APPLICATION OF FAST EXPANSIONS TO OBTAIN EXACT SOLUTIONS TO A PROBLEM ON RECTANGULAR MEMBRANE DEFLECTION UNDER ALTERNATING LOAD

The problem of rectangular membrane deflection under alternating loads is solved in general terms by means of the method of fast expansions. The exact solution is represented by the finite expression borrowed from the theory of fast expansions as a sum of the boundary function and Fourier sine series with two Fourier coefficients taken into account. The obtained exact solution includes free parameters. Changing the values of these parameters, one can derive many new exact solutions. Obtaining of exact solutions to a problem of the rigidly fixed membrane under two types of loads (dome-shaped and sinusoidal) is shown as an example. Graphs of the dome-shaped and sinusoidal loads on the membrane and the curves of the corresponding deflections and stress components are presented in the paper. From the analysis of the exact solutions, it is obvious that only when a symmetrical alternating load is used, the membrane maximum deflection is attained in the center of the membrane, and the stresses reach the highest values in the middle of both long sides. In the case of a non-symmetrical load, the maximum stress occurs in the middle of either one of two long sides of the rectangular membrane, and the maximum deflection is found in the central region.

THE MOLLUSC IONIC CURRENTS CHANGES AFTER ADMINISTRATION OF N-PHENYLALKYL DERIVATIVES OF TAURINE

The transmembrane sodium, potassium and calcium ionic currents were studied after extracellular administration of N-phenylalkyl derivatives of taurine in concentrations 1, 10, 100 and 1000 mM. The method of intracellular dialysis with fixed membrane potential was used in model of isolated neurons of the mollusks Lymnaea stagnalis and Planorbarius corneus. The solutions containing 1 and 10 mM of the compounds studied did not change ionic channels activity in isolated neurons. Concentrations 100 and mM depressed reversibly all currents in the dose-dependent manner: taurine < TAU-02 < TAY-15 < TAU-60. The voltage-amplitude membrane characteristics as well as kinetics of the currents did not change.

COLLECTIVE BEHAVIORS OF SPIRAL WAVES IN THE NETWORKS OF HODGKIN-HUXLEY NEURONS IN PRESENCE OF CHANNEL NOISE

Collective behaviors of spiral waves in the networks of Hodgkin-Huxley neuron are investigated. A stable rotating spiral wave can be developed to occupy the quiescent areas in networks of neurons by selecting appropriate initial values for the variables in the networks of neurons. In our numerical studies, most neurons are quiescent and finite (few) numbers of neurons are selected with different values to form a spiral seed. In this way, neurons communicating are carried by propagating spiral wave to break through the quiescent domains (areas) in networks of neurons. The effect of membrane temperature on the formation of spiral wave is investigated by selecting different fixed membrane temperatures in the networks, and it is found that a spiral wave cannot be developed if the membrane temperature is close to a certain threshold. A quantitative factor of synchronization is defined to measure the statistical properties and collective behaviors of the spiral wave. And a distinct phase transition, which indicates the critical condition for spiral survival, is observed in the sudden changing point of the factors of synchronization curve vs. certain bifurcation parameter. Internal noise is introduced into ion channels (channel noise) with the Langevin method. It is found that a stable rotating spiral wave is developed and the spiral wave is robust to weak channel noise (the membrane patch is not small). The spiral wave can not grow up and the stable rotating spiral wave encounters instability in presence of strong channel noise. Coherence resonance-like behavior is observed in calculating the factors of synchronization in presence of channel noise.

Membrane Phosphatidylserine and Plasma Calcium Levels Switch Factor Xa From An Inactive Dimer to An Active Monomer.

