On the dynamics of the microfilament system in HeLa cells

We measured the pools of unpolymerized and filamentous actin in homogenates of HeLa cells made in several different lysis buffers, as well as after treatment of cells with a variety of chemicals or trypsin, and after adenovirus (type 2) infection. This was possible when a series of factors concerning the basic culture conditions were kept constant: e.g., serum type used, serum batch, cell density, time after subcultivation of cells, and buffering substance in the medium. Homogenates from untreated cells usually contain 35-45 percent of the total actin in an unpolymerized form. With some batches of cells this number can be as high as 50 percent. In sparse cultures (3 x 10(4) cell/cm(2)), HeLa cells contain approximately 10 pg actin/cell, while the corresponding number is only 5 pg in dense cultures (3 x 10(5) cells/cm(2)). Treatment of cells with cytochalasin B increases the pool of unpolymerized actin by approximately 30-40 percent, while colchicine decreases the fraction of unpolymerized actin by 20 percent. The oxidant diamide increases the filamentous actin pool 25-50 percent. Glucose, sodium azide, dinitrophenol, serum starvation, or thymidine treatment does not affect the distribution between unpolymerized and filamentous actin to any significant extent. Trypsin and EDTA induced rounding up of cells but did not change the actin distribution. The distribution of actin between G- and F-forms was unchanged after adenovirus infection. These results show that significant changes in the actin pools can be induced in nucleated cells. However, several treatments which alter the morphology and motility of cells are not accompanied by an alteration in the G-/F-actin ratio.     

Global dynamics of a ratio-dependent predator-prey system

Recently, ratio-dependent predator-prey systems have been regarded by some researchers to be more appropriate for predator-prey interactions where predation involves serious searching processes. However, such models have set up a challenging issue regarding their dynamics near the origin since these models are not well-defined there. In this paper, the qualitative behavior of a class of ratio-dependent predator-prey system at the origin in the interior of the first quadrant is studied. It is shown that the origin is indeed a critical point of higher order. There can exist numerous kinds of topological structures in a neighborhood of the origin including the parabolic orbits, the elliptic orbits, the hyperbolic orbits, and any combination of them. These structures have important implications for the global behavior of the model. Global qualitative analysis of the model depending on all parameters is carried out, and conditions of existence and non-existence of limit cycles for the model are given. Computer simulations are presented to illustrate the conclusions.     

On the stability of a model of testosterone dynamics

We prove the global asymptotic stability of a well-known delayed negative-feedback model of testosterone dynamics, which has been proposed as a model of oscillatory behavior. We establish stability (and hence the impossibility of oscillations) even in the presence of delays of arbitrary length.Supported in part by AFOSR Grant F49620-01-1-0063, NIH Grant P20 GM64375, and Dimacs.E.D. Sontag: Supported in part by AFOSR Grant F49620-01-1-0063 and NIH Grant R01 GM46383.Acknowledgement We would like to thank Augusto Ponce for useful suggestions.     

On the dynamics of a simple biochemical control circuit

The quantitative dynamics of a biochemical control circuit that regulates enzyme or protein synthesis by end-product feedback is analyzed. We first study a simplified repressible system, which is known to exhibit either a steady state or an oscillatory solution. By showing the analogy of thisn-dimensional system with a time-delay equation for a single variable the mechanism of the self-sustained oscillations becomes transparent. In a more sophisticated system we will find as well either steady state or oscillatory solutions. We determine the role of the parameters with respect to stability and frequency. The most general case will be treated by means of the concept of Lyapunov exponents.     

On the nanoscale relaxation dynamics of a lipid bilayer

The Seifert–Langer theory of the relaxation dynamics of a one-component bilayer lipid membrane was extended to include a term that involves the gradient of the area per lipid molecule in the bilayer free energy per molecule. The extended theory is applicable over length scales comparable with the membrane thickness.     

The stabilizability of a controlled system describing the dynamics of a fishery

This work presents two stock-effort dynamical models describing the evolution of a fish population growing and moving between two fishing zones, on which it is harvested by a fishing fleet, distributed on the two zones. The first model corresponds to the case of constant displacement rates of the fishing effort, and the second one to fish stock-dependent displacement rates. In equations of the fishing efforts, a control function is introduced as the proportion of the revenue to be invested, for each fleet. The stabilizability analysis of the aggregated model, in the neighborhood of the equilibrium point, enables the determination of a Lyapunov function, which ensures the existence of a stabilizing discontinuous feedback for this model. This enables us to control the system and to lead, in an uniform way, any solution of this system towards this desired equilibrium point.     

