Mathematical theory of biological periodicities: Formulation of then-body case

In a series of papers, L. Danziger and G. Elmergreen (Bull. Math. Biophysics,16, 15–21, 1954;18, 1–13, 1956;19, 9–18, 1957) showed that a non-linear biochemical interaction between the anterior pituary gland and the thyroid gland may result under certain conditions in sustained periodical oscillations of the rates of production and of the blood level of the thyrotropic and of the thyroid hormone. They treated the systems, however, as a homogeneous one. N. Rashevsky (Some Medical Aspects of Mathematical Biology, Springfield, Illinois: Charles C. Thomas, Publisher, 1965;Bull. Math. Biophysics,29, 395–401, 1967) generalized the above results by taking into account the histological structures of the two glands as well as the diffusion coefficients and permeabilities of cells involved. The present paper is the first step toward the theory of interaction of any numbern of glands or, more generally,n components. The differential equations which govern the behavior of such a system represent a system of2n ²+n non-linear first order ordinary equations and involve a total of 7 n ²+3n parameters of partly histological, partly biochemical nature. The requirements of the existence of sustained oscillations demand 4n ²+2n+2 inequalities between those 7n ²+3n parameters.     

Mathematical theory of biological periodicities II. Effect of active transport

A previous study (Bull. Math. Biophysics,30, 735–749) is generalized to the case of active transport, which acts together in general with ordinary diffusion. The basic results obtained are the same except for an additional important conclusion. In principle it is possible to obtain sustained oscillations even when the secretions of the different glands do not affect the rates of formation or decay of each other at all, but affect the “molecular pumps,” which are responsible for the active transports in various parts of the system. Thus no biochemical interactions need necessarily take place between then-metabolites to make sustained oscillations possible in principle. This is an addition to a previous finding (Bull. Math. Biophysics,30, 751–760) that due to effects of the secreted hormones on target organs, non-linearity of biochemical interactions is not needed for production of sustained oscillations.     

Mathematical model of the role of intercellular signalling in intercellular cooperation during tumorigenesis

Objectives: Intercellular cooperation has been hypothesized to enhance cell proliferation during cancer metastasis through autocrine signalling cascades and mathematical models can provide valuable insights into underlying mechanisms of metastatic tumorigenesis. Here, we present a model that incorporates signal‐stimulated cell proliferation, and investigate influences of diffusion‐driven heterogeneity in signal concentration on proliferation dynamics. Materials and methods: Our model incorporates signal production through both autocrine and paracrine pathways, and signal diffusion and loss for a metastasizing cell population at a host site. We use the signalling pathway of IL‐6 for illustration where this signalling species forms an intermediate complex with its receptor IL‐6R. This in turn forms a heterodimeric complex with transmembrane protein gp130, ultimately resulting in production of downstream signals. Cell population dynamics are taken to follow a modified logistic equation for which the rate term is dependent on local IL‐6 concentration. Results and conclusions: Our spatiotemporal model agrees closely with experimental results. The model is also able to predict two phenomena typical of metastatic tumorigenesis – host tissue preference and long periods of proliferation dormancy. It confirms that diffusivity of the signalling species in a host tissue plays a significant role during the process. Our results show that the proliferation–apoptosis balance is tipped in favour of the former for host sites that have relatively smaller signal diffusivities.     

Reactions of peroxynitrite with globin proteins and their possible physiological role

It is now widely accepted that, besides their well-established function in O(2) transport, hemoglobin and myoglobin also undergo several redox reactions aimed to scavenge toxic free radicals and reactive oxygen and nitrogen species. At least some of these reactions are believed to play an important physiological role in the defense against oxidative stress. This aspect is exemplified by the recently discovered neuroglobin, a globin expressed in the brain. Rather than being considerably involved in reversible O(2) binding, neuroglobin is likely to undergo redox reactions to protect neurons against oxidative and potentially pathogenic pathways, as those operating after episodes of tissue hypoxia or ischemia. A major part of the cellular damage occurring under such conditions has been ascribed to formation of peroxynitrite, that originates from the reaction between two biologically important free radicals, nitric oxide (NO ) and superoxide. Here we review the current knowledge of the reactions of different forms of hemoglobin, myoglobin, and neuroglobin with peroxynitrite and discuss their physiological role on the basis of measured rate constants and on the probability of occurrence of these reactions in vivo.     

