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Global existence and regularity results are provided for weakly coupled first order hyperbolic systems modeling the propagation of the Feline Leukemia Virus (FeLV), a retrovirus of domestic cats (Felis catus). In a simple example we find a threshold parameter yielding endemic stationary states.
We used a simple experimental approach to clarify some contradictory predictions of the collision coupling and equilibrium models (e.g. ternary complex, two-state ternary complex or quinternary complex), which describe G-protein-mediated beta-adrenergic receptor signalling in essentially different manners. Analysis of the steady-state coupling of beta-adrenoceptors to adenylate cyclase in turkey erythrocyte membranes showed that: (1) in the absence of an agonist, Gpp(NH)p (a hydrolysis-resistant analogue of GTP) can activate adenylate cyclase very slowly; (2) this activity reaches a steady state in approx. 5 h, the extent of activity depending on the concentration of the nucleotide; (3) isoprenaline-activated steady-state adenylate cyclase can be inactivated by propranolol (a competitive antagonist that relaxes the receptor activation), in the presence of Gpp(NH)p (which provides a virtual absence of GTPase) and millimolar concentrations of Mg2+ (the rate of this inactivation is relatively fast); (4) increasing the concentration of Gpp(NH)p can saturate the steady-state activity of adenylate cyclase. The saturated enzyme activity was lower than that induced by isoprenaline under the same conditions. This additional agonist-induced activation was reversible. In the light of these results, we conclude that agonist can also activate the guanine nucleotide-saturated system in the absence of GTPase by a mechanism other than guanine nucleotide exchange. We explain these phenomena in the framework of a quinternary complex model as an agonist-induced and receptor-mediated dissociation of guanine nucleotide-saturated residual heterotrimer, the equilibrium concentration of which is not necessarily zero. These results, which suggest a continuous interaction between receptor and G-protein, can hardly be accommodated by the collision coupling model that was originally suggested for the present experimental system and then applied to many other G-protein systems. Therefore we attempt to unify the equilibrium and collision coupling approaches to provide a consistent theoretical basis for the G-protein-mediated beta-adrenergic receptor signalling in turkey erythrocyte membranes.
An electrocardiogram taken from a 29-year-old man with old myocardial infarction is presented as an exemplary case of ventricular extrasystoles with fixed coupling. To explain the mechanism of ventricular extrasystoles with fixed coupling, a theoretical model is derived from the concept of longitudinal dissociation in the reentrant pathway. In the model, functional longitudinal dissociation divides the reentrant pathway into dual pathways F and S. When a sinus impulse is blocked in pathway F and passes only through pathway S, it becomes a manifest reentrant extrasystole because of marked conduction delay in pathway S. When the sinus rate does not exceed a certain value, such an impulse always becomes a manifest extrasystole with fixed coupling. Part of the impulse passing through pathway S enters pathway. F retrogradely. In some cases, thereafter, it reenters pathway S and initiates ventricular reentrant tachycardia. When, on the other hand, a sinus impulse passes through both of pathways F and S, it becomes a concealed reentrant extrasystole because of insufficient conduction delay in the pathways.
Two samples of committed gay and lesbian cohabiting couples and two samples of married couples (couples in which the woman presented the conflict issue to the man, and couples in which the man presented the conflict issue to the woman) engaged in three conversations: (1) an events of the day conversation (after being apart for at least 8 hours), (2) a conflict resolution conversation, and (3) a pleasant topic conversation. The observational data were coded with a system that categorized specific affects displayed. Data were weighted and two time-series created, one for the husband and one of the wife. The time series were modeled with nonlinear difference equations (Cook et al., 1995), and parameters were estimated that indexed uninfluenced steady state, influenced steady state, emotional inertia, repair effectiveness and threshold, and the power of positive and negative affect of one partner to affect the other partner.