Unique coevolutionary dynamics in a predator-prey system

In this paper, we study the predator-prey coevolutionary dynamics when a prey's defense and a predator's offense change in an adaptive manner, either by genetic evolution or phenotypic plasticity, or by behavioral choice. Results are: (1) The coevolutionary dynamics are more likely to be stable if the predator adapts faster than the prey. (2) The prey population size can be nearly constant but the predator population can show very large amplitude fluctuations. (3) Both populations may oscillate in antiphase. All of these are not observed when the handling time is short and the prey's density dependence is weak. (4) The population dynamics and the trait dynamics show resonance: the amplitude of the population fluctuation is the largest when the speed of adaptation is intermediate. These results may explain experimental studies with microorganisms.     

Complex dynamics in a model microbial system

The forced double-Monod model (for a chemostat with a predator, a prey and periodically forced inflowing substrate) displays quasiperiodicity, phase locking, period doubling and chaotic dynamics. Stroboscopic sections reveal circle maps for the quasiperiodic regimes and noninvertible maps of the interval for the chaotic regimes. Criticality in the circle maps sets the stage for chaos in the model. This criticality may arise with an increase in the period or amplitude of forcing.     

New spatial-temporal dynamics in a reaction-electrodiffusion system

The properties of a system reaction-electrodiffusion were studied using two-component model of interaction and diffusion of charged particles near membrane in solutions of low ionic strength to which traditional assumptions about local electroneutrality of medium are not applicable. It is shown that the effect of self-consistent electric field leads to bistability, the appearance of localized structures with contrast charge distribution and regimes aperiodical in time and in space.     

Effects of a disease affecting a predator on the dynamics of a predator-prey system

We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We consider two time scales, a fast one for the disease and a comparatively slow one for predator-prey interactions and for predator mortality. We use the classical “aggregation method” in order to obtain a reduced equivalent model. We show that there are two possible asymptotic behaviors: either the predator population dies out and the prey tends to its carrying capacity, or the predator and prey coexist. In this latter case, the predator population tends either to a “disease-free” or to a “disease-endemic” state. Moreover, the total predator density in the disease-endemic state is greater than the predator density in the “disease-free” equilibrium (DFE).     

Biogeomorphologic succession dynamics in a Mediterranean river system

Biogeomorphologic succession (i.e. reciprocal adjustments between vegetation and geomorphologic dynamics) of the Mediterranean River Tech, France, was analysed using aerial photographs over a period of sixty years between 1942 and 2000. A spatial analysis of the biogeomorphologic succession was undertaken considering effects of flood regime. Interactions between vegetation dynamics and flood events largely controlled the spontaneous replacement of the dense riparian forest removed in October 1940 during an exceptional high magnitude flood event with a recurrence time >100 yr. In response to this major disturbance event, the fluvial landscape demonstrated a very high resilience emphasizing the existence of a positive feedback driven by pioneer riparian vegetation. The observed feedback corresponded to landform accretion, vegetation succession and to an increase of biogeomorphologic stability under current hydrogeomorphologic and bioclimatic conditions. The evolution of the biogeomorphologic system toward stabilisation appeared to be non‐linear with a threshold occurring thirty years after the exceptional destructive flood event. This threshold materialized a reinforcement of biogeomorphologic cohesive forces driven by vegetation dynamics. This study showed the control of riparian vegetation on the dynamics of Mediterranean fluvial landscapes and pointed to the need to improve our knowledge about biogeomorphologic succession cycles and threshold dynamics within different biogeomorphologic settings.     

On modelling the immune system as a complex system

We argued that immune system is an adaptive complex system. It is shown that it has emergent properties. Its network structure is of the small world network type. The network is of the threshold type, which helps in avoiding autoimmunity. It has the property that every antigen (e.g. virus or bacteria) is typically attacked by more than one effector. This stabilizes the equilibrium state. Modelling complex systems is discussed. Cellular automata (CA)-type models are successful, but there are much less analytic results about CA than about other less successful models e.g. partial differential equations (PDE). A compromise is proposed.     

On the dynamics of asymmetric games

A game dynamical analysis of a simple asymmetric game (two roles with two alternatives each) shows that an interesting class of “semi-stable” heteroclinic cycles leading to a highly unpredictable behaviour can occur in a robust way. Biological examples related to conflicts over ownership and parental investment are analysed.     

On the dynamics of evolutionary discontinuities

Intraspecific competition and selection in polymorphic populations are considered as gradual, yet highly nonlinear, processes which possibly lead to structurally unstable states in species and ecosystems. Discontinuous genetic and morphological changes may thus occur, which are interpreted as evolutionary “catastrophes,” that is, instantaneous transitions between distant, secularly stable evolutionary branches. It is argued that evolutionary gradualism and saltationism represent complementary modes of macroevolution corresponding respectively to the local and global topographical structure of adaptive surfaces.     

