RESUMO
The Frank-Starling law of the heart is a filling-force mechanism (FFm), a positive relationship between the distension of a ventricular chamber and its force of ejection, and such a mechanism is found across all the studied vertebrate lineages. The functioning of the cardiovascular system is usually described by means of the cardiac and vascular functions, the former related to the contractility of the heart and the latter related to the afterload imposed on the ventricle. The crossing of these functions is the so-called 'operation point', and the FFm is supposed to play a stabilizing role for the short-term variations in the working of the system. In the present study, we analyze whether the FFm is truly responsible for such a stability within two different settings: one-ventricle and two-ventricle hearts. To approach the query, we linearized the region around an arbitrary operation point and put forward a dynamical system of differential equations to describe the relationship among volumes in face of blood flows governed by pressure differences between compartments. Our results show that the FFm is not necessary to give stability to an operation point. Thus, which forces selected and maintained such a mechanism in all vertebrates? The present results indicate three different and complementary roles for the FFm: (1) it decreases the demands of a central controlling system over the circulatory system; (2) it smooths out perturbations in volumes; and (3) it guarantees faster transitions between operation points, i.e. it allows for rapid changes in cardiac output.
Assuntos
Débito Cardíaco , Coração/fisiologia , Contração Miocárdica , Função Ventricular , Vertebrados/fisiologia , AnimaisRESUMO
The allometric scaling exponent of the relationship between standard metabolic rate (SMR) and body mass for homeotherms has a long history and has been subject to much debate. Provided the external and internal conditions required to measure SMR are met, it is tacitly assumed that the metabolic rate (B) converges to SMR. If SMR does indeed represent a local minimum, then short-term regulatory control mechanisms should not operate to sustain it. This is a hidden assumption in many published articles aiming to explain the scaling exponent in terms of physical and morphological constraints. This paper discusses the findings of a minimalist body temperature (Tb) control model in which short-term controlling operations, related to the difference between Tb and the set-point temperatures by specific gains and time delays in the control loops, are described by a system of differential equations of Tb, B and thermal conductance. We found that because the gains in the control loops tend to increase as body size decreases (i.e. changes in B and thermal conductance are speeded-up in small homeotherms), the equilibrium point of the system potentially changes from asymptotically stable to a centre, transforming B and Tb in oscillating variables. Under these specific circumstances the very concept of SMR no longer makes sense. A series of empirical reports of metabolic rate in very small homeotherms supports this theoretical prediction, because in these animals B seems not to converge to a SMR value. We conclude that the unrestricted use of allometric equations to relate metabolic rate to body size might be misleading because metabolic control itself experiences size effects that are overlooked in ordinary allometric analysis.
Assuntos
Metabolismo Basal/fisiologia , Tamanho Corporal , Regulação da Temperatura Corporal/fisiologia , Metabolismo Energético/fisiologia , Modelos Biológicos , AnimaisRESUMO
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.
Assuntos
Metabolismo Energético/fisiologia , Modelos Biológicos , Temperatura , Simulação por Computador , Teoria de SistemasRESUMO
BACKGROUND: Blood 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. RESULTS: The 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. CONCLUSIONS: This 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.
Assuntos
Movimento Celular , Leucócitos/fisiologia , Modelos Teóricos , Animais , Movimento Celular/efeitos dos fármacos , Epinefrina/farmacologia , Leucócitos/imunologia , Camundongos , Monócitos/efeitos dos fármacos , Monócitos/fisiologia , Neoplasias Experimentais/imunologia , Condicionamento Físico AnimalRESUMO
Q(10) 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 Q(10) 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 Q(10) 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 Q(10), derived from a reference system composed from the metabolic rate and the Q(10). Such an equation has more than one unknown variable and thus is unsolvable. This problem disappears only if the Q(10) is assumed to be a known parameter. Therefore, it is concluded that typical Q(10) calculations are inappropriate for addressing questions about the regulatory control of a metabolism unless the Q(10) 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.