Synchronization of non-linear biochemical oscillators coupled by diffusion

The behaviour of similar coupled non-linear oscillators of the type \(\dot x\) =f(x, y, µ \(\dot y\) =g(x, y, µ is to be investigated. The oscillators are assumed to be coupled by diffusion gradients. If some conditions on the magnitude of the diffusion coefficients are satisfied, it is proved that: 1) if the oscillators have the same period (identical value of the parameter μ) and different phases before coupling, after coupling they tend to synchronize the phases; 2) if the periods of the oscillators are not too different (in terms of the values of the parameter μ) before coupling, after coupling they tend to oscillate with the same period. It is suggested the possible role of diffusion as a synchronizing mechanism in some biological phenomena.     

Evolution of specialization in a spatially continuous environment

We study the evolution of specialization in a spatially continuous (one‐dimensional) environment divided into two habitats; we use a general trade‐off function relating fitnesses in the two habitats and illustrate our results with two classical trade‐off functions. We show that the population can either reach an intermediate value of the trait and be moderately adapted to both habitats (1 generalist), or split into two locally adapted subpopulations (2 specialists). We recover the qualitative results obtained with simpler metapopulation models with island migration: the evolutionary outcome depends on the concavity of the trade‐off, on the proportion of each habitat and on migration. Our quantitative prediction on migration, however, depends on isolation by distance. Our spatially explicit model may thus be particularly useful to describe the evolutionary dynamics of specialization in, perhaps, more realistic ecological scenarios.     

Analysis of oscillations in yeast continuous cultures by a new simplified model

The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod’s classical chemostat model. Two main cell phases or states are considered to account for the experimentally observed changes occurring in the cell growth course: the budded phase and the unbudded one. Thus, a sort of two compartment structure is given to the total biomass. The model so far obtained allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates. Necessary conditions for the local instability are derived and the existence of stable limit cycles is shown by computer simulation. With respect to the qualitative changes in the metabolic parameters, this analysis agrees with the results obtained by simulation of complex structured and segregated models. However, the oscillation period is too long compared with the experimental one and this fact may be mainly due to the strong simplifying assumptions on the dynamic evolution of the transfer rates between the two compartments. The model’s usefulness seems until now restricted to the identification of the relationships between the cell cycle regulation and the oscillation triggering.     

Synchronization of oscillations of proliferation of keratinocytes in psoriatic skin by external periodic force: a mathematical model

A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to these states. It was shown that in the norm, a single stable equilibrium of a "focus" type exists in the system; whereas in psoriasis, owing to an increase in the growing fraction, hyperproliferation, and enhanced migration of interacting keratinocytes, a stable limit cycle arises from the state of unstable focus. In this paper we also report on the results of computer modeling of synchronization of self-excited oscillations of keratinocyte population density in psoriatic lesions by an external periodic force. This synchronization is viewed as a possible mechanism of the clinically observed dependence of psoriasis course on some natural factors of cyclic nature.     

Control of glycolytic oscillations by temperature

External control of oscillatory glycolysis in yeast extract has been performed by application of either homogeneous temperature oscillations or stationary, spatial temperature gradients. Entrainment of the glycolytic oscillations by the 1/2- and 1/3-harmonic, as well as the fundamental input frequency, could be observed. From the phase response curve to a single temperature pulse, a distinct sensitivity of NADH-oxidizing processes, compared with NAD-reducing processes, is visible. Determination of glycolytic intermediates shows that the feedback-regulated phosphofructokinase as well as the glyceraldehyde-3-phosphate dehydrogenase are the most temperature-sensitive steps of glycolysis. We also find strong concentration changes in ATP and AMP at varying temperatures and, accordingly, in the energy charge. Construction of a feedback loop for spatial control of temperature by means of a Peltier element allowed us to apply a temperature gradient to the yeast extract. With this setup it is possible to initiate traveling waves and to control the wave velocity.     

Persistent behavior in a phase-shift sequence of periodical biochemical oscillations

We present the analysis of a phase-shift sequence obtained from random transitions between periodic solutions of a biochemical dynamical model, formed by a system of three differential equations and which represent an instability-generating multienzymatic mechanism. The phase-shift series was studied in terms of Hurst’s rescaled range analysis. We found that the data were characterized by a Hurst exponent H = 0.69, which was clearly indicative of long-term trends. This result had a high significance level, as was confirmed through Monte Carlo simulations in which the data were scrambled in the series, destroying its original ordering. For these series we obtained a Hurst exponent which was consistent with the expectation of H = 0.5 for a random independent process. This clearly showed that, although the transitions between the periodic solutions were provoked randomly, the stochastic process obtained exhibited long-term persistence. The fractal dimension was also estimated and found to be consistent with the value of the Hurst exponent.     

Switches and latches: a biochemical tug-of-war between the kinases and phosphatases that control mitosis

Activation of the cyclin-dependent kinase (Cdk1) cyclin B (CycB) complex (Cdk1:CycB) in mitosis brings about a remarkable extent of protein phosphorylation. Cdk1:CycB activation is switch-like, controlled by two auto-amplification loops--Cdk1:CycB activates its activating phosphatase, Cdc25, and inhibits its inhibiting kinase, Wee1. Recent experimental evidence suggests that parallel to Cdk1:CycB activation during mitosis, there is inhibition of its counteracting phosphatase activity. We argue that the downregulation of the phosphatase is not just a simple latch that suppresses futile cycles of phosphorylation/dephosphorylation during mitosis. Instead, we propose that phosphatase regulation creates coherent feed-forward loops and adds extra amplification loops to the Cdk1:CycB regulatory network, thus forming an integral part of the mitotic switch. These network motifs further strengthen the bistable characteristic of the mitotic switch, which is based on the antagonistic interaction of two groups of proteins: M-phase promoting factors (Cdk1:CycB, Cdc25, Greatwall and Endosulfine/Arpp19) and interphase promoting factors (Wee1, PP2A-B55 and a Greatwall counteracting phosphatase, probably PP1). The bistable character of the switch implies the existence of a CycB threshold for entry into mitosis. The end of G2 phase is determined by the point where CycB level crosses the CycB threshold for Cdk1 activation.     

Control of blood pressure oscillation elicited by bleeding.

1) A control objective regarding the blood pressure oscillation is to decrease the heart rate. 2) The transfusion of a small amount of blood at the bottom of a cycle in the oscillation is usually useful as a control plan for the blood pressure oscillation. 3) A partial occlusion of the abdominal aorta is effective in arresting the oscillation, but the oscillation starts again after releasing the abdominal aorta from the partial occlusion.     

Dynamical modeling of viral spread in spatially distributed populations: stochastic origins of oscillations and density dependence

In order to understand the spatio-temporal structure of epidemics beyond that permitted with classical SIR (susceptible-infective-recovered)-type models, a new mathematical model for the spread of a viral disease in a population of spatially distributed hosts is described. The positions of the hosts are randomly generated in a rectangular habitat. Encounters between any pair of individuals are according to a Poisson process with a mean rate that declines exponentially as the distance between them increases. The contact rate allows the mean rates to be set at a certain number of encounters per day on average. The relevant state variables for each individual at any time are given by the solution of a pair of coupled differential equations for the viral load and the quantity of general immune system effectors which reduce the viral load. The parameters describing within-host viral-immune system dynamics are generated randomly to reflect variability across a population. Transmission is assumed to depend on the viral loads in donors and occurs with a probability ptrans. The initial conditions are such that one randomly chosen individual carries a randomly chosen amount of the virus, whereas the rest of the population is uninfected. Simulations reveal local or whole-population responses. Whole-population disease spread may be in the form of isolated or multiple occurrences, the latter often being approximately periodic. The mechanisms of this oscillatory behaviour are analyzed in terms of several parameters and the distribution of critical points in the host dynamical systems. Increased contact rate, increased probability of transmission and decreased threshold for viral transmission, decreased immune strength and increased viral growth rate all increase the probability of multiple outbreaks and the distribution of the critical points also plays a role.     

Electric fields generated by synchronized oscillations of microtubules, centrosomes and chromosomes regulate the dynamics of mitosis and meiosis

ABSTRACT: Super-macromolecular complexes play many important roles in eukaryotic cells. Classical structural biological studies focus on their complicated molecular structures, physical interactions and biochemical modifications. Recent advances concerning intracellular electric fields generated by cell organelles and super-macromolecular complexes shed new light on the mechanisms that govern the dynamics of mitosis and meiosis. In this review we synthesize this knowledge to provide an integrated theoretical model of these cellular events. We suggest that the electric fields generated by synchronized oscillation of microtubules, centrosomes, and chromatin fibers facilitate several events during mitosis and meiosis, including centrosome trafficking, chromosome congression in mitosis and synapsis between homologous chromosomes in meiosis. These intracellular electric fields are generated under energy excitation through the synchronized electric oscillations of the dipolar structures of microtubules, centrosomes and chromosomes, three of the super-macromolecular complexes within an animal cell.     

Physiological, biochemical, and mathematical studies of micro-aerobic continuous ethanol fermentation by Saccharomyces cerevisiae. I: hysteresis, oscillations, and maximum specific ethanol productivities in chemostat culture

The growth and metabolism of Saccharomyces cerevisiae was studied in steady-state chemostat cultures under conditions of scarce oxygen and excess glucose. The specific ethanol productivity and specific glucose uptake rate were stimulated by 50% within a narrow range of air/nitrogen mixtures to the fermentor. Fermentation was inhibited at slightly higher and lower air/nitrogen ratios, confirming similar results by previous investigators. This stimulation could not be caused by obvious mechanisms, such as the Pasteur or Crabtree effects. Since this maximum in the fermentation rate occurred in a steady-state chemostat and at a constant dilution rate, the ATP yield of the culture necessarily attained a minimum. Thus, changes in the energetic efficiency of growth or the degree of wasting of ATP were surmised. The steady-state biomass concentration at various oxygenation rates exhibited hysteresis phenomena. Ignition and extinction of the biomass concentration occurred as critical oxygen feed rates were passed. The hysteresis was prevented by adding yeast extract to or reducing the antifoam concentration in the medium. These medium alterations had the simultaneous effect of stimulating the fermentation rate, suggesting that ATP has a critical role in dictating the biomass concentration in micro-aerobic culture. Silicone polymer antifoam was found to stimulate glycerol production at the expense of ethanol production, having consequences for the energy generation and the biomass concentration of the culture.     

Effective dispersal rate is a function of habitat size and corridor shape: mechanistic formulation of a two‐patch compartment model for spatially continuous systems

Two‐patch compartment models have been explored to understand the spatial processes that promote species coexistence. However, a phenomenological definition of the inter‐patch ‘dispersal rate’ has limited the quantitative predictability of these models to community dynamics in spatially continuous habitats. Here, we mechanistically rederived a two‐patch Lotka–Volterra competition model for a spatially continuous reaction‐diffusion system where a narrow corridor connects two large habitats. We provide a mathematical formula of the dispersal rate appearing in the two‐patch compartment model as a function of habitat size, corridor shape (ratio of its width to its length), and organism diffusion coefficients. For most reasonable settings, the two‐patch compartment model successfully approximated not only the steady states, but also the transient dynamics of the reaction–diffusion model. Further numerical simulations indicated the general applicability of our formula to other types of community dynamics, e.g. driven by resource‐competition, in spatially homogeneous and heterogeneous environments. Our results suggest that the spatial configuration of habitats plays a central role in community dynamics in space. Furthermore, our new framework will help to improve experimental designs for quantitative test of metacommunity theories and reduce the gaps among modeling, empirical studies, and their application to landscape management.     

Control of mitosis,inflammation, and cell motility by limited leakage of lysosomes

Lysosomal membrane permeabilization and subsequent leakage of lysosomal hydrolases into the cytosol are considered as the major hallmarks of evolutionarily conserved lysosome-dependent cell death. Contradicting this postulate, new sensitive methods that can detect a minimal lysosomal membrane damage have demonstrated that lysosomal leakage does not necessarily equal cell death. Notably, cells are not only able to survive minor lysosomal membrane permeabilization, but some of their normal functions actually depend on leaked lysosomal hydrolases. Here we discuss emerging data suggesting that spatially and temporally controlled lysosomal leakage delivers lysosomal hydrolases to specific subcellular sites of action and controls at least three essential cellular processes, namely mitotic chromosome segregation, inflammatory signaling, and cellular motility.     

SpatialDemography: a spatially explicit,stage‐structured,metacommunity model

The responses of species and populations to changes in the environment (e.g. changes in climate and land use) are often complex and difficult to predict. We have created the SpatialDemography model (R package: spatialdemography). The model is a spatially explicit, stage‐structured, matrix‐based metacommunity model, with the potential for modeling species’ and populations’ potential responses to environmental heterogeneity and change. The SpatialDemography model assumes a cellular landscape populated by organisms with four life stages: a mobile dispersing stage, two sessile non‐reproductive stages, and a reproductive adult stage. Individuals are assumed to originate at the center of a given cell and disperse according to a specified dispersal kernel (e.g. log‐normal). All adult individuals are capable of producing offspring. The model approach and framework are described in the context of a hypothetical example with multiple competing species in a four cell landscape. In this example simulation, both spatial location and species interactions were important for understanding population dynamics. SpatialDemography can be applied to questions where an understanding of transient and long‐term demographic responses to spatiotemporal changes is desired. It is primarily applicable to metapopulations and metacommunities of organisms with early dispersal and sessile adults (i.e. modular organisms such as plants and some marine organisms). SpatialDemography differs from other population models in that it is spatially explicit, can incorporate biotic interactions, and is implemented in R.     

Control of substrate concentration in a continuous bioprocess

This paper is the first one presenting an application of the control law based on the ratio of measured and optimal values for a real fermentation pilot plant operated in continuous mode. A controller of this type takes into account the process variables and may be designed by using classical linear methods. A simple algorithm is applied for a real CSTR to control the substrate concentration. The results obtained confirm that this approach offers the possibility to combine simplicity and effectiveness in bioprocess control.