Simulation strategies for calcium microdomains and calcium-regulated calcium channels

Quantum Calculations on Ion Channels: Why Are They More Useful Than Classical Calculations, and for Which Processes Are They Essential?

There are reasons to consider quantum calculations to be necessary for ion channels, for two types of reasons. The calculations must account for charge transfer, and the possible switching of hydrogen bonds, which are very difficult with classical force fields. Without understanding charge transfer and hydrogen bonding in detail, the channel cannot be understood. Thus, although classical approximations to the correct force fields are possible, they are unable to reproduce at least some details of the behavior of a system that has atomic scale. However, there is a second class of effects that is essentially quantum mechanical. There are two types of such phenomena: exchange and correlation energies, which have no classical analogues, and tunneling. Tunneling, an intrinsically quantum phenomenon, may well play a critical role in initiating a proton cascade critical to gating. As there is no classical analogue of tunneling, this cannot be approximated classically. Finally, there are energy terms, exchange and correlation energy, whose values can be approximated classically, but these approximations must be subsumed within classical terms, and as a result, will not have the correct dependence on interatomic distances. Charge transfer, and tunneling, require quantum calculations for ion channels. Some results of quantum calculations are shown.

Calcium, TRPC channels, and regulation of the actin cytoskeleton in podocytes: towards a future of targeted therapies

With more than 6,000 new pediatric patients with treatment-resistant nephrotic syndrome in the US each year alone, the unmet need for novel, podocyte-specific therapies is substantial. Recently, the established therapeutic benefit of angiotensin-converting enzyme (ACE) inhibitors and angiotensin receptor blockers (ARB) was used as a starting point to gain insight into the pathomechanism of primary podocytopathies. A calcium (Ca(2+))-mediated pathway has been identified that connects the angiotensin type 1 receptor (AT1R) to podocyte cytoskeletal dynamics, essential for a functioning glomerular filtration barrier. This discovery provided an important missing piece in our understanding of the pathomechanism of filter barrier damage, revealing Ca(2+) signaling as critical for podocyte health and disease. The identification of the two Ca(2+) permeant channels TRPC5 and TRPC6 as mediators of this pathway not only bolstered the importance of podocyte cytoskeleton dynamics but also revealed promising drug targets for treatment-resistant nephrotic syndrome. This review will focus on this novel signaling pathway in primary podocytopathies and its implications for next-generation therapies for glomerular disease.

The influence of Ca²⁺ buffers on free [Ca²⁺] fluctuations and the effective volume of Ca²⁺ microdomains

Intracellular calcium (Ca(2+)) plays a significant role in many cell signaling pathways, some of which are localized to spatially restricted microdomains. Ca(2+) binding proteins (Ca(2+) buffers) play an important role in regulating Ca(2+) concentration ([Ca(2+)]). Buffers typically slow [Ca(2+)] temporal dynamics and increase the effective volume of Ca(2+) domains. Because fluctuations in [Ca(2+)] decrease in proportion to the square-root of a domain's physical volume, one might conjecture that buffers decrease [Ca(2+)] fluctuations and, consequently, mitigate the significance of small domain volume concerning Ca(2+) signaling. We test this hypothesis through mathematical and computational analysis of idealized buffer-containing domains and their stochastic dynamics during free Ca(2+) influx with passive exchange of both Ca(2+) and buffer with bulk concentrations. We derive Langevin equations for the fluctuating dynamics of Ca(2+) and buffer and use these stochastic differential equations to determine the magnitude of [Ca(2+)] fluctuations for different buffer parameters (e.g., dissociation constant and concentration). In marked contrast to expectations based on a naive application of the principle of effective volume as employed in deterministic models of Ca(2+) signaling, we find that mobile and rapid buffers typically increase the magnitude of domain [Ca(2+)] fluctuations during periods of Ca(2+) influx, whereas stationary (immobile) Ca(2+) buffers do not. Also contrary to expectations, we find that in the absