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Biomedical subjects

C A Condat

Publications and source records attributed to C A Condat.

13 recordsLinked to original sources
PubMed2005

Randomly curved runs interrupted by tumbling: a model for bacterial motion.

Small bacteria are strongly buffeted by Brownian forces that make completely straight runs impossible. A model for bacterial motion is formulated in which the effects of fluctuational forces and torques on the run phase are taken into account by using coupled Langevin equations. An integrated description of the motion, including runs and tumbles, is then obtained by the use of convolution and Laplace transforms. The properties of the velocity-velocity correlation function, of the mean displacement, and of the two relevant diffusion coefficients are examined in terms of the bacterial sizes and of the magnitude of the propelling forces. For bacteria smaller than E. coli, the integrated diffusion coefficient crosses over from a jump-dominated to a rotational-diffusion-dominated form.

Algorithms↗
PubMed2005

Bridging the Gap between mesoscopic and macroscopic models: the case of multicellular tumor spheroids.

Multicellular tumor spheroids are valuable experimental tools in cancer research. By introducing an intermediate model, we have been able to successfully relate mesoscopic and macroscopic descriptions of spheroid growth. Since these descriptions stem from completely different roots (cell dynamics, and energy conservation and scaling arguments, respectively), their consistency validates both approaches and allows us to establish a direct correspondence between parameters characterizing processes occurring at different scales. Our approach may find applications as an example of bridging the gap between models at different scale levels in other contexts.

Cell Growth Processes↗
PubMed2002

Competition effects in the dynamics of tumor cords.

A general feature of cancer growth is the cellular competition for available nutrients. This is also the case for tumor cords, neoplasms forming cylindrical structures around blood vessels. Experimental data show that, in their avascular phase, cords grow up to a limit radius of about 100 microm, reaching a quasi-steady-state characterized by a necrotized area separating the tumor from the surrounding healthy tissue. Here we use a set of rules to formulate a model that describes how the dynamics of cord growth is controlled by the competition of tumor cells among themselves and with healthy cells for the acquisition of essential nutrients. The model takes into account the mechanical effects resulting from the interaction between the multiplying cancer cells and the surrounding tissue. We explore the influence of the relevant parameters on the tumor growth and on its final state. The model is also applied to investigate cord deformation in a region containing multiple nutrient sources and to predict the further complex growth of the tumor.

Journal Article↗
PubMed2002

Dynamic analysis of a parasite population model.

We study the dynamics of a model that describes the competitive interaction between an invading species (a parasite) and its antibodies in an living being. This model was recently used to examine the dynamical competition between Tripanosoma cruzi and its antibodies during the acute phase of Chagas' disease. Depending on the antibody properties, the model yields three types of outcomes, corresponding, respectively, to healing, chronic disease, and host death. Here, we study the dynamics of the parasite-antibody interaction with the help of simulations, obtaining phase trajectories and phase diagrams for the system. We show that, under certain conditions, the size of the parasite inoculation can be crucial for the infection outcome and that a retardation in the stimulated production of an antibody species may result in the parasite gaining a definitive advantage. We also find a criterion for the relative sizes of the parameters that are required if parasite-generated decoys are indeed to help the invasion. Decoys may also induce a qualitatively different outcome: a limit cycle for the antibody-parasite population phase trajectories.

Animals↗
PubMed2002

Anomalous diffusion in the nonasymptotic regime.

We analyze some properties of the one-dimensional Lévy flights, assuming that the one-step transition rates depend on the flight length x as p(alpha)(x) equivalent to x(-(alpha+2)). For flights on a finite, (2M+1)-site lattice, we can define an effective, size-dependent, diffusion coefficient D(alpha)(M) equivalent to [M(1-alpha) - 1]/(1 - alpha) if alpha < 1, with D1(M) equivalent to ln(M). Using the generalization of statistical mechanics given by Tsallis, we show that for flights on infinite systems, the generalized displacement moments are well defined provided that alpha > R - 3. These moments exhibit a power-law singularity if alpha --> 1(-) and R>2/3. The short- and intermediate-time properties of the generalized mean-square displacement are then studied numerically. This work suggests the conditions under which the asymptotic analytical formulas (obtained in the literature by the use of the generalized central limit theorem) could be applied to finite-time experiments. These formulas should work much better if alpha is close to zero than in the alpha -->1(-) neighborhood.

Journal Article↗
PubMed2001

Diffusion with evolving sources and competing sinks: development of angiogenesis.