Abstract 3180 Poster Board III-103 Factor Xa has a prominent role in amplifying both inflammation and coagulation cascades. In the coagulation cascade, its main role is catalyzing the proteolytic activation of prothrombin to thrombin. Efficient proteolysis is well known to require phosphatidylserine (PS)-containing membranes that are provided by platelets in vivo. PS, in the presence of Ca2+, triggers tight association of factor Xa with its cofactor, factor Va. PS also triggers tight association of factor Xa with factor Xa, at least in solution (Majumder R, Wang JF, and Lentz BR. Biophys. J. 2003, 84:1238-1251) to form an inactive factor Xa dimer (Chattopadhyay et al. Biophys. J. 96(3) pp. 974 – 986, 2009). We report here that PS-triggered factor Xa dimer formation is a sharp sigmoidal function of Ca2+ concentration and that this Ca2+ switch occurs just below plasma Ca2+ concentrations. We have determined the proteolytic activity of human factor Xa towards human prethrombin2 as a substrate both at fixed membrane concentration and increasing factor Xa concentration, and at fixed factor Xa concentration and increasing membrane concentration. Neither of these experiments showed the expected behavior of an increase in activity as factor Xa bound to membranes. Factor Xa activity actually decreased as low concentrations of PS-containing membranes were added, and increased only at higher membrane concentrations. At fixed membrane concentrations, the total factor Xa activity did not increase proportionally with factor Xa concentration. These observations showed that membranes actually inhibited factor Xa activity under conditions of high factor Xa or low membrane concentrations, suggesting the existence of inactive membrane-bound oligomers of factor Xa. The binding of factor Xa to PS-containing membranes also appeared to be tighter at low than at high membrane concentration. Because factor Xa forms dimers in solution (Majumder R, Wang JF, and Lentz BR. Biophys. J. 2003, 84:1238-1251), we attempted to explain these observations in terms of a model that takes into account dimerization of factor Xa after binding to a membrane. This dimer model successfully described all our data, with the parameters of best fit being kcat/KMdimer = 0 M-1s-1, kcat/KMmonomer = 9000 M-1s-1, kcat/KMsolution = 94 M-1s-1, and Kd,surfacedimer = ( 40±25) · 10-15 mol/(dm)2. This surface dimerization constant corresponds to a solution-phase Kddimer = 1 nM at 10 mM lipid concentration, nearly what we observed for formation of bovine factor Xa dimer in the presence of short-chain PS (20 nM; Majumder et al. Biophys. J. 2003, 84:1238-1251). As we observed for soluble-PS-induced dimer formation in solution, dimer formation on a membrane was Ca2+ dependent. Unlike in solution, factor Xa was activated by membrane binding below 1.5 mM Ca2+, but inactivated above this Ca2+ concentration. The transition of factor Xa from monomer to inactive dimer state on PS-containing membranes is a sensitive function of Ca2+ concentration. Just below the normal range of plasma Ca2+ concentration, addition of PS-containing membranes promotes factor Xa activity, while just above this level PS-containing membranes inhibit factor Xa. This suggests that Ca2+-dependent formation of inactive factor Xa dimers might have an important role in factor Xa activity during the initial phase of the blood coagulation process when generation of a small amount of thrombin in a short period of time activates platelets. Supported by USPHS grant HL072827. Disclosures No relevant conflicts of interest to declare.

A Ca2+ Switch Triggers Formation of Inactive Factor Xa Dimers on Phosphatidylserine-Containing Membranes.

Factor Xa has a prominent role in amplifying both inflammation and coagulation cascades. In the coagulation cascade, its main role is catalyzing the proteolytic activation of prothrombin to thrombin. Efficient proteolysis is well known to require phosphatidylserine (PS)-containing membranes that are provided by platelets in vivo. PS, in the presence of Ca2+, triggers tight association of factor Xa with its cofactor, factor Va. An interesting complication is that PS also triggers tight association of factor Xa with factor Xa, at least in solution (Majumder R, Wang JF, and Lentz BR. Biophys. J. 2003, 84:1238–1251), to form an inactive factor Xa dimer (Sen S, and Lentz BR, unpublished). In this work, we ask whether Ca2+ and PS also trigger formation of an inactive factor Xa dimer on a membrane and explore the possible physiological significance of this. We have determined the proteolytic activity of human factor Xa towards human prethrombin2 as a substrate both at fixed membrane concentration (increasing factor Xa concentration) and at fixed factor Xa concentration (increasing membrane concentration). Neither of these experiments showed the expected behavior of an increase in activity as factor Xa bound to membranes. The total factor Xa activity actually decreased as low concentrations of PS-containing membranes were added, and increased at higher membrane concentrations. At fixed membrane concentrations, the total factor Xa activity did not increase proportionally with factor Xa concentration. Both observations suggested the existence of membrane-bound and inactive multimeric forms of factor Xa. Because we have observed factor Xa to form dimers in solution (Majumder R, Wang JF, and Lentz BR. Biophys. J. 2003, 84:1238–1251), we tried to fit globally four such data sets to a model that takes into account dimerization of factor Xa after binding to a membrane. This dimer model successfully described all our data, with the parameters of best fit being kcat/KMdimer = 0 M−1s−1, kcat/KMmonomer = 430 M−1s−1, kcat/KMsolution = 38 M−1s−1, and Kd,surfacedimer = 4·10−12 mol/(dm)2. This surface dimerization constant corresponds to a solution-phase Kddimer = 10 nM at 100 μM lipid concentration, nearly what we observed for formation of bovine factor Xa dimer in the presence of short-chain PS (20 nM; Majumder R, Wang JF, and Lentz BR. Biophys. J. 2003, 84:1238–1251). Also consistent with the dimer hypothesis, we observed that the binding of factor Xa to PS-containing membranes appears to be tighter at low than at high membrane concentration. As we observed for soluble-PS-induced dimer formation in solution, dimer formation on a membrane was Ca2+ dependent. Unlike in solution, factor Xa was activated by membrane binding below 1.5 mM Ca2+, but inactivated above this Ca2+ concentration. This suggests that factor Xa activity may be regulated by Ca2+ concentrations close to plasma Ca2+ levels. We conclude that:factor Xa dimerizes on PS-containing membranes;, factor Xa dimer is inactive; and, the transition from monomer to dimer state depends critically on Ca2+ concentration.