Simulating diffusion from a cluster of point sources using propagation integrals

From the outer ear to the nerve: A complete computer model of the peripheral auditory system

Computer models of the individual components of the peripheral auditory system - the outer, middle, and inner ears and the auditory nerve - have been developed in the past, with varying level of detail, breadth, and faithfulness of the underlying parameters. Building on previous work, we advance the modeling of the ear by presenting a complete, physiologically justified, bottom-up computer model based on up-to-date experimental data that integrates all of these parts together seamlessly. The detailed bottom-up design of the present model allows for the investigation of partial hearing mechanisms and their defects, including genetic, molecular, and microscopic factors. Also, thanks to the completeness of the model, one can study microscopic effects in the context of their implications on hearing as a whole, enabling the correlation with neural recordings and non-invasive psychoacoustic methods. Such a model is instrumental for advancing quantitative understanding of the mechanism of hearing, for investigating various forms of hearing impairment, as well as for devising next generation hearing aids and cochlear implants.

Stationary Ca2+ nanodomains in the presence of buffers with two binding sites

We examine closed-form approximations for the equilibrium Ca²⁺ and buffer concentrations near a point Ca²⁺ source representing a Ca²⁺ channel, in the presence of a mobile buffer with two Ca²⁺ binding sites activated sequentially and possessing distinct binding affinities and kinetics. This allows us to model the impact on Ca²⁺ nanodomains of realistic endogenous Ca²⁺ buffers characterized by cooperative Ca²⁺ binding, such as calretinin. The approximations we present involve a combination or rational and exponential functions, whose parameters are constrained using the series interpolation method that we recently introduced for the case of simpler Ca²⁺ buffers with a single Ca²⁺ binding site. We conduct extensive parameter sensitivity analysis and show that the obtained closed-form approximations achieve reasonable qualitative accuracy for a wide range of buffer's Ca²⁺ binding properties and other relevant model parameters. In particular, the accuracy of the derived approximants exceeds that of the rapid buffering approximation in large portions of the relevant parameter space.

Simulating cardiac Ca2+ release units: effects of RyR cluster size and Ca2+ buffers on diastolic Ca2+ leak

Leak of Ca²⁺ out of the cardiac sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) during diastole is vital to regulate SR Ca²⁺ levels. This leak can become deleterious when large spontaneous RyR-mediated Ca²⁺ release events evoke proarrhythmic Ca²⁺ waves that can lead to delayed after-depolarizations. Here, we model diastolic SR Ca²⁺ leak at individual SR Ca²⁺ release sites using computer simulations of RyR arrays like those in the dyadic cleft. The results show that RyR arrays size has a significant effect on SR Ca²⁺ leak, with bigger arrays producing larger and more frequent Ca²⁺ release events. Moreover, big RyR arrays are more susceptible to small changes in the levels of dyadic Ca²⁺ buffers. Such changes in buffering shift Ca²⁺ leak from small Ca²⁺ release events (involving few open RyRs) to larger events (with many open RyRs). Moreover, by analyzing a large parameter space of possible buffering and SR Ca²⁺ loads, we find further evidence for the hypothesis that SR Ca²⁺ leak by RyR arrays can undergo a sudden phase transition.

Efficient Approximations for Stationary Single-Channel Ca2+ Nanodomains across Length Scales

We consider the stationary solution for the Ca²⁺ concentration near a point Ca²⁺ source describing a single-channel Ca²⁺ nanodomain in the presence of a single mobile Ca²⁺ buffer with 1:1 Ca²⁺ binding. We present computationally efficient approximants that estimate stationary single-channel Ca²⁺ nanodomains with great accuracy in broad regions of parameter space. The presented approximants have a functional form that combines rational and exponential functions, which is similar to that of the well-known excess buffer approximation and the linear approximation but with parameters estimated using two novel, to our knowledge, methods. One of the methods involves interpolation between the short-range Taylor series of the free buffer concentration and its long-range asymptotic series in inverse powers of distance from the channel. Although this method has already been used to find Padé (rational-function) approximants to single-channel Ca²⁺ and buffer concentrations, extending this method to interpolants combining exponential and rational functions improves accuracy in a significant fraction of the relevant parameter space. A second method is based on the variational approach and involves a global minimization of an appropriate functional with respect to parameters of the chosen approximations. An extensive parameter-sensitivity analysis is presented, comparing these two methods with previously developed approximants. Apart from increased accuracy, the strength of these approximants is that they can be extended to more realistic buffers with multiple binding sites characterized by cooperative Ca²⁺ binding, such as calmodulin and calretinin.