Javier Segura

Monte Carlo Simulation of 3-D Buffered Ca2+ Diffusions in Neuroendocrine Cells

Buffered Ca(2+) diffusion in the cytosol of neuroendocrine cells is a plausible explanation for the slowness and latency in the secretion of hormones. We have developed a Monte Carlo simulation to treat the problem of 3-D diffusion and kinetic reactions of ions and buffers. The 3-D diffusion is modeled as a random walk process that follows the path of each ion and buffer molecule, combined locally with a stochastic treatment of the first-order kinetic reactions involved. Such modeling is able to predict [Ca(2+)] and buffer concentration time courses regardless of how low the calcium influx is, and it is therefore a convenient method for dealing with physiological calcium currents and concentrations. We study the effects of the diffusional and kinetic parameters of the model on the concentration time courses as well as on the local equilibrium of buffers with calcium. An in-mobile and fast endogenous buffer as described by, Biophys. J. 72:674-690) was able to reach local equilibrium with calcium; however, the exogenous buffers considered are displaced drastically from equilibrium at the start of the calcium pulse, particularly below the pores. The versatility of the method also allows the effect of different arrangements of calcium channels on submembrane gradients to be studied, including random distribution of calcium channels and channel clusters. The simulation shows how the particular distribution of channels or clusters can be of relevance for secretion in the case where the distribution of release granules is correlated with the channels or clusters.

Modeling Study of Exocytosis in Neuroendocrine Cells: Influence of the Geometrical Parameters

Exocytosis in neuroendocrine cells is a process triggered by Ca(2+). A Monte Carlo simulation of secretion has been developed which, together with the diffusion of calcium, buffered by endogenous and/or exogenously added chelators, also accounts for the dynamics of exocytosis for a pool of readily releasable vesicles. Different distributions of channels and vesicles (random or correlated) are studied. A local study of exocytosis is carried out by obtaining capacitance time courses for the different types of release-ready vesicle pools (correlated or not with Ca(2+) channels). Also, depending upon the kinetic constants for the exocytotic process, we study the levels of local Ca(2+) needed to trigger secretion. Our simulations show that a strong heterogeneity in the calcium concentrations at the different sites of exocytosis is a requirement for reproducing the experimentally observed biphasic response in chromaffin cells in situ (Voets, T., E. Neher, and T. Moser. 1999. Neuron. 23:607-615). Correlated nonuniform distributions of channels and vesicles and the existence of diffusion barriers are shown to quantitatively explain the experimental data on chromaffin cells in situ. The first description requires a deeply heterogeneous distribution, with vesicles attached to the channels or far from them, but never at middle distances. The second description is able to reproduce biphasic release even for uniformly (readily releasable) distributed vesicles. We quantify the degree of inhomogeneity in the distribution of vesicles and how porous the diffusion barriers should be to account for the observed biphasic response.

Evaluation of toroidal harmonics

Abstract Three algorithms to evaluate toroidal harmonics, i.e., Legendre functions of integral order and half-odd degree of the first and second kinds for real arguments larger than one, are presented. The first algorithm (DTORH1) allows the evaluation of the set { P n −1/2 m ( x ), Q n −1/2 m ( x )} for fixed (integer and positive) values of m and n =0,1,…, N . The algorithms DTORH2 and DTORH3 extend the method used in DTORH1 to obtain the set { P n −1/2 m ( x ), Q n −1/2 m ( x )} for m =0,…, M and n =0,1,…, N . The output of DTORH2 is equivalent to the result of the application of DTORH1 M times ( m =0,1,…, M ). However, due to the organization of the algorithm, DTORH2 is faster than DTORH1 when several orders and degrees are calculated. DTORH2 is better suited than DTORH3 when high orders and degrees are needed. On the other hand DTORH3, though more restrictive on the maximum evaluable degrees N, is even faster than DTORH2. Our tests of accuracy, show that the three codes achieve a precision of one part in 10 12 . We discuss the performance of our codes, their speed and their range of validity. The application of the algorithms to solve Laplaces and Poissons equations in toroidal coordinates is discussed and an explicit numerical example is shown.

The F-actin cortical network is a major factor influencing the organization of the secretory machinery in chromaffin cells

We have studied how the F-actin cytoskeleton is involved in establishing the heterogeneous intracellular Ca2+ levels ([Ca2+]i) and in the organization of the exocytotic machinery in cultured bovine chromaffin cells. Simultaneous confocal visualization of [Ca2+]i and transmitted light studies of the cytoskeleton showed that, following cell stimulation, the maximal signal from the Ca2+-sensitive fluorescent dye Fluo-3 was in the empty cytosolic spaces left by cytoskeletal cages. This was mostly due to the accumulation of the dye in spaces devoid of cytoskeletal components, as shown by the use of alternative Ca2+-insensitive fluorescent cytosolic markers. In addition to affecting the distribution of such compounds in the cytosol, the cytoskeleton influenced the location of L- and P-Q-type Ca2+ channel clusters, which were associated with the borders of cytoskeletal cages in resting and stimulated cells. Indeed, syntaxin-1 and synaptotagmin-1, which are components of the secretory machinery, were present in the same location. Furthermore, granule exocytosis took place at these sites, indicating that the organization of the F-actin cytoskeletal cortex shapes the preferential sites for secretion by associating the secretory machinery with preferential sites for Ca2+ entry. The influence of this cortical organization on the propagation of [Ca2+]i can be modelled, illustrating how it serves to define rapid exocytosis.

Algorithm 822: GIZ, HIZ: two Fortran 77 routines for the computation of complex Scorer functions

Two Fortran 77 routines for the evaluation of Airy functions of complex arguments Ai(z), Bi(z) and their first derivatives are presented. The routines are based on the use of Gaussian quadrature, Maclaurin series and asymptotic expansions. Comparison with a previous code by D. E. Amos [1986] is provided.

The Zeros of Special Functions from a Fixed Point Method

A scheme for the computation of the zeros of special functions and orthogonal polynomials is developed. We study the structure of the first order difference-differential equations (DDEs) satisfied by two fundamental sets of solutions of second order ODEs

A code to evaluate prolate and oblate spheroidal harmonics

y_n^{\prime\prime}(x)+A_{n}(x)y_n (x)=0

Interlacing of the zeros of contiguous hypergeometric functions

, n being the order of the solutions and An (x) a family of continuous functions. It is proved that, with a convenient normalization of the solutions,

Efficient and Accurate Algorithms for the Computation and Inversion of the Incomplete Gamma Function Ratios

T_{\pm1}(z)=z\pm \mbox{\rm sign}(d)\arctan(y_n (x(z))/y_{n\pm 1}(x(z)))

Evaluation of legendre functions of argument greater than one

are globally convergent iterations with fixed points