Abstract
Calcium ions act as messengers in a broad range of processes such as learning, apoptosis, and muscular movement. The transient profile and the temporal accumulation of calcium signals have been suggested as the two main characteristics in which calcium cues encode messages to be forwarded to downstream pathways. We address the analytical quantification of calcium temporal-accumulation in a long, thin section of a nonexcitable cell by solving a boundary value problem. In these expressions we note that the cytosolic Ca(2+) accumulation is independent of every intracellular calcium flux and depends on the Ca(2+) exchange across the membrane, cytosolic calcium diffusion, geometry of the cell, extracellular calcium perturbation, and initial concentrations. In particular, we analyse the time-integrated response of cytosolic calcium due to i) a localised initial concentration of cytosolic calcium and ii) transient extracellular perturbation of calcium. In these scenarios, we conclude that i) the range of calcium progression is confined to the vicinity of the initial concentration, thereby creating calcium microdomains; and ii) we observe a low-pass filtering effect in the response driven by extracellular Ca(2+) perturbations. Additionally, we note that our methodology can be used to analyse a broader range of stimuli and scenarios.
Highlights
CALCIUM ions (Ca2þ) are the most ubiquitous secondary messenger mediating a large number of cellular functions, such as cell growth and differentiation, membrane excitability, and cell death [1], [2]
We focused on the derivation of analytical formulae that describe the [Ca2þ]c accumulation in astrocytes; and further analysed them to determine its relationship with cellular processes
Ca2þ cues are of paramount relevance as they trigger a large variety of physiological phenomena, some of which may determine cellular fate
Summary
CALCIUM ions (Ca2þ) are the most ubiquitous secondary messenger mediating a large number of cellular functions, such as cell growth and differentiation, membrane excitability, and cell death [1], [2]. Some Ca2þ-triggered processes depend on the continuous presence of elevated cytosolic Ca2þ or just require certain Ca2þ load to trigger specific downstream mechanism [4], while other Ca2þ-dependent processes are regulated separately through distinct signalling pathways linked to specific routes/locations of Ca2þ To overcome this difficulty, in silico analyses have been useful as forecast tools or hypotheses test-beds to study the role of Ca2þ signalling in a wide variety of conditions and prominent diseases, such as ageing [8], cardiac diseases [9], or neurodegenerative disorders [10]. We base our study on the model in [21] and adopt biologically motivated assumptions, which allow us to rewrite the integral above as the analytical solution of a boundary value problem (BVP) We note that these conditions are mild and allow us to compute the [Ca2þ]c accumulation under the presence of nonlinearities representing different calcium fluxes in a thin and long nonexcitable cell. We refer the interested reader to [24], [25] for more details on general conditions for the computation of the integrated response in a class of nonlinear reactiondiffusion systems
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