A mathematical model of an absorbing leaky epithelium is developed for analysis of solute coupled water transport. The non-charged driving solute diffuses into cells and is pumped from cells into the lateral intercellular space (lis). All membranes contain water channels with the solute passing those of tight junction and interspace basement membrane by convection-diffusion. With solute permeability of paracellular pathway large relative to paracellular water flow, the paracellular flux ratio of the solute (influx/outflux) is small (2-4) in agreement with experiments. The virtual solute concentration of fluid emerging from lis is then significantly larger than the concentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emerging downstream lis is taken up by cells through the serosal membrane and pumped back into lis, i.e., the solute would have to be recirculated. With input variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Ussing, J. Membr. Biol. 168:241-251), computations predict that 60-80% of the pumped flux stems from serosal bath in agreement with the experimental estimate of the recirculation flux. Robust solutions are obtained with realistic concentrations and pressures of lis, and with the following features. Rate of fluid absorption is governed by the solute permeability of mucosal membrane. Maximum fluid flow is governed by density of pumps on lis-membranes. Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is accomplished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent drag occurs when back flux of water through cells exceeds inward water flux between cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water, i.e., the model generates pseudo-solvent drag. The associated flux-ratio equation is derived.
Gliomas can display marked changes in the concentrations of energy metabolism molecules such as creatine (Cr), phosphocreatine (PCr) and lactate, as measured using magnetic resonance spectroscopy (MRS). Moreover, the BOLD (blood oxygen level dependent) contrast enhancement in functional magnetic resonance imaging (fMRI) can be reduced or missing within or near gliomas, while neural activity is not significantly reduced (so-called neurovascular decoupling), so that the location of functionally eloquent areas using fMRI can be erroneous. In this paper, we adapt a previously developed model of the coupling between neural activation, energy metabolism and hemodynamics, by including the venous dilatation "Balloon model" of Buxton and Frank. We show that decreasing the cerebral blood flow (CBF) baseline value, or the CBF increase fraction, results in a decrease of the BOLD signal and an increase of the lactate peak during a sustained activation. Baseline lactate and PCr levels are not significantly affected by CBF baseline reduction, but are altered even by a moderate decrease of mitochondrial respiration. Decreasing the total Cr and PCr concentration reduces the BOLD signal after the initial overshoot. In conclusion, we suggest that the coupled use of BOLD fMRI and MRS could contribute to a better understanding of the neurovascular and metabolic decoupling in gliomas.
The superfamily of G-protein-coupled receptors (GPCRs) could be subclassified into 7 families (A, B, large N-terminal family B-7 transmembrane helix, C, Frizzled/Smoothened, taste 2, and vomeronasal 1 receptors) among mammalian species. Cloning and functional studies of GPCRs have revealed that the superfamily of GPCRs comprises receptors for chemically diverse native ligands including (1) endogenous compounds like amines, peptides, and Wnt proteins (i.e., secreted proteins activating Frizzled receptors); (2) endogenous cell surface adhesion molecules; and (3) photons and exogenous compounds like odorants. The combined use of site-directed mutagenesis and molecular modeling approaches have provided detailed insight into molecular mechanisms of ligand binding, receptor folding, receptor activation, G-protein coupling, and regulation of GPCRs. The vast majority of family A, B, C, vomeronasal 1, and taste 2 receptors are able to transduce signals into cells through G-protein coupling. However, G-protein-independent signaling mechanisms have also been reported for many GPCRs. Specific interaction motifs in the intracellular parts of these receptors allow them to interact with scaffold proteins. Protein engineering techniques have provided information on molecular mechanisms of GPCR-accessory protein, GPCR-GPCR, and GPCR-scaffold protein interactions. Site-directed mutagenesis and molecular dynamics simulations have revealed that the inactive state conformations are stabilized by specific interhelical and intrahelical salt bridge interactions and hydrophobic-type interactions. Constitutively activating mutations or agonist binding disrupts such constraining interactions leading to receptor conformations that associates with and activate G-proteins.
It is assumed that certain drug receptors are so coupled with certain physiological receptors that stimulation of either receptor increases the sensitivity of the other. If the drug receptor suffers tolerance (i.e. slow desensitization) and if insensitivity of the drug receptor also makes the physiological receptor insensitive, then tolerance must be responsible for a physiological deficiency. This may be remedied by increased drug administration which will raise the sensitivity of the remaining physiological receptors so that a normal or near-normal physiological situation is achieved. Thus the organism is not only tolerant to the drug but also dependent on it. If such theoretical considerations apply to opiate receptors (as drug receptors) and to catecholamine receptors (as physiological receptors), then the theory predicts that acute morphine administration increases the sensitivity of dopamine receptors, that sympathetic stimulation decreases pain sensitivity, that opioid tolerance provokes increased catecholamine activity, that alpha-receptor stimulants attenuate and alpha-receptor antagonists exacerbate morphine abstinence, and that catecholaminergic inhibition results in increased morphine toxicity. All of these predictions have been verified experimentally.
