A quantitative model for linking Na+/Ca2+ exchanger to SERCA during refilling of the sarcoplasmic reticulum to sustain [Ca2+] oscillations in vascular smooth muscle

We have developed a quantitative model for the creation of cytoplasmic Ca²⁺ gradients near the inner surface of the plasma membrane (PM). In particular we simulated the refilling of the sarcoplasmic reticulum (SR) via PM–SR junctions during asynchronous [Ca²⁺]_i oscillations in smooth muscle cells of the rabbit inferior vena cava. We have combined confocal microscopy data on the [Ca²⁺]_i oscillations, force transduction data from cell contraction studies and electron microscopic images to build a basis for computational simulations that model the transport of calcium ions from Na⁺/Ca²⁺ exchangers (NCX) on the PM to sarcoplasmic/endoplasmic reticulum Ca²⁺ ATPase (SERCA) pumps on the SR as a three-dimensional random walk through the PM–SR junctional cytoplasmic spaces. Electron microscopic ultrastructural images of the smooth muscle cells were elaborated with software algorithms to produce a very clear and dimensionally accurate picture of the PM–SR junctions. From this study, we conclude that it is plausible and possible for enough Ca²⁺ to pass through the PM–SR junctions to replete the SR during the regenerative Ca²⁺ release, which underlies agonist induced asynchronous Ca²⁺ oscillations in vascular smooth muscle.     

Sensitivity and control analysis of periodically forced reaction networks using the Green's function method

A general sensitivity and control analysis of periodically forced reaction networks with respect to small perturbations in arbitrary network parameters is presented. A well-known property of sensitivity coefficients for periodic processes in dynamical systems is that the coefficients generally become unbounded as time tends to infinity. To circumvent this conceptual obstacle, a relative time or phase variable is introduced so that the periodic sensitivity coefficients can be calculated. By employing the Green's function method, the sensitivity coefficients can be defined using integral control operators that relate small perturbations in the network's parameters and forcing frequency to variations in the metabolite concentrations and reaction fluxes. The properties of such operators do not depend on a particular parameter perturbation and are described by the summation and connectivity relationships within a control-matrix operator equation. The aim of this paper is to derive such a general control-matrix operator equation for periodically forced reaction networks, including metabolic pathways. To illustrate the general method, the two limiting cases of high and low forcing frequency are considered. We also discuss a practically important case where enzyme activities and forcing frequency are modulated simultaneously. We demonstrate the developed framework by calculating the sensitivity and control coefficients for a simple two reaction pathway where enzyme activities enter reaction rates linearly and specifically.     

T cell development in the thymus: from periodic seeding to constant output

T cell development occurs in the thymus throughout life. Recent experimental findings show that the seeding of the thymus by multi-potent stem cells from the bone marrow is periodic rather than continuous, as previously assumed. However it is well known that the output rate of cells from the thymus is relatively constant. A quantitative model is used to verify the current hypotheses regarding T cell development in the steady state mouse thymus. The results show that the thymus could be at a periodic steady state with out-of-phase thymocyte populations. Experiments to examine possible periodic fluctuations in the thymus are proposed and methods for further analysis are outlined.     

Sustained oscillations via coherence resonance in SIR

Sustained oscillations in a stochastic SIR model are studied using a new multiple scale analysis. It captures the interaction of the deterministic and stochastic elements together with the separation of time scales inherent in the appearance of these dynamics. The nearly regular fluctuations in the infected and susceptible populations are described via an explicit construction of a stochastic amplitude equation. The agreement between the power spectral densities of the full model and the approximation verifies that coherence resonance is driving the behavior. The validity criteria for this asymptotic approximation give explicit expressions for the parameter ranges in which one expects to observe this phenomenon.     

The vicissitudes of the pacemaker current <Emphasis Type="Italic">I</Emphasis><Subscript>Kdd</Subscript> of cardiac purkinje fibers

Summary The mechanisms underlying the pacemaker current in cardiac tissues is not agreed upon. The pacemaker potential in Purkinje fibers has been attributed to the decay of the potassium current I _Kdd. An alternative proposal is that the hyperpolarization-activated current I _f underlies the pacemaker potential in all cardiac pacemakers. The aim of this review is to retrace the experimental development related to the pacemaker mechanism in Purkinje fibers with reference to findings about the pacemaker mechanism in the SAN as warranted. Experimental data and their interpretation are critically reviewed. Major findings were attributed to K⁺ depletion in narrow extracellular spaces which would result in a time dependent decay of the inward rectifier current I _K1. In turn, this decay would be responsible for a “fake” reversal of the pacemaker current. In order to avoid such a postulated depletion, Ba²⁺ was used to block the decay of I _K1. In the presence of Ba²⁺ the time-dependent current no longer reversed and instead increased with time and more so at potentials as negative as −120 mV. In this regard, the distinct possibility needs to be considered that Ba²⁺ had blocked I _Kdd (and not only I _K1). That indeed this was the case was demonstrated by studying single Purkinje cells in the absence and in the presence of Ba²⁺. In the absence of Ba²⁺, I _Kdd was present in the pacemaker potential range and reversed at E _K. In the presence of Ba²⁺, I _Kdd was blocked and I _f appeared at potentials negative to the pacemaker range. The pacemaker potential behaves in a manner consistent with the underlying I _Kdd but not with I _f. The fact that I _f is activated on hyperpolarization at potential negative to the pacemaker range makes it suitable as a safety factor to prevent the inhibitory action of more negative potentials on pacemaker discharge. It is concluded that the large body of evidence reviewed proves the pacemaker role of I _Kdd (but not of I _f) in Purkinje fibers.     