Pig red blood cell hexokinase: Regulatory characteristics and possible physiological role

The regulatory properties of pig erythrocyte hexokinase III have been studied. Among mammalian erythrocyte hexokinases, the pig enzyme shows the highest affinity for glucose and a positive cooperative effect with n_H = 1.5 at all the MgATP concentrations studied (for 0.5 to 5 mm). Glucose at high concentrations is also an inhibitor of hexokinase III. Similarly, the apparent affinity constant for MgATP is independent of glucose concentration. Uncomplexed ATP and Mg are both competitive inhibitors with respect to MgATP. Glucose 6-phosphate, known as a stronger inhibitor of all mammalian erythrocyte hexokinases, is a poor inhibitor for the pig enzyme (K_i = 120 μm). Furthermore, this inhibition is not relieved by orthophosphate as with other mammalian red blood cell hexokinases. A variety of red blood cell-phosphorylated compounds were tested and found to be inhibitors of pig hexokinase III. Of these, glucose 1,6-diphosphate and 2,3-diphosphoglycerate displayed inhibition constants in the range of their intracellular concentrations. In an attempt to investigate the role of hexokinase type III in pig erythrocytes some metabolic properties of this cell have been studied. The adult pig erythrocyte is able to utilize 0.27 μmol of glucose/h/ml red blood cells (RBC) compared with values of 0.56–2.85 μmol/h/ml RBC for the other mammalian species. This reduced capacity to metabolize glucose results from a relatively poor ability of the cell membrane to transport glucose. In fact, all the glycolytic enzymes were present and a low intracellular glucose concentration was measured (0.5 mm against a plasma level of 5 mm). Furthermore, transport and utilization were concentration-dependent processes. Inosine, proposed as the major energy substrate of the pig erythrocyte, at physiological concentrations is not as efficient as glucose in maintaining reduced glutathione levels under oxidative stress. Furthermore, newborn pig erythrocytes (fully permeable to glucose) possess hexokinase type II as the predominant glucose-phosphorylating activity. This fact and the information derived from the study of the regulatory characteristics of hexokinase III and from metabolic studies on intact pig erythrocytes permit the hypothesis that the presence of this peculiar hexokinase isozyme (type III) enables the adult pig erythrocyte to metabolize low but appreciable amounts of glucose.     

Export of metabolites by the proteins of the DMT and RhtB families and its possible role in intercellular communication

The earlier published and new experimental data are summarized on the properties of the genes encoding the membrane proteins of the DMT family (RhtA (YbiF), EamA (YdeD), YijE, YddG, YedA, PecM, eukaryotic nucleotide sugar, triose phosphate/phosphate, and hexose phosphate transporters), the RhtB/LysE family (RhtB, RhtC, LeuE, YahN, EamB (YfiK), ArgO (YggA), CmaU), as well as some other families (YicM, YdhC, YdeAB, YdhE (NorE)). These proteins are involved in the export of amino acids, purines, and other metabolites from the cell. The expression of most of the genes encoding these proteins is not induced by the substrates they transport but is controlled by the global regulation systems, such as the Lrp protein, and activated by the signal compounds involved in the intracellular communication. The level of expression, assessed in experiments on translational fusion of the corresponding bacterial genes with the β-galactosidase gene, depends on the growth phase of the bacterial culture, composition of the medium, and some stress factors, such as pH, osmolarity or decreased aeration. The efflux of normal cell metabolites is assumed to be the natural function of these proteins. This function may play a role in density-dependent behavior of cell populations (quorum sensing). It may have been enhanced in the course of evolution via specialization of these proteins in the efflux of compounds derived from metabolic intermediates and adjusted to the role of transmitters.     