The dependence of ATP-synthesis and mitochondria respiration rates on membrane potential was analyzed in frames of proton-chemical hypothesis of oxidative phosphorylation. The mathematical and electrical models of the unit of energy coupling are proposed. Computer analysis of the mathematical model allowed to obtain the theoretical dependence of the rates of ATP synthesis and of the respiration on the membrane potential. Both of all are in good qualitative agreement with experimental data, contradicting chemiosmotic hypothesis.
It is proven that any model of localized protonmotive energy coupling that relies upon properties of a homogeneous surface phase must, when operated in the steady state, lead to bulk phase electrochemical potentials for protons that are as large as those required by the delocalized chemiosmotic theory. To obtain models consistent with experiments supporting localized energy coupling requires some kind of surface heterogeneity for the proton conducting pathways. Two general classes of heterogeneous surface models are mentioned. One class involves phase-separated lipid domains. The second class involves hydrogen-bonded chains in proteins that traverse the membrane laterally.
We propose a model of the human circadian system. The sleep-wake and body temperature rhythms are assumed to be driven by a pair of coupled nonlinear oscillators described by phase variables alone. The novel aspect of the model is that its equations may be solved analytically. Computer simulations are used to test the model against sleep-wake data pooled from 15 studies of subjects living for weeks in unscheduled, time-free environments. On these tests the model performs about as well as the existing models, although its mathematical structure is far simpler.
A quantitative model is presented of diffusion mediated coupling of adenylate cyclase to multivalent plasma membrane receptors which accounts for a wide range of phenomena including non linear occupation-activation plots with either positive or negative second derivatives, spare receptors, silent receptors, and negative and positive binding cooperativity. A non linear least square fit of the predicted equation for cyclase activation to available data predicts translational diffusion coefficients in the range of (10(-10) - 10(-11))cm2/s.
The initiation of a reentrant circuit requires a zone of slow conduction and a zone of unidirectional block. This study used computer model conditions under which partial coupling between segments of cardiac Purkinje tissue resulted in unidirectional block. The structure used was one-dimensional and divided into three segments: a middle segment of variable length coupled to two long (semi-infinite in concept) segments. The DiFrancesco-Noble equations represented the ionic currents of the membrane. The results show that the possibility of unidirectional block depends on the size of the middle segment and the coupling resistances between the segments. No combination of coupling resistances allowed unidirectional block for middle segments with a length of two space constants (4 mm) or longer. Unidirectional block occurred for many combinations of coupling resistances as the length of the middle segment decreased to around half a space constant (1 mm). The number of length combinations that caused unidirectional block decreased again as segment length further decreased. These results provide a possible mechanism of unidirectional block for situations where islands of viable tissue are connected through nonviable tissue, such as in a healed myocardial infarction.
Coherence resonance in a coupled excitable system is studied, through both a computer simulation and a circuit experiment, using a piecewise linear version of the FitzHugh-Nagumo model. White noise is added to the first element and spikes are accordingly generated and transmitted to the second element. The mean, standard deviation, and coefficient of variation of the interspike intervals in the second element have multiple peaks as the noise strengthens, when the coupling strength is small. This results from the phase locking to the spikes that the noise generates.
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Couple and family treatment data present particular challenges to statistical analyses. Partners and family members tend to be more similar to one another than to other individuals, which raises interesting possibilities in the data analysis but also causes significant problems with classical, statistical methods. The present article presents multilevel models (also called hierarchical linear models, mixed-effects models, or random coefficient models) as a flexible analytic approach to couple and family longitudinal data. The article reviews basic properties of multilevel models but focuses primarily on 3 important extensions: missing data, power and sample size, and alternative representations of couple data. Information is presented as a tutorial, with a Web appendix providing datasets with SPSS and R code to reproduce the examples.
A global kinetic analysis is presented of a model of an enzyme autocatalytic process, to which a reaction is coupled, in which the enzyme acts upon one of its substrates. The kinetic equations of both the transient phase and the steady state are derived for this mechanism. In addition, we determine the corresponding kinetic equations for several particular cases which are characterized by certain relations between the rate constants. Finally, a kinetic data analysis is proposed for one of these particular cases. It can easily be extended to any of the other cases.