Two guard cell mitogen‐activated protein kinases,MPK9 and MPK12, function in methyl jasmonate‐induced stomatal closure in Arabidopsis thaliana

Methyl jasmonate (MeJA) and abscisic acid (ABA) signalling cascades share several signalling components in guard cells. We previously showed that two guard cell‐preferential mitogen‐activated protein kinases (MAPKs), MPK9 and MPK12, positively regulate ABA signalling in Arabidopsis thaliana. In this study, we examined whether these two MAP kinases function in MeJA signalling using genetic mutants for MPK9 and MPK12 combined with a pharmacological approach. MeJA induced stomatal closure in mpk9‐1 and mpk12‐1 single mutants as well as wild‐type plants, but not in mpk9‐1 mpk12‐1 double mutants. Consistently, the MAPKK inhibitor PD98059 inhibited the MeJA‐induced stomatal closure in wild‐type plants. MeJA elicited reactive oxygen species (ROS) production and cytosolic alkalisation in guard cells of the mpk9‐1, mpk12‐1 and mpk9‐1 mpk12‐1 mutants, as well in wild‐type plants. Furthermore, MeJA triggered elevation of cytosolic Ca²⁺ concentration ([Ca²⁺]_cyt) in the mpk9‐1 mpk12‐1 double mutant as well as wild‐type plants. Activation of S‐type anion channels by MeJA was impaired in mpk9‐1 mpk12‐1. Together, these results indicate that MPK9 and MPK12 function upstream of S‐type anion channel activation and downstream of ROS production, cytosolic alkalisation and [Ca²⁺]_cyt elevation in guard cell MeJA signalling, suggesting that MPK9 and MPK12 are key regulators mediating both ABA and MeJA signalling in guard cells.     

无创性颈动脉瞬时减速度波强测定评价左心室舒张功能的研究

目的：探讨无创检测心功能的指标—颈动脉瞬时减速度波强（W2）评价左心室舒张功能的价值。方法：测量40例高血压病患者和43例健康对照者的左、右侧颈总动脉W2,组织多普勒测定二尖瓣环运动速度和血清脑利钠肽前体（N-terminal probrain natriuretic peptide,NT-proBNP）,分析W2与各参数间的相关性。结果：①高血压组W2低于对照组,以左侧明显（1126±996vs1690±1126 mmHg.m/s3,P〈0.01）;②高血压组与对照组比较：E/Em（二尖瓣舒张早期峰值速度/二尖瓣环舒张早期纵向运动峰值速度）增大（9.37±3.32vs7.39±1.83,P〈0.01）,NT-proB-NP升高（94.6±48.5vs45.2±13.8,P〈0.01）;③相关性分析：W2与E/Em负相关（r=-0.46,P〈0.05）,与NT-proBNP负相关（r=-0.21,P〈0.05）。结论：无创性评价血流动力学的新技术指标W2是反映早期左室舒张功能受损的敏感指标。     

Transient oscillations induced by delayed growth response in the chemostat

In this paper, in order to try to account for the transient oscillations observed in chemostat experiments, we consider a model of single species growth in a chemostat that involves delayed growth response. The time delay models the lag involved in the nutrient conversion process. Both monotone response functions and nonmonotone response functions are considered. The nonmonotone response function models the inhibitory effects of growth response of certain nutrients when concentrations are too high. By applying local and global Hopf bifurcation theorems, we prove that the model has unstable periodic solutions that bifurcate from unstable nonnegative equilibria as the parameter measuring the delay passes through certain critical values and that these local periodic solutions can persist, even if the delay parameter moves far from the critical (local) bifurcation values.When there are two positive equilibria, then positive periodic solutions can exist. When there is a unique positive equilibrium, the model does not have positive periodic oscillations and the unique positive equilibrium is globally asymptotically stable. However, the model can have periodic solutions that change sign. Although these solutions are not biologically meaningful, provided the initial data starts close enough to the unstable manifold of one of these periodic solutions they may still help to account for the transient oscillations that have been frequently observed in chemostat experiments. Numerical simulations are provided to illustrate that the model has varying degrees of transient oscillatory behaviour that can be controlled by the choice of the initial data.Mathematics Subject Classification: 34D20, 34K20, 92D25Research was partially supported by NSERC of Canada.This work was partly done while this author was a postdoc at McMaster.     

Yeast glycolytic oscillations that are not controlled by a single oscillophore: a new definition of oscillophore strength

Biochemical oscillations, such as glycolytic oscillations, are often believed to be caused by a single so-called ‘oscillophore’. The main characteristics of yeast glycolytic oscillations, such as frequency and amplitude, are however controlled by several enzymes. In this paper, we develop a method to quantify to which extent any enzyme determines the occurrence of oscillations. Principles extrapolated from metabolic control analysis are applied to calculate the control exerted by individual enzymes on the real and imaginary parts of the eigenvalues of the Jacobian matrix. We propose that the control exerted by an enzyme on the real part of the smallest eigenvalue, in terms of absolute value, quantifies to which extent that enzyme contributes to the emergence of instability. Likewise the control exerted by an enzyme on the imaginary part of complex eigenvalues may serve to quantify the extent to which that enzyme contributes to the tendency of the system to oscillate. The method was applied both to a core model and to a realistic model of yeast glycolytic oscillations. Both the control over stability and the control over oscillatory tendency were distributed among several enzymes, of which glucose transport, pyruvate decarboxylase and ATP utilization were the most important. The distributions of control were different for stability and oscillatory tendency, showing that control of instability does not imply control of oscillatory tendency nor vice versa. The control coefficients summed up to 1, suggesting the existence of a new summation theorem. These results constitute proof that glycolytic oscillations in yeast are not caused by a single oscillophore and provide a new, subtle, definition for the oscillophore strength of an enzyme.