Temperature responses of dark respiration in relation to leaf sugar concentration

Changes in leaf sugar concentrations are a possible mechanism of short‐term adaptation to temperature changes, with natural fluctuations in sugar concentrations in the field expected to modify the heat sensitivity of respiration. We studied temperature‐response curves of leaf dark respiration in the temperate tree Populus tremula (L.) in relation to leaf sugar concentration (1) under natural conditions or (2) leaves with artificially enhanced sugar concentration. Temperature‐response curves were obtained by increasing the leaf temperature at a rate of 1°C min^?1. We demonstrate that respiration, similarly to chlorophyll fluorescence, has a break‐point at high temperature, where respiration starts to increase with a faster rate. The average break‐point temperature (T_RD) was 48.6 ± 0.7°C at natural sugar concentration. Pulse‐chase experiments with ¹⁴CO₂ demonstrated that substrates of respiration were derived mainly from the products of starch degradation. Starch degradation exhibited a similar temperature‐response curve as respiration with a break‐point at high temperatures. Acceleration of starch breakdown may be one of the reasons for the observed high‐temperature rise in respiration. We also demonstrate that enhanced leaf sugar concentrations or enhanced osmotic potential may protect leaf cells from heat stress, i.e. higher sugar concentrations significantly modify the temperature‐response curve of respiration, abolishing the fast increase of respiration. Sugars or enhanced osmotic potential may non‐specifically protect respiratory membranes or may block the high‐temperature increase in starch degradation and consumption in respiratory processes, thus eliminating the break‐points in temperature curves of respiration in sugar‐fed leaves.     

Temperature dependence of monoamine-induced pulmonary respiration of mollusc Lymnaea stagnalis

Pulmonary respiration of molluscs (spontaneous and mediated by intracavital injection of monoamines) was studied at different environmental temperatures (5, 15, and 25 degrees C). It was established that monoamines (dopamine, serotonin, adrenalin) did not enlarge the temperature diapason, in which the respiratory behavior was realized. Microelectrode studies of spontaneous electrical activity of neurons from the respiratory network of Lymnaea stagnalis (RPeD1, VD4, cells of the Vi cluster) have shown that the respiratory program, both spontaneous and the monoamine-induced, is terminated in hypothermia. The indicated effects are suggested to be due to temperature dependence of the chemical, predominantly peptidergical, transmission of signal between neurons of the central pattern generator of respiratory pattern in Lymnaea.     

A theory of drug tolerance and dependence II: the mathematical model

The preceding paper presented a model of drug tolerance and dependence. The model assumes the development of tolerance to a repeatedly administered drug to be the result of a regulated adaptive process. The oral detection and analysis of exogenous substances is proposed to be the primary stimulus for the mechanism of drug tolerance. Anticipation and environmental cues are in the model considered secondary stimuli, becoming primary in dependence and addiction or when the drug administration bypasses the natural-oral-route, as is the case when drugs are administered intravenously. The model considers adaptation to the effect of a drug and adaptation to the interval between drug taking autonomous tolerance processes. Simulations with the mathematical model demonstrate the model's behaviour to be consistent with important characteristics of the development of tolerance to repeatedly administered drugs: the gradual decrease in drug effect when tolerance develops, the high sensitivity to small changes in drug dose, the rebound phenomenon and the large reactions following withdrawal in dependence. The present paper discusses the mathematical model in terms of its design. The model is a nonlinear, learning feedback system, fully satisfying control theoretical principles. It accepts any form of the stimulus-the drug intake-and describes how the physiological processes involved affect the distribution of the drug through the body and the stability of the regulation loop. The mathematical model verifies the proposed theory and provides a basis for the implementation of mathematical models of specific physiological processes.     

Quantitative dependence of mitochondrial oxidative phosphorylation on oxygen concentration: a mathematical model.