Export of metabolites by the proteins of the DMT and RhtB families and its possible role in intercellular communication

The earlier published and new experimental data are summarized on the properties of the genes encoding the membrane proteins of the DMT family (RhtA (YbiF), EamA (YdeD), YijE, YddG, YedA, PecM, eukaryotic nucleoside phosphate sugar and hexose phosphate transporters), the RhtB/LysE family (RhtB, RhtC, LeuE, YahN, EamB (YfiK), ArgO (YggA), CmaU), as well as some other families (YicM, YdhC, YdeAB, YdhE (NorE)). These proteins are involved in the export of amino acids, purines, and other metabolites from the cell. The expression of most of the genes encoding these proteins is not induced by the substrates they transport but is controlled by the global regulation systems, such as the Lrp protein, and activated by the signal compounds involved in the intracellular communication. The level of expression, assessed in experiments on translational fusion of the corresponding bacterial genes with the beta-galactosidase gene, depends on the growth phase of the bacterial culture, composition of the medium, and some stress factors, such as pH osmolarity or decreased aeration. The efflux of normal cell metabolites is assumed to be the natural function of these proteins. This function may play a role in density-dependent behavior of cell populations (quorum sensing). It may have been enhanced in the course of evolution via specialization of these proteins in the efflux of compounds derived from metabolic intermediates and adjusted to the role of transmitters.     

Slow exciton trapping in Photosystem II: A possible physiological role

Photosystem II, which has a primary photochemical charge separation time of about 300 ps, is the slowest trapping of all photosystems. On the basis of an analysis of data from the literature this is shown to be due to a number of partly independent factors: a shallow energy funnel in the antenna, an energetically shallow trap, exciton dynamics which are partly trap limited and a large antenna. It is argued that the first three of these properties of Photosystem II can be understood in terms of protective mechanisms against photoinhibition. These protective mechanisms, based on the generation of non photochemical quenching states mostly in the peripheral antenna, are able to decrease pheophytin reduction under conditions in which the primary quinone, Q_A, is already reduced, due to the slow trapping properties. The shallow antenna funnel is important in allowing quenching state-protective mechanisms in the peripheral antenna.Abbreviations chl chlorophyll - PS I Photosystem I - PS II Photosystem II - Q_A the primary quinone acceptor - RC reaction centre - RT room temperature     

A possible stress physiological role of abscisic acid conjugates in root-to-shoot signalling

Abscisic acid (ABA) conjugates, predominantly their glucose esters, have recently been shown to occur in the xylem sap of different plants. Under stress conditions, their concentration can rise substantially to levels that are higher than the concentration of free ABA. External ABA conjugates cannot penetrate apoplastic barriers in the root. They have to be hydrolysed by apoplastic enzymes in the root cortex. Liberated free ABA can then be redistributed to the root symplast and dragged directly across the endodermis to the stele. Endogenous ABA conjugates are formed in the cytosol of root cells, transported symplastically to the xylem parenchyma cells and released to the xylem vessels. The mechanism of release is unknown; it may include the action of ABC-transporters. Because of its extremely hydrophilic properties, ABA-GE is translocated in the xylem of the stem without any loss to the surrounding parenchyma. After arrival in the leaf apoplast, transporters for ABA-GE in the plasmalemma have to be postulated to redistribute the conjugates to the mesophyll cells. Additionally, apoplastic esterases can cleave the conjugate and release free ABA to the target cells and tissues. The activity of these esterases is increased when barley plants are subjected to salt stress.     

Formation of lactate dehydrogenase complexes with proteins and polyelectrolytes. A possible physiological role

The effect of polymers (proteins, polyaminoacids, polyethylenimine) on kinetic parameters of lactate dehydrogenase (LDH) from porcine skeletal muscle was studied. Activation of the enzyme which was partially due to the association of LDH dimers was observed. A hypothesis was proposed, according to which the contribution of dissociation of oligomeric enzymes in the regulation of their activity in vivo is negligible due to the equilibrium shift towards association in dissociable enzyme systems.     

Mechanosensitivity and intercellular communication in HOBIT osteoblastic cells: a possible role for gap junction hemichannels

Mechanically induced intercellular Ca2+ signalling was investigated in differentiated HOBIT osteoblastic cells. HOBIT cells express connexin43 clustered at the cell-to-cell boundary and display functional intercellular coupling assessed by intercellular transfer of Lucifer yellow. Mechanical stimulation of single cells, besides leading to an intracellular Ca2+ rise, induced a wave of increased Ca2+ that was radially propagated to surrounding cells. Treatment of cells with thapsigargin blocked mechanically induced signal propagation. Intercellular Ca2+ spreading was inhibited by 18alpha-glycyrrhetinic acid, demonstrating the involvement of gap junctions in signal propagation. Suramin and apyrase decreased the extent of wave propagation, suggesting that ATP-mediated paracrine stimulation contribute to cell-to-cell signalling. The functional expression of gap-junctional hemichannels was evidenced in experiments of Mn2+ quenching, extracellular dye uptake and intracellular Ca2+ release, activated by uptake of inositol 1,4,5-trisphosphate from the external medium. Gap-junctional hemichannels were activated by low extracellular Ca2+ concentrations and inhibited by 18alpha-glycyrrhetinic acid.     

