Extension of Rapid Buffering Approximation to Ca ²⁺ Buffers with Two Binding Sites

Fundamental cell processes such as synaptic neurotransmitter release, endocrine hormone secretion, and myocyte contraction are controlled by highly localized calcium (Ca ²⁺ ) signals resulting from brief openings of trans-membrane Ca ²⁺ channels. On short temporal and spatial scales, the corresponding local Ca ²⁺ nanodomains formed in the vicinity of a single or several open Ca ²⁺ 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 Ca ²⁺ buffering reaction, combined with the conservation condition for the total Ca ²⁺ and buffer molecule numbers. Previously, RBA has been generalized to an arbitrary arrangement of Ca ²⁺ channels on a flat membrane, in the presence of any number of simple Ca ²⁺ buffers with one-to-one Ca ²⁺ binding stoichiometry. However, many biological buffers have multiple binding sites. For example, buffers and sensors phylogenetically related to calmodulin consist of two Ca ²⁺ -binding domains (lobes), with each domain binding two Ca ²⁺ ions in a cooperative manner. Here we consider an extension of RBA to such buffers with two interdependent Ca ²⁺ 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 Ca ²⁺ buffer. We examine in detail the dependence of RBA accuracy on buffering parameters, to reveal conditions under which RBA provides sufficient precision.