Tumors ensure their long-time growth by emitting molecular messengers that induce cellular modifications in neighboring capillaries. These modifications are conducive to the enlargement of the vascular system feeding the tumor. This phenomenon, termed angiogenesis, is controlled by the diffusion and competitive trapping of nutrients and molecular messengers by several cell species. The number, location, and properties of these traps change continuously. The angiogenic process also implies that nutrient sources are time dependent. Starting from assumptions at the cellular level, we formulate a mathematical model that predicts the evolution of angiogenesis and the increase in the blood flow to the tumor. The model also predicts the emergence of directed growth and the possibility of therapeutical synergy. Simulations permit a careful analysis of the influence of the main parameters.

Absorption↗
PubMed2001

Emergence of taxis and synergy in angiogenesis.

Angiogenesis, the expansion of the vascular system feeding a tumor, is crucial to both primary tumors long-time growth and for the successful implantation of metastases. We formulate a model that relates the energetic requirements of the cancer cells to the production and diffusion of an angiogenic factor and to the ensuing evolution of neighboring endothelial cells. The model yields predictions for the development of neovascularization and for the increase in the blood flow to the tumor. We show that the directed growth of the vascular net is an emergent property and that therapies targeting different stages of the angiogenic process might have a synergistic effect.

Angiogenesis Inducing Agents↗
PubMed2001

A simple model for the interaction between T. cruzi and its antibodies during Chagas infection.

The evolution of the acute phase of the Chagas infection is analysed from the viewpoint of the dynamic competition between parasite and antibody populations. A simple model for the growth and annihilation of these populations is shown to provide a suitable description of the experimental data. We also find that it is possible to classify antibody response to Trypanosoma cruzi, into three main cases, defined by antibody efficiency, initial number and creation rate. The model clearly indicates the most relevant parameters determining the evolution of the Chagas infection, yielding a simple asymptotic criterion for the host survival.

Acute Disease↗
PubMed1999

Effect of transport and competition on ligand binding.

We present a model to describe the physics of chemoreception in processes determined by competitive ligand binding. Our model describes the competition between various populations, such as ligands vs. blockers and receptors vs. decoys, in protein activation when diffusion is rate-determining. Full spatio-temporal solutions can be obtained numerically. The model structure is kept simple enough as to permit its easy generalization to describe a large subset of the manifold of possible situations occurring in nature. The power and simplicity of the proposed method are exhibited through the solution of several examples which are discussed in detail.

Journal Article↗
PubMed1999

Non-linear model of cancer growth and metastasis: a limiting nutrient as a major determinant of tumor shape and diffusion.

A new approach for modelling the spatio-temporal evolution of tumors is presented. To test its validity, a very basic model is considered, which, in spite of its simplicity, is capable of generating a multiplicity of morphologies and growth and migration rates. From an in-vivo scenario of basic life processes, cancer cell proliferation is described as a competition for basic nutrients. The chosen mathematical treatment and simulation techniques permit a direct implementation of the local nonlinear couplings existing between the various cell populations and the free and bound nutrient concentration. A discussion of the results and proposed improvements and applications of the model is also presented.

Cell Division↗
PubMed1999

Observability of stochastic resonance in neutron scattering.

The observability of the stochastic resonance phenomenon in a neutron scattering experiment is investigated, considering that the scatterer can hop between two sites. Under stochastic resonance conditions scattered intensity is transferred from the quasielastic region to two inelastic peaks. The magnitude of the signal-to-noise ratio is shown to be similar to that arising in the corresponding power spectrum. Effects of potential asymmetry are discussed in detail. Asymmetry leads to a reduction of the signal-to-noise ratio by a factor of 1-xi(2), where xi is an asymmetry parameter which is zero for symmetric problems and equal to unity in a completely asymmetric case.

Journal Article↗
PubMed1989

Closed-time distribution of ionic channels. Analytical solution to a one-dimensional defect-diffusion model.

A one-dimensional version of the model recently proposed by Läuger (1988) to explain the closed-time distribution of ionic channels in cell membranes is solved analytically. While the probability density f(t) for closed-time lengths may show a well-defined exponential behavior at short times, a power-law decay is predicted at long times. The influence of an additional random distribution of defects in the current-conducting protein is investigated and found to be dominating at long times. Explicit expressions that may be used for fitting experimental data are given for the closed-time distribution. Some of the available data are discussed and shown to be in good agreement with the predictions of the model.

Animals↗