Mathematical modelling of ciliary propulsion of an electrically-conducting Johnson-Segalman physiological fluid in a channel with slip

Bionic systems frequently feature electromagnetic pumping and offer significant advantages over conventional designs via intelligent bio-inspired properties. Complex wall features observed in nature also provide efficient mechanisms which can be utilized in biomimetic designs. The characteristics of biological fluids are frequently non-Newtonian in nature. In many natural systems super-hydrophobic slip is witnessed. Motivated by these phenomena, in this paper, we discussed a mathematical model for the cilia-generated propulsion of an electrically-conducting viscoelastic physiological fluid in a ciliated channel under the action of magnetic field. The rheological behavior of the fluid is simulated with the Johnson-Segalman constitutive model which allows internal wall slip. The regular or coordinated movement of the ciliated edges (which line the internal walls of the channel) is represented by a metachronal wave motion in the horizontal direction which generates a two-dimensional velocity profile. This mechanism is imposed by a periodic boundary condition which generates propulsion in the channel flow. Under the classical lubrication approximation, the boundary value problem is non-dimensionalized and solved analytically with a perturbation technique. The influence of the geometric, rheological (slip and Weissenberg number) and magnetic parameters on velocity, pressure gradient and the pressure rise (evaluated via the stream function in symbolic software) are presented graphically and interpreted at length.     

Mathematical models of eye movements in reading: a possible role for autonomous saccades

 An efficient method for the exact numerical simulation of semi-Markov processes is used to study minimal models of the control of eye movements in reading. When we read a text, typical sequences of fixations form a rather complicated trajectory – almost like a random walk. Mathematical models of eye movement control can account for this behavior using stochastic transition rules between few discrete internal states, which represent combinations of certain stages of lexical access and saccade programs. We show that experimentally observed fixation durations can be explained by residence-time-dependent transition probabilities. Stochastic processes with this property are known as semi-Markov processes. For our numerical simulations we use the minimal process method (Gillespie algorithm), which is an exact and efficient simulation algorithm for this class of stochastic processes. Within this mathematical framework, we study different forms of coupling between eye movements and shifts of covert attention in reading. Our model lends support to the existence of autonomous saccades, i.e., the hypothesis that initiations of saccades are not completely determined by lexical access processes. Received: 21 March 2000 / Accepted in revised form: 10 January 2001     

The possible role of ADP ribosylation in physiological regulation of sporulation in Streptomyces griseus.

The role of ADP ribosylation of proteins in the physiological regulation of sporulation in Streptomyces griseus was studied. We report here that both the activity of NAD+: arginine ADP-ribosyltransferase (ADPRT) and the pattern of ADP-ribosylated proteins showed characteristic changes during the life cycle in S. griseus 2682. Analysis off ADP-ribosylated proteins revealed that in a nonsporulating mutant of the parental wild-type (wt) strain (Bld7 mutant), both the activity of ADPRT and the pattern of ADP-ribosylated proteins were different from those of the parental strain. Addition of 3-aminobenzamide (3AB), the most potent inhibitor of ADPRT, inhibited sporulation of S. griseus 2682 and the A-factor (AF)-induced sporulation of S. griseus Bld7, but in both cases the inhibitory effect of 3AB was strictly age-dependent. Using [alpha-32P]GTP, we have demonstrated the presence of GTP-binding proteins in purified cell membranes of S. griseus 2682 and S. griseus Bld7. The same GTP-binding proteins were observed in Bld7 and the wt. AF stimulated the basal GTPase activity of cell membranes of S. griseus 2682 in a concentration-dependent manner, suggesting that GTP-binding proteins might be involved in the AF-induced sporulation process.