Biomedical subjects

Ofer Biham

Publications and source records attributed to Ofer Biham.

8 recordsLinked to original sources

PubMed2006

Dissipative sandpile models with universal exponents.

We consider a dissipative variant of the stochastic-Abelian sandpile model on a two-dimensional lattice. The boundaries are closed and the dissipation is due to the fact that each toppled grain is removed from the lattice with probability epsilon. It is shown that the scaling properties of this model are in the universality class of the stochastic-Abelian models with conservative dynamics and open boundaries. In particular, the dissipation rate epsilon can be adjusted according to a suitable function epsilon = f(L), such that the avalanche size distribution will coincide with that of the conservative model on a finite lattice of size L.

Journal Article↗

PubMed2006

Genetic toggle switch without cooperative binding.

Genetic switch systems with mutual repression of two transcription factors are studied using deterministic and stochastic methods. Numerous studies have concluded that cooperative binding is a necessary condition for the emergence of bistability in these systems. Here we show that, for a range of biologically relevant conditions, a suitable combination of network structure and stochastic effects gives rise to bistability even without cooperative binding.

Animals↗

PubMed2005

Modeling of negative autoregulated genetic networks in single cells.

We discuss recent developments in the modeling of negative autoregulated genetic networks. In particular, we consider the temporal evolution of the population of mRNA and proteins in simple networks using rate equations. In the limit of low copy numbers, fluctuation effects become significant and more adequate modeling is then achieved using the master equation formalism. The analogy between regulatory gene networks and chemical reaction networks on dust grains in the interstellar medium is discussed. The analysis and simulation of complex reaction networks are also considered.

Cell Physiological Phenomena↗

PubMed2005

Reaction kinetics in a tight spot.

The standard analysis of reaction networks based on deterministic rate equations fails in confined geometries, commonly encountered in fields such as astrochemistry, thin-film growth and cell biology. In these systems the small reactant population implies anomalous behavior of reaction rates, which can be accounted for only by following the full distribution of reactant numbers.

Catalysis↗

PubMed2004

Efficient simulations of gas-grain chemistry in interstellar clouds.

Chemical reactions on dust grains are of crucial importance in interstellar chemistry because they produce molecular hydrogen and various organic molecules. Because of the submicron size of the grains and the low flux, the surface populations of reactive species are small and strongly fluctuate. Under these conditions rate equations fail and the master equation is needed for modeling these reactions. However, the number of equations grows exponentially with the number of reactive species, severely limiting its feasibility. Here we present a method which dramatically reduces the number of equations, thus enabling the incorporation of the master equation in models of interstellar chemistry.

Journal Article↗

PubMed2003

Sandpile models and random walkers on finite lattices.

Abelian sandpile models, both deterministic, such as the Bak, Tang, Wiesenfeld (BTW) model [P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987)] and stochastic, such as the Manna model [S.S. Manna, J. Phys. A 24, L363 (1991)] are studied on finite square lattices with open boundaries. The avalanche size distribution P(L)(n) is calculated for a range of system sizes, L. The first few moments of this distribution are evaluated numerically and their dependence on the system size is examined. The sandpile models are conservative in the sense that grains are conserved in the bulk and can leave the system only through the boundaries. It is shown that the conservation law provides an interesting connection between the sandpile models and random-walk models. Using this connection, it is shown that the average avalanche sizes (L) for the BTW and Manna models are equal to each other, and both are equal to the average path length of a random walker starting from a random initial site on the same lattice of size L. This is in spite of the fact that the sandpile models with deterministic (BTW) and stochastic (Manna) toppling rules exhibit different critical exponents, indicating that they belong to different universality classes.

Journal Article↗

PubMed2002

Exact results for hydrogen recombination on dust grain surfaces.

The recombination of hydrogen in the interstellar medium, taking place on surfaces of microscopic dust grains, is an essential process in the evolution of chemical complexity in interstellar clouds. Molecular hydrogen plays an important role in absorbing the heat that emerges during gravitational collapse, thus enabling the formation of structure in the universe. The H2 formation process has been studied theoretically, and in recent years also by laboratory experiments. The experimental results were analyzed using a rate equation model. The parameters of the surface that are relevant to H2 formation were obtained and used in order to calculate the recombination rate under interstellar conditions. However, it turned out that, due to the microscopic size of the dust grains and the low density of H atoms, the rate equations may not always apply. A master equation approach that provides a good description of the H2 formation process was proposed. It takes into account both the discrete nature of the H atoms and the fluctuations in the number of atoms on a grain. In this paper we present a comprehensive analysis of the H2 formation process, under steady state conditions, using an exact solution of the master equation. This solution provides an exact result for the hydrogen recombination rate and its dependence on the flux, the surface temperature, and the grain size. The results are compared with those obtained from the rate equations. The relevant length scales in the problem are identified and the parameter space is divided into two domains. One domain, characterized by first order kinetics, exhibits high efficiency of H2 formation. In the other domain, characterized by second order kinetics, the efficiency of H2 formation is low. In each of these domains we identify the range of parameters in which, due to the small size of the grains, the rate equations do not account correctly for the recombination rate and the master equation is needed.

Journal Article↗

PubMed2002

Theoretical analysis and simulations of the generalized Lotka-Volterra model.

The dynamics of generalized Lotka-Volterra systems is studied by theoretical techniques and computer simulations. These systems describe the time evolution of the wealth distribution of individuals in a society, as well as of the market values of firms in the stock market. The individual wealths or market values are given by a set of time dependent variables w(i), i=1,...,N. The equations include a stochastic autocatalytic term (representing investments), a drift term (representing social security payments), and a time dependent saturation term (due to the finite size of the economy). The w(i)'s turn out to exhibit a power-law distribution of the form P(w) approximately w(-1-alpha). It is shown analytically that the exponent alpha can be expressed as a function of one parameter, which is the ratio between the constant drift component (social security) and the fluctuating component (investments). This result provides a link between the lower and upper cutoffs of this distribution, namely, between the resources available to the poorest and those available to the richest in a given society. The value of alpha is found to be insensitive to variations in the saturation term, which represent the expansion or contraction of the economy. The results are of much relevance to empirical studies that show that the distribution of the individual wealth in different countries during different periods in the 20th century has followed a power-law distribution with 1<alpha<2.

Journal Article↗