Calcium buffering and diffusion: on the resolution of an outstanding problem.
Explore the source record for details and available documents.
Animals↗
Biomedical subjects
J Sneyd
Publications and source records attributed to J Sneyd.
A model for the propagation of intercellular calcium waves.
In response to mechanical stimulation of a single cell, intercellular Ca2+ waves propagate through airway epithelial and glial cell cultures, providing a mechanism for intercellular communication. Experiments indicate that intercellular propagation of the Ca2+ wave is mediated by the movement of inositol 1,4,5-trisphosphate (IP3) through gap junctions. To explore the validity of this hypothesis, we have constructed and solved a system of partial differential equations that models the Ca2+ changes induced by the movement of IP3 between cells. The model is in good qualitative agreement with experimental data, including the behavior of the wave in the absence of extracellular Ca2+, the shape of the subsequent asynchronous Ca2+ oscillations, and the passage of a wave through a cell exhibiting Ca2+ oscillations. However, the concentration of IP3 that is required in each cell to propagate the wave may not be achieved by passive diffusion of IP3 through gap junctions from the stimulated cell. We therefore suggest that Ca(2+)-independent regenerative production of IP3 might be necessary for the propagation of intercellular Ca2+ waves.
Animals↗
Stress distributions in vascular aneurysms: factors affecting risk of aneurysm rupture.
Aneurysm rupture occurs when local wall stresses exceed the tensile strength of vascular tissues. Knowledge of vascular wall stresses, and insight into the factors that change wall stresses, will lead to a better understanding of how aneurysms grow and rupture. In this study, stress distributions in the walls of small aneurysms were calculated using finite element analysis (FEA), a numerical technique able to predict stress distributions with greater accuracy than the Law of Laplace. Stresses were calculated for an initial small aneurysm and compared to stresses produced by increasing the aneurysm diameter, decreasing the wall thickness, and changing the material properties of the aneurysm wall. FEA calculations indicate that wall stresses are generally greatest on the inner surface of an aneurysm, and decrease nonlinearly as the outer wall is approached. Maximum wall stresses occur along the region of greatest diameter, and circumferential stresses tend to be significantly greater than longitudinal stresses. Doubling the diameter of an aneurysm produced a twofold increase in the maximum wall stress. Decreasing the wall thickness by half also produced a doubling of the maximum wall stress. Changing material properties produced no appreciable change in wall stresses. However, weaker materials fail at lower stresses, thus halving material strength would be equivalent to doubling wall stresses. We conclude that the Law of Laplace is inaccurate in predicting the complicated stress distributions that exist in aneurysm walls, and that more sophisticated tools, such as FEA, will be needed to understand this complex phenomenon. We also conclude that proportional changes in the diameter, wall thickness, or aneurysm tissue strength have roughly equivalent effects on aneurysm growth and rupture.
Aneurysm↗
Calcium wave propagation by calcium-induced calcium release: an unusual excitable system.
We discuss in detail the behaviour of a model, proposed by Goldbeter et al. (1990. Proc. natn. Acad. Sci. 87, 1461-1465), for intracellular calcium wave propagation by calcium-induced calcium release, focusing our attention on excitability and the propagation of waves in one spatial dimension. The model with no diffusion behaves like a generic excitable system, and threshold behaviour, excitability and oscillations can be understood within this general framework. However, when diffusion is included, the model no longer behaves like a generic excitable system; the fast and slow variables are not distinct and previous results on excitable systems do not necessarily apply. We consider a piecewise linear simplification of the model, and construct travelling pulse and periodic plane wave solutions to the simplified model. The analogous behaviour in the full model is studied numerically. Goldbeter's model for calcium-induced calcium release is an excitable system of a type not previously studied in detail.
Animals↗
A single-pool model for intracellular calcium oscillations and waves in the Xenopus laevis oocyte.
We construct a minimal model of cytosolic free Ca2+ oscillations based on Ca2+ release via the inositol 1,4,5-trisphosphate (IP3) receptor/Ca2+ channel (IP3R) of a single intracellular Ca2+ pool. The model relies on experimental evidence that the cytosolic free calcium concentration ([Ca2+]c) modulates the IP3R in a biphasic manner, with Ca2+ release inhibited by low and high [Ca2+]c and facilitated by intermediate [Ca2+]c, and that channel inactivation occurs on a slower time scale than activation. The model produces [Ca2+]c oscillations at constant [IP3] and reproduces a number of crucial experiments. The two-dimensional spatial model with IP3 dynamics, cytosolic diffusion of IP3 (Dp = 300 microns 2 s-1), and cytosolic diffusion of Ca2+ (Dc = 20 microns 2 s-1) produces circular, planar, and spiral waves of Ca2+ with speeds of 7-15 microns.s-1, which annihilate upon collision. Increasing extracellular [Ca2+] influx increases wave speed and baseline [Ca2+]c. A [Ca2+]c-dependent Ca2+ diffusion coefficient does not alter the qualitative behavior of the model. An important model prediction is that channel inactivation must occur on a slower time scale than activation in order for waves to propagate. The model serves to capture the essential macroscopic mechanisms that are involved in the production of intracellular Ca2+ oscillations and traveling waves in the Xenopus laevis oocyte.
