Presentation link (July 20, 9:00-10:00pm): http://meet.google.com/vjz-ypjs-fsm
Victor Matveev,
Yinbo ChenCalcium ion (Ca2+) elevations produced in the vicinity of single open Ca2+ channels are termed Ca2+ nanodomains, and play an important role in triggering secretory vesicle exocytosis, myocyte contraction, and other fundamental physiological processes. Ca2+ nanodomains are shaped by the interplay between Ca2+ influx, Ca2+ diffusion and its binding to Ca2+ buffers, which absorb most of the Ca2+ entering the cell during a depolarization event. In qualitative studies of local Ca2+ signaling, the dependence of Ca2+ concentration on the distance from the Ca2+ channel source can be approximated with a reasonable accuracy by analytic approximations of quasi-stationary solutions of the corresponding reaction-diffusion equations. Such closed-form approximations help to reveal the qualitative dependence of nanodomain characteristics on Ca2+ buffering and diffusion parameters, without resorting to computationally expensive numerical simulations, and can be incorporated into single-comparment conductance-based models. Although a range of nanodomain approximations had been developed for the case of Ca2+ buffers with a single Ca2+ binding site, for example the Rapid Buffer Approximation, the Excess Buffer Approximation, and the Linear approximation [1-3], most biological buffers have more complex Ca2+-binding stoichiometry. Further, several important Ca2+ buffers and sensors such as calretinin and calmodulin consist of distinct EF- hand domains, each possessing two Ca2+ binding sites exhibiting significant cooperativity in binding, whereby the affinity of the second Ca2+ binding reaction is much higher compared to the first binding reaction. To date, only the Rapid Buffer Approximation (RBA) has been generalized to Ca2+ buffers with two binding sties [4]. However, the performance of RBA in the presence of cooperative Ca2+ buffers is limited by the complex interplay between the condition of slow diffusion implied by the RBA, and the slow rate of the first Ca2+ binding reaction characterizing cooperative Ca2+ binding. To resolve this problem, we present modified versions of several Ansatze recently introduced for the case of simple buffers [5], extending them to the case of Ca2+ buffers with 2-to-1 stoichiometry. These new approximants interpolate between the short-range and long-range distance-dependence of Ca2+ nanodomain concentration using a combination of rational and exponential functions. We examine in detail the parameter-dependence of the approximation accuracy, and show that this method is superior to RBA for a wide ranges of buffering parameter values. In particular, the new approximants accurately estimate the distance-dependence of Ca2+ concentration in the case of calretinin or calmodulin. Supported in part by NSF DMS-1517085 (V.M)
References
[1] Neher E. Usefulness and limitations of linear approximation for the understanding of Ca2+ siglals, Cell Calcium 1998, 24: 345-357
[2] Neher E Vesicle pools and Ca2+ nanodomains: new tools for understanding their roles in neurostransmitter release. Neuron 1998, 20: 389-399.
[3] Smith GD, Dai L, Miura RM, Sherman A. Asymptotic Analysis of Buffered Calcium Diffusion Near a Point Source. SIAM J App Math. 2001, 6, 1816-1838.
[4] Matveev V. Extension of Rapid Buffering Approximation to Ca2+ Buffers with Two Binding Sites. Biophys J, 2018, 114, 1204-1215.
[5] Chen Y, Muratov C, Matveev V. Efficient approximations for stationary single-channel Ca2+ nanodomains across length scales. bioRxiv. 2020, 2020.01.16.909036.
