Extension of Rapid Buffering Approximation to Ca2+ Buffers with Two Binding Sites

Abstract

Fundamental cell processes such as synaptic neurotransmitter release, endocrine hormone secretion, and myocyte contraction are controlled by highly localized calcium (Ca2+) signals resulting from brief openings of trans-membrane Ca2+ channels. On short temporal and spatial scales, the corresponding local Ca2+ nanodomains formed in the vicinity of a single or several open Ca2+ channels can be effectively approximated by quasi-stationary solutions. The rapid buffering approximation (RBA) is one of the most powerful of such approximations, and is based on the assumption of instantaneous equilibration of the bimolecular Ca2+ buffering reaction, combined with the conservation condition for the total Ca2+ and buffer molecule numbers. Previously, RBA has been generalized to an arbitrary arrangement of Ca2+ channels on a flat membrane, in the presence of any number of simple Ca2+ buffers with one-to-one Ca2+ binding stoichiometry. However, many biological buffers have multiple binding sites. For example, buffers and sensors phylogenetically related to calmodulin consist of two Ca2+-binding domains (lobes), with each domain binding two Ca2+ ions in a cooperative manner. Here we consider an extension of RBA to such buffers with two interdependent Ca2+ binding sites. We show that in the presence of such buffers, RBA solution is given by the solution to a cubic equation, analogous to the quadratic equation describing RBA in the case of a simple, one-to-one Ca2+ buffer. We examine in detail the dependence of RBA accuracy on buffering parameters, to reveal conditions under which RBA provides sufficient precision.