Animals↗
Two-dimensional model of calcium waves reproduces the patterns observed in Xenopus oocytes.
Biological excitability enables the rapid transmission of physiological signals over distance. Using confocal fluorescence microscopy, we previously reported circular, planar, and spiral waves of Ca2+ in Xenopus laevis oocytes that annihilated one another upon collision. We present experimental evidence that the excitable process underlying wave propagation depends on Ca2+ diffusion and does not require oscillations in inositol (1,4,5)trisphosphate (IP3) concentration. Extending an existing ordinary differential equation (ODE) model of Ca2+ oscillations to two spatial dimensions, we develop a partial differential equation (PDE) model of Ca2+ excitability. The model assumes that cytosolic Ca2+ couples neighboring Ca2+ release sites. This simple PDE model qualitatively reproduces our experimental observations.
Animals↗
Light adaptation in turtle cones. Testing and analysis of a model for phototransduction.
Light adaptation in cones was characterized by measuring the changes in temporal frequency responses to sinusoidal modulation of light around various mean levels spanning a range of four log units. We have shown previously that some aspects of cone adaptation behavior can be accounted for by a biochemical kinetic model for phototransduction in which adaptation is mediated largely by a sigmoidal dependence of guanylate cyclase activity on the concentration of free cytoplasmic Ca2+, ([Ca2+]i) (Sneyd and Tranchina, 1989). Here we extend the model by incorporating electrogenic Na+/K+ exchange, and the model is put to further tests by simulating experiments in the literature. It accounts for (a) speeding up of the impulse response, transition from monophasic to biphasic waveform, and improvement in contrast sensitivity with increasing background light level, I0; (b) linearity of the response to moderate modulations around I0; (c) shift of the intensity-response function (linear vs. log coordinates) with change in I0 (Normann and Perlman, 1979); the dark-adapted curve adheres closely to the Naka-Rushton equation; (d) steepening of the sensitivity vs. I0 function with [Ca2+]i fixed at its dark level, [Ca2+]i dark; (Matthews et al., 1988, 1990); (e) steepening of the steady-state intensity-response function when [Ca2+]i is held fixed at its dark level (Matthews et al., 1988; 1990); (f) shifting of a steep template saturation curve for normalized photocurrent vs. light-step intensity when the response is measured at fixed times and [Ca2+]i is held fixed at [Ca2+]i dark (Nakatani and Yau, 1988). Furthermore, the predicted dependence of guanylate cyclase activity on [Ca2+] closely matches a cooperative inhibition equation suggested by the experimental results of Koch and Stryer (1988) on cyclase activity in bovine rods. Finally, the model predicts that some changes in response kinetics with background light will still be present, even when [Ca2+]i is held fixed at [Ca2]i dark.
Animals↗
Phototransduction in cones: an inverse problem in enzyme kinetics.
Phototransduction is a process which links the absorption of photons by a rod or cone to the modulation of voltage across the cell membrane. An important feature of many vertebrate photoreceptors is a mechanism that adjusts the sensitivity and dynamics of the response to light according to the level of illumination. We construct a system of ordinary differential equations that models what are currently thought to be the important molecule mechanisms involved in phototransduction: this includes consideration of both intracellular enzyme kinetics and the properties of light-insensitive and light-sensitive conductances in the cone membrane. The system contains negative feedback whose functional form is determined by constraining the steady-state behaviour of the system. Despite the highly nonlinear nature of the system of ordinary differential equations, our methods permit us to derive an analytic expression for the first-order frequency response parametric in the steady-state value of only one dynamic variable, the light input. Various unknown kinetic parameters are found by fitting the model to experimental data on the first-order frequency response of cones measured at several mean light levels spanning a range of four log units. Good fits are obtained to the data, and the computed shape of the feedback function agrees qualitatively with recent experiment. Moreover, the model accounts for the dramatic speeding up of the response kinetics and the decrease in response gain with increasing light level.
Animals↗
A comparison of three models of the inositol trisphosphate receptor.
The inositol (1,4,5)-trisphosphate receptor (IPR) plays a crucial role in calcium dynamics in a wide range of cell types, and is often a central feature in quantitative models of calcium oscillations and waves. We compare three mathematical models of the IPR, fitting each of them to the same data set to determine ranges for the parameter values. Each of the fits indicates that fast activation of the receptor, followed by slow inactivation, is an important feature of the model, and also that the speed of inositol trisphosphate IP3 binding cannot necessarily be assumed to be faster than Ca2+ activation. In addition, the model which assumed saturating binding rates of Ca2+ to the IPR demonstrated the best fit. However, lack of convergence in the fitting procedure indicates that responses to step increases of Ca2+ and IP3 provide insufficient data to determine the parameters unambiguously in any of the models.
Animals↗