The model of Wilson and co-workers (2., 3., Arch. Biochem. Biophys. 182, 749–762) for the regulation of mitochondrial oxidative phosphorylation has been extended to include the dependence on oxygen tension. The derived rate expression correctly describes the observed dependence of cellular energy metabolism on oxygen tension, including the oxygen dependence at “normoxic” physiological values. Experimental evidence is presented that oxidative phosphorylation by suspensions of isolated rat liver mitochondria is also dependent on oxygen concentration up to values of at least 100 μM.     

Temperature dependence of two parameters in a photosynthesis model

The temperature dependence of the photosynthetic parameters V_cmax, the maximum catalytic rate of the enzyme Rubisco, and J_max, the maximum electron transport rate, were examined using published datasets. An Arrehenius equation, modified to account for decreases in each parameter at high temperatures, satisfactorily described the temperature response for both parameters. There was remarkable conformity in V_cmax and J_max between all plants at T_leaf < 25 °C, when each parameter was normalized by their respective values at 25 °C (V_cmax0 and J_max0), but showed a high degree of variability between and within species at T_leaf > 30 °C. For both normalized V_cmax and J_max, the maximum fractional error introduced by assuming a common temperature response function is < ± 0·1 for most plants and < ± 0·22 for all plants when T_leaf < 25 °C. Fractional errors are typically < ± 0·45 in the temperature range 25–30 °C, but very large errors occur when a common function is used to estimate the photosynthetic parameters at temperatures > 30 °C. The ratio J_max/V_cmax varies with temperature, but analysis of the ratio at T_leaf = 25 °C using the fitted mean temperature response functions results in J_max0/V_cmax0 = 2·00 ± 0·60 (SD, n = 43).     

A mathematical study of a two-regional population growth model

The paper provides a mathematical study of a model of urban dynamics, adjusting to an ecological model proposed by Lotka and Volterra. The model is a system of two first-order non-linear ordinary differential equations. The study proposed here completes the original proof by using the main tools such as a Lyapunov function.     

Allocation of carbon to growth, storage and respiration in the vegetative barley plant

Abstract. It is proposed that the growing plant can be divided into three compartments with reference to carbon: soluble, storage and structural. Experiments carried out at 10, 15, 20 and 30°C in the light followed changes in size of these compartments in barley plants 10–24 days old. The redistribution of ^I4C photo-assimilated by 10 day old plants was monitored simultaneously. The soluble and storage compartments are a higher percentage of plant weight at lower temperatures, and are turned over rapidly at all temperatures; they form the source of respired ¹⁴C. About 30% of the ¹⁴C fixed enters structural material; in the first 24 h after labelling, for each unit of ¹⁴C entering the structural compartment, between 0–9 (at 15°C) and 3.2 (at 30°C) units of ¹⁴C are lost by respiration. At 15°C in the dark, respiratory loss of ¹⁴C is initially from soluble and storage compartments; thereafter respiration of ^I4C occurs at the expense of structural material.     

Describing force-induced bone growth and adaptation by a mathematical model

This work proposes a mathematical model that qualitative describes the process of mechanically force-induced bone growth and adaptation. The mathematical model includes osteocytes as the key interfacing layer connecting tissue, cellular and molecular signaling levels. Specifically, in the presence of an increase in the mechanical stimuli, osteocytes respond by mechano-transduction releasing the local factors nitric oxide (NO) and prostaglandin E(2) (PGE(2)). These local factors act as the signaling recruitment signals for bone cells progenitors and influence the coupling activity among osteoblasts and osteoclasts during the process of bone remodeling. The model is in agreement with qualitative observations found in the literature concerning the process of bone adaptation and the cellular interactions during a local bone remodeling cycle induced by mechanical stimulation.     

Virtual glioblastoma: growth, migration and treatment in a three-dimensional mathematical model

Objectives:  Glioblastomas are aggressive primary brain cancers that are characterized by extensive infiltration into the brain and are highly resistant to treatment. Through mathematical modelling, we model the process of invasion and predict the relative importance of mechanisms contributing to malignant invasion. Clinically, we predict patterns of tumour recurrence following various modes of therapeutic intervention.
Materials and methods:  Our mathematical model uses a realistic three-dimensional brain geometry and considers migrating and proliferating cells as separate classes. Several mechanisms for infiltrative migration are considered. Methods are developed for simulating surgical resection, radiotherapy and chemotherapy.
Results:  The model provides clinically realistic predictions of tumour growth and recurrence following therapeutic intervention. Specific results include (i) invasiveness is governed largely by the ability of glioblastoma cells to degrade and migrate through the extracellular matrix and the ability of single migrating cells to form colonies; (ii) tumours originating deeper in the brain generally grow more quickly than those of superficial origin; (iii) upon surgery, the margins and geometry of resection significantly determine the extent and pattern of postoperative recurrence; (iv) radiotherapy works synergistically with greater resection margins to reduce recurrence; (v) simulations in both two- and three-dimensional geometries give qualitatively similar results; and (vi) in an actual clinical case comprising several surgical interventions, the model provides good qualitative agreement between the simulated and observed course of the disease.
Conclusions:  The model provides a useful initial framework by which biological mechanisms of invasion and efficacy of potential treatment regimens may be assessed.     

Analysis of a mathematical model for the growth of tumors

 In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary condition for the existence of a unique stationary solution with radius r=R ₀ (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that (i) lim inf _t→∞ s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that (ii) If c is sufficiently small then s(t)→R ₀ exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further, (iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then lim sup _t→∞ s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞. Received: 25 February 1998 / Revised version: 30 April 1998     

Plant population growth and competition in a light gradient: a mathematical model of canopy partitioning

Can a difference in the heights at which plants place their leaves, a pattern we call canopy partitioning, make it possible for two competing plant species to coexist? To find out, we examine a model of clonal plants living in a nonseasonal environment that relates the dynamical behavior and competitive abilities of plant populations to the structural and functional features of the plants that form them. This examination emphasizes whole plant performance in the vertical light gradient caused by self-shading. This first of three related papers formulates a prototype single species Canopy Structure Model from biological first principles and shows how all plant properties work together to determine population persistence and equilibrium abundance. Population persistence is favored, and equilibrium abundance is increased, by high irradiance, high maximum photosynthesis rate, rapid saturation of the photosynthetic response to increased irradiance, low tissue respiration rate, small amounts of stem and root tissue necessary to support the needs of leaves, and low density of leaf, stem, and root tissues. In particular, equilibrium abundance decreases as mean leaf height increases because of the increased cost of manufacturing and maintaining stem tissue. All conclusions arise from this formulation by straightforward analysis. The argument concludes by stating this formulation's straightforward extension, called a Canopy Partitioning Model, to two competing species.     

A mathematical model of tumour-induced capillary growth

The corneal limbal vessels of an animal host respond to the presence of a source of Tumour Angiogenesis Factor (TAF) implanted in the cornea by the formation of new capillaries which grow towards the source. This neovasculature can be easily seen and studied and this paper describes a mathematical model of some of the important features of the growth. The model includes the diffusion of TAF, the formation of sprouts from pre-existing vessels and models the movement of these sprouts to form new capillaries as a chemotactic response to the presence of TAF. Numerical results are produced for various values of the parameters which characterize the model and it is suggested that the model might form the framework for further theoretical work on related phenomena such as wound healing or to develop strategies for the investigation of anti-angiogenesis.     

A simplified mathematical model of tumor growth

A one-dimensional model of tumor tissue growth is presented in which the source of mitotic inhibitor is nonuniformly distributed within the tissue (in contrast to many earlier models). As a result, stable and unstable regimes of growth become significantly modified from the uniform-source case, indicating that the model, schematic though it is, is very sensitive to the type of source term assumed, and this has implications for experimental and theoretical comparisons in more realistic geometries.