size expansion, the Linear Noise Approximation and effective mesoscopic rate equations, which to-date have not been available to non-expert users, into an easy-to-use graphical user interface. In particular, the present methods allow for quick approximate analysis of time-dependent mean concentrations, variances, covariances and correlations coefficients, which typically outperforms stochastic simulations. These analytical tools are complemented by automated multi-core stochastic simulations with direct statistical evaluation and visualization. We showcase iNAβs performance by using it to explore the stochastic properties of cooperative and non-cooperative enzyme kinetics and a gene network associated with circadian rhythms. The software iNA is freely available as executable binaries for Linux, MacOSX and Microsoft Windows, as well as the full source code under an open source license
Overexpression of Parkinson's Disease-Associated Mutation LRRK2 G2019S in Mouse Forebrain Induces Behavioral Deficits and alpha-Synuclein Pathology
Citation: Xiong, Y. L., Neifert, S., Karuppagounder, S. S., Stankowski, J. N., Lee, B. D., Grima, J. C., . . . Dawson, V. L. (2017). Overexpression of Parkinson's Disease-Associated Mutation LRRK2 G2019S in Mouse Forebrain Induces Behavioral Deficits and alpha-Synuclein Pathology. Eneuro, 4(2), 10.
https://doi.org/10.1523/eneuro.0004-17.2017Mutations in the leucine-rich repeat kinase 2 (LRRK2) gene have been identified as an unambiguous cause of late-onset, autosomal-dominant familial Parkinson's disease (PD) and LRRK2 mutations are the strongest genetic risk factor for sporadic PD known to date. A number of transgenic mice expressing wild-type or mutant LRRK2 have been described with varying degrees of LRRK2-related abnormalities and modest pathologies. None of these studies directly addressed the role of the kinase domain in the changes observed and none of the mice present with robust features of the human disease. In an attempt to address these issues, we created a conditional LRRK2 G2019S (LRRK2 GS) mutant and a functionally negative control, LRRK2 G2019S/D1994A (LRRK2 GS/DA). Expression of LRRK2 GS or LRRK2 GS/DA was conditionally controlled using the tet-off system in which the presence of tetracycline-transactivator protein (tTA) with a CAMKII alpha promoter (CAMKII alpha-tTA) induced expression of TetP-LRRK2 GS or TetP-LRRK2 GS/DA in the mouse forebrain. Overexpression of LRRK2 GS in mouse forebrain induced behavioral deficits and alpha-synuclein pathology in a kinase-dependent manner. Similar to other genetically engineered LRRK2 GS mice, there was no significant loss of dopaminergic neurons. These mice provide an important new tool to study neurobiological changes associated with the increased kinase activity from the LRRK2 G2019S mutation, which may ultimately lead to a better understanding of not only the physiologic actions of LRRK2, but also potential pathologic actions that underlie LRRK2 GS-associated PD
Multi-step self-guided pathways for shape-changing metamaterials
Multi-step pathways, constituted of a sequence of reconfigurations, are
central to a wide variety of natural and man-made systems. Such pathways
autonomously execute in self-guided processes such as protein folding and
self-assembly, but require external control in macroscopic mechanical systems,
provided by, e.g., actuators in robotics or manual folding in origami. Here we
introduce shape-changing mechanical metamaterials, that exhibit self-guided
multi-step pathways in response to global uniform compression. Their design
combines strongly nonlinear mechanical elements with a multimodal architecture
that allows for a sequence of topological reconfigurations, i.e., modifications
of the topology caused by the formation of internal self-contacts. We realized
such metamaterials by digital manufacturing, and show that the pathway and
final configuration can be controlled by rational design of the nonlinear
mechanical elements. We furthermore demonstrate that self-contacts suppress
pathway errors. Finally, we demonstrate how hierarchical architectures allow to
extend the number of distinct reconfiguration steps. Our work establishes
general principles for designing mechanical pathways, opening new avenues for
self-folding media, pluripotent materials, and pliable devices in, e.g.,
stretchable electronics and soft robotics.Comment: 16 pages, 3 main figures, 10 extended data figures. See
https://youtu.be/8m1QfkMFL0I for an explanatory vide
Confining Domains Lead to Reaction Bursts: Reaction Kinetics in the Plasma Membrane
Confinement of molecules in specific small volumes and areas within a cell is likely to be a general strategy that is developed during evolution for regulating the interactions and functions of biomolecules. The cellular plasma membrane, which is the outermost membrane that surrounds the entire cell, was considered to be a continuous two-dimensional liquid, but it is becoming clear that it consists of numerous nano-meso-scale domains with various lifetimes, such as raft domains and cytoskeleton-induced compartments, and membrane molecules are dynamically trapped in these domains. In this article, we give a theoretical account on the effects of molecular confinement on reversible bimolecular reactions in a partitioned surface such as the plasma membrane. By performing simulations based on a lattice-based model of diffusion and reaction, we found that in the presence of membrane partitioning, bimolecular reactions that occur in each compartment proceed in bursts during which the reaction rate is sharply and briefly increased even though the asymptotic reaction rate remains the same. We characterized the time between reaction bursts and the burst amplitude as a function of the model parameters, and discussed the biological significance of the reaction bursts in the presence of strong inhibitor activity
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