On the dynamics of bursting systems

The dynamics of three-variable models of bursting are studied. It is shown that under certain conditions, the dynamics on the attractor can be essentially reduced to two dimensions. The salient dynamics on the attractor can thus be completely described by the return map of a section which is a logistic interval map. Two specific bursting models from the literature are shown to fit in the general framework which is developed. Bifurcation of the full system for one case in investigated and the dynamical behavior on the attractor is shown to depend on the position of a certain nullcline.Supported in part by N.S.F.On leave at University of Maryland     

Population dynamics of host-parasite interactions in a cockroach-oxyuroid system

Host-parasite interactions of an urban cockroach, Blattella germanica , and its oxyuroid parasite, Blatticola blattae , were investigated. Life history data of host and parasites were collected under laboratory conditions. These data were used to model the effect of the parasite on the population dynamics of the host in order to understand the parasite's impact on the host population. The aggregation of parasites within a host was under-dispersed. Hosts normally were found to be infected with only one male and one female and rarely two or three. However, the primary sex ratio after hatching was 1.1 (males/females). Female parasite longevity equalled the life span of its host. B. blattae had a significant impact on the survival rate of the cockroach larvae and their time to reach maturity, but no effect on the survival rate of the adults. Infected host females produced fewer first oothecae than uninfected ones. Using the population parameters a simple model was developed to estimate the parasite's effect on the population dynamics of its host. According to the model the parasite suppresses the cockroach populations by ca 11%. Hence, the effect of the parasite does not appear strong enough to be used as a biological control agent by itself.     

On the dynamics of cell cleavage

A completely fluid model of cleavage dynamics is studied in which the forces exerted within the boundary structure of a cell are approximated by an effective surface tension. The hypothesis that surface tension depends in part on the concentration of tension elements implies a contraction of the surface towards the equator resulting from a dynamical instability that once triggered develops spontaneously into cleavage. The circulation of the cytoplasm induced by surface stresses collects and aligns the surface-bound tension elements into an equatorial belt. This flow may be a means of assembling a contractile ring.     

Impact of spatial heterogeneity on a predator-prey system dynamics

This paper deals with the study of a predator-prey model in a patchy environment. Prey individuals moves on two patches, one is a refuge and the second one contains predator individuals. The movements are assumed to be faster than growth and predator-prey interaction processes. Each patch is assumed to be homogeneous. The spatial heterogeneity is obtained by assuming that the demographic parameters (growth rates, predation rates and mortality rates) depend on the patches. On the predation patch, we use a Lotka-Volterra model. Since the movements are faster that the other processes, we may assume that the frequency of prey and predators become constant and we would get a global predator-prey model, which is shown to be a Lotka-Volterra one. However, this simplified model at the population level does not match the dynamics obtained with the complete initial model. We explain this phenomenom and we continue the analysis in order to give a two-dimensional predator-prey model that gives the same dynamics as that provided by the complete initial one. We use this simplified model to study the impact of spatial heterogeneity and movements on the system stability. This analysis shows that there is a globally asymptotically stable equilibrium in the positive quadrant, i.e. the spatial heterogeneity stabilizes the equilibrium.     

On the dynamics of operant conditioning

Simple psychological postulates are presented which are used to derive possible anatomical and physiological substrates of operant conditioning. These substrates are compatible with much psychological data about operants. A main theme is that aspects of operant and respondent conditioning share a single learning process. Among the phenomena which arise are the following: UCS-activated arousal; formation of conditioned, or secondary, reinforcers; a non-specific arousal system distinct from sensory and motor representations whose activation is required for sensory processing; polyvalent cells responsive to the sum of CS and UCS inputs and anodal d.c. potential shifts; neural loci responsive to the combined effect of sensory events and drive deprivation; “go”-like or “now print”-like mechanisms which, for example, influence incentive-motivational increases in general activity; a mechanism for learning repetitively to press a bar which electrically stimulates suitable arousal loci in the absence of drive reduction; uniformly distributed potentials, driven by the CS, in the “cerebral cortex” of a trained network; the distinction between short-term and long-term memory, and the possibility of eliminating transfer from short-term to long-term memory in the absence of suitable arousal; networks that can learn and perform arbitrarily complex sequences of acts or sensory memories, without continuous control by sensory feedback, whose rate of performance can be regulated by the level of internal arousal; networks with idetic memory; network analogs of “therapeutic resistance” and “repression”; the possibility of conditioning the sensory feedback created by a motor act to the neural controls of this act, with consequences for sensory-motor adaptation and child development. This paper introduces explicit minimal anatomies and physiological rules that formally give rise to analogous phenomena. These networks consider only aspects of positive conditioning. They are derived from simple psychological facts.