arXiv subjects

O. Radulescu

Publications and source records attributed to O. Radulescu.

9 recordsLinked to original sources

arXiv2019

Identifying the Parametric Occurrence of Multiple Steady States for some Biological Networks

We consider a problem from biological network analysis of determining regions in a parameter space over which there are multiple steady states for positive real values of variables and parameters. We describe multiple approaches to address the problem using tools from Symbolic Computation. We describe how progress was made to achieve semi-algebraic descriptions of the multistationarity regions of parameter space, and compare symbolic results to numerical methods. The biological networks studied are models of the mitogen-activated protein kinases (MAPK) network which has already consumed considerable effort using special insights into its structure of corresponding models. Our main example is a model with 11 equations in 11 variables and 19 parameters, 3 of which are of interest for symbolic treatment. The model also imposes positivity conditions on all variables and parameters. We apply combinations of symbolic computation methods designed for mixed equality/inequality systems, specifically virtual substitution, lazy real triangularization and cylindrical algebraic decomposition, as well as a simplification technique adapted from Gaussian elimination and graph theory. We are able to determine multistationarity of our main example over a 2-dimensional parameter space. We also study a second MAPK model and a symbolic grid sampling technique which can locate such regions in 3-dimensional parameter space.

cs.SC↗

arXiv2012

Flexible and robust networks

We consider networks with two types of nodes. The v-nodes, called centers, are hyper- connected and interact one to another via many u-nodes, called satellites. This central- ized architecture, widespread in gene networks, possesses two fundamental properties. Namely, this organization creates feedback loops that are capable to generate practically any prescribed patterning dynamics, chaotic or periodic, or having a number of equilib- rium states. Moreover, this organization is robust with respect to random perturbations of the system.

q-bio.MN↗

arXiv2010

Asymptotology of Chemical Reaction Networks

The concept of the limiting step is extended to the asymptotology of multiscale reaction networks. Complete theory for linear networks with well separated reaction rate constants is developed. We present algorithms for explicit approximations of eigenvalues and eigenvectors of kinetic matrix. Accuracy of estimates is proven. Performance of the algorithms is demonstrated on simple examples. Application of algorithms to nonlinear systems is discussed.

physics.chem-ph↗

arXiv2008

Dynamic and static limitation in multiscale reaction networks, revisited

The concept of limiting step gives the limit simplification: the whole network behaves as a single step. However, in its simplest form this idea is applicable only to the simplest linear cycles in steady states. For such the simplest cycles the nonstationary behaviour is also limited by a single step, but not the same step that limits the stationary rate. We develop a general theory of static and dynamic limitation for all linear multiscale networks. New estimates of eigenvectors for diagonally dominant matrices are used. Multiscale ensembles of reaction networks with well separated constants are introduced and typical properties of such systems are studied. For any given ordering of reaction rate constants the explicit approximation of steady state, relaxation spectrum and related eigenvectors ("modes") is presented. The obtained multiscale approximations that we call "dominant systems" are computationally cheap and robust. These dominant systems can be used for direct computation of steady states and relaxation dynamics, especially when kinetic information is incomplete, for design of experiments and mining of experimental data, and could serve as a robust first approximation in perturbation theory or for preconditioning.

physics.chem-ph↗

arXiv2007

Dynamical robustness of biological networks with hierarchical distribution of time scales

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First, we obtain the following result for linear networks: for large multiscale systems with hierarchical distribution of time scales the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. We argue that similar phenomena are valid in the nonlinear case as well. As a numerical illustration we use a model of signalling network that can be applied to important transcription factors such as NFkB.

q-bio.MN↗

arXiv2006

A model for regulated fatty acid metabolism in liver; equilibria and their changes

We build a model for the hepatic fatty acid metabolism and its metabolic and genetic regulations. The model has two functioning modes: synthesis and oxidation of fatty acids. We provide a sufficient condition (the strong lipolytic condition) for the uniqueness of its equilibrium. Under this condition, modifications of the glucose input produce equilibrium shifts, which are gradual changes from one functioning mode to the other. We also discuss the concentration variations of various metabolites during equilibrium shifts. The model can explain a certain amount of experimental observations, assess the role of poly-unsaturated fatty acids in genetic regulation, and predict the behavior of mutants. The analysis of the model is based on block elimination of variables and uses a modular decomposition of the system dictated by mathematical global univalence conditions.

q-bio.CB↗

arXiv2002

Timescales in shear banding of wormlike micelles

We show the existence of three well defined time scales in the dynamics of wormlike micelles after a step between two shear rates on the stress plateau. These time scales are compatible with the presence of a structured interface between bands of different viscosities and correspond to the isotropic band destabilization during the stress overshoot, reconstruction of the interface after the overshoot and travel of a fully formed interface. The last stage can be used to estimate a stress diffusion coefficient.

cond-mat.mtrl-sci↗

arXiv2002

Dynamics of modulated and composite aperiodic crystals: the signature of the inner polarization in the neutron coherent inelastic scattering

We compare within an unifying formalism the dynamical properties of modulated and composite aperiodic (incommensurate) crystals. We discuss the concept of inner polarization and we define an inner polarization parameter beta that distinguishes between different acoustic modes of aperiodic crystals. Although this concept has its limitations, we show that it can be used to extract valuable information from neutron coherent inelastic scattering experiments. Within certain conditions, the ratio between the dynamic and the static structure factors at various Bragg peaks depends on beta. We show how the knowledge of beta for modes of an unknown structure can be used to decide whether the structure is composite or modulated. Furthermore, the same information can be used to predict scattered intensity within unexplored regions of the reciprocal space, being thus a guide for experiments

cond-mat.mtrl-sci↗

arXiv1999

The Johnson-Segalman model with a diffusion term in Couette flow

We study the Johnson-Segalman (JS) model as a paradigm for some complex fluids which are observed to phase separate, or ``shear-band'' in flow. We analyze the behavior of this model in cylindrical Couette flow and demonstrate the history dependence inherent in the local JS model. We add a simple gradient term to the stress dynamics and demonstrate how this term breaks the degeneracy of the local model and prescribes a much smaller (discrete, rather than continuous) set of banded steady state solutions. We investigate some of the effects of the curvature of Couette flow on the observable steady state behavior and kinetics, and discuss some of the implications for metastability.

cond-mat.soft↗