Luiz Henrique Alves Monteiro

Temperature effects on energy metabolism: a dynamic system analysis.

Q10 factors are widely used as indicators of the magnitude of temperature-induced changes in physico–chemical and physiological rates. However, there is a long–standing debate concerning the extent to which Q10 values can be used to derive conclusions about energy metabolism regulatory control. The main point of this disagreement is whether or not it is fair to use concepts derived from molecular theory in the integrative physiological responses of living organisms. We address this debate using a dynamic systems theory, and analyse the behaviour of a model at the organismal level. It is shown that typical Q10 values cannot be used unambiguously to deduce metabolic rate regulatory control. Analytical constraints emerge due to the more formal and precise equation used to compute Q10, derived from a reference system composed from the metabolic rate and the Q10. Such an equation has more than one unknown variable and thus is unsolvable. This problem disappears only if the Q10 is assumed to be a known parameter. Therefore, it is concluded that typical Q10 calculations are inappropriate for addressing questions about the regulatory control of a metabolism unless the Q10 values are considered to be true parameters whose values are known beforehand. We offer mathematical tools to analyse the regulatory control of a metabolism for those who are willing to accept such an assumption.

The oxygen gain of diving insects.

The gas gill of diving insects allows gas exchange with the surrounding water, thus extending diving time. Incompressible gas gills can potentially last indefinitely underwater, but compressible gas gills have a definite lifetime. Theoretical models of a dive event have reached opposite conclusions about the oxygen gain (G, the ratio between the duration of the diving event and the time that the initial oxygen content of the bubble would allow the insect to stay underwater). While some authors claim that G has a fixed value independently of the parameters of the dive (e.g. oxygen consumption rate) others claim the contrary. However, these claims are based on numerical solutions of the models. In this study we offer an analytical solution to the problem. The analysis of a model with constant area for gas exchange demonstrates that G cannot have a fixed value, for a fixed gain would imply in a P(O(2)) inside the bubble different from the one occurring as a result of physical constraints of the gas exchange process.

Temperature effects on a whole metabolic reaction cannot be inferred from its components

Changes in temperature affect the kinetic energy of the constituents of a system at the molecular level and have pervasive effects on the physiology of the whole organism. A mechanistic link between these levels of organization has been assumed and made explicit through the use of values of organismal Q10 to infer control of metabolic rate. To be valid this postulate requires linearity and independence of the isolated reaction steps, assumptions not accepted by all. We address this controversy by applying dynamic systems theory and metabolic control analysis to a metabolic pathway model. It is shown that temperature effects on isolated steps cannot rigorously be extrapolated to higher levels of organization.

Oscillatory pattern in oxygen consumption of Hummingbirds

b P ! os-Gradua- Abstract Mammals and birds offer the most conspicuous example of homeothermic endothermy, a metabolic feature that implies maintenance of a constant body temperature along broad ranges of ambient temperature. The concept of homeothermic endothermy has been developed in close association with the terms thermoneutral zone and basal metabolic rate. These two metabolic parameters, however, are not easily estimated in micro-endotherms, a difficulty that might emerge from intrinsic aspects of endothermy in minute animals. To address this issue, we used empirical work derived from theoretical considerations. Our theoretical analysis is based on a model of body temperature control by shifts in metabolic rate, and assumes that micro-endotherms lose heat very quickly due to body size, and exhibit a remarkable capacity to rapidly increase metabolic output. We found that these two metabolic traits can lead to non-equilibrium metabolic rate and body temperature. We then measured metabolic rate and body temperature during euthermia in two species of hummingbirds, and analyzed data using the w 2 periodogram statistic and a power spectral analysis. We found long-range correlation in both oxygen consumption and body temperature during euthermia, a finding that suggests non-random 1=f oscillations. A similar pattern was not found in the rat, a much larger endotherm. Hummingbirds, then, do not appear to maintain steady-state metabolic conditions during euthermia. If, as we suggest, this pattern applies to micro-endotherms in general, the traditional concepts of thermoneutral zone and basal rate of metabolism might not apply to these animals. r 2002 Elsevier Science Ltd. All rights reserved.

A theoretical model for estimating the margination constant of leukocytes.

BackgroundBlood leukocytes constitute two interchangeable sub-populations, the marginated and circulating pools. These two sub-compartments are found in normal conditions and are potentially affected by non-normal situations, either pathological or physiological. The dynamics between the compartments is governed by rate constants of margination (M) and return to circulation (R). Therefore, estimates of M and R may prove of great importance to a deeper understanding of many conditions. However, there has been a lack of formalism in order to approach such estimates. The few attempts to furnish an estimation of M and R neither rely on clearly stated models that precisely say which rate constant is under estimation nor recognize which factors may influence the estimation.ResultsThe returning of the blood pools to a steady-state value after a perturbation (e.g., epinephrine injection) was modeled by a second-order differential equation. This equation has two eigenvalues, related to a fast- and to a slow-component of the dynamics. The model makes it possible to identify that these components are partitioned into three constants: R, M and SB; where SB is a time-invariant exit to tissues rate constant. Three examples of the computations are worked and a tentative estimation of R for mouse monocytes is presented.ConclusionsThis study establishes a firm theoretical basis for the estimation of the rate constants of the dynamics between the blood sub-compartments of white cells. It shows, for the first time, that the estimation must also take into account the exit to tissues rate constant, SB.

Conditions for pathogen elimination by immune systems.

SummaryA continuous harvest effort can lead a population to extinction. How an “unconscious” immune system would perpetrate such an effort in order to eliminate a self-replicating antigen (a pathogen) becomes an intriguing problem if the system responses are functions of the pathogen population: the responses cannot be a continuous effort as the pathogen vanishes. On theoretical grounds, we show some qualities an immune response must have to support pathogen elimination. Then, three specific mechanisms are addressed: a pathogen-independent positive feedback loop among the responding cells of the system (e.g., B-lymphocyte and T-helper); the persistence of antigen bound to presenting cells; and the programmed expansion/contraction of a pool of responding cells. The maintenance of responding cells due to these mechanisms is the essential feature to the effective clearance of self-replicating agents. Thus, evolutionarily, the primary function of a helper lymphocyte would be to amplify a response and the primary function of memory would be the very elimination of pathogens.

A Linear Analysis of Coupled Wilson-Cowan Neuronal Populations

Let a neuronal population be composed of an excitatory group interconnected to an inhibitory group. In the Wilson-Cowan model, the activity of each group of neurons is described by a first-order nonlinear differential equation. The source of the nonlinearity is the interaction between these two groups, which is represented by a sigmoidal function. Such a nonlinearity makes difficult theoretical works. Here, we analytically investigate the dynamics of a pair of coupled populations described by the Wilson-Cowan model by using a linear approximation. The analytical results are compared to numerical simulations, which show that the trajectories of this fourth-order dynamical system can converge to an equilibrium point, a limit cycle, a two-dimensional torus, or a chaotic attractor. The relevance of this study is discussed from a biological perspective.

Clustering in coupled maps on small-world networks

Coupled map lattices and globally coupled maps are able to create clusters in which elements show synchronized oscillation. These behaviors can also be found in disordered networks like small-world models with the advantage of combining small average distances between elements with few edges. Here the partial synchronization of coupled maps on three different small-world models are investigated and compared.

Symmetry Detection Using Global-Locally Coupled Maps

Symmetry detection through a net of coupled maps is proposed. Logistic maps are associated with each element of a pixel image where the symmetry is intended to be verified. The maps are locally and globally coupled and the reflection-symmetry structure can be embedded in local couplings. Computer simulations are performed by using random gray level images with different image sizes, asymmetry levels and noise intensity. The symmetry detection is also done under dynamic scene changing. Finally the extensions and the adherence of the present model to biological systems are discussed.

Explorando Analiticamente o Modelo de Rede Neural de Wilson-Cowan

Considere duas populacoes de neuronios, uma excitatoria e outra inibitoria, de modoxa0que essas populacoes estao intra e interconectadas. O modelo de Wilson-Cowan descreve axa0evolucao temporal da atividade dessa rede neural. Aqui, estuda-se analiticamente uma versaoxa0desse modelo e mostra-se que tal atividade pode ser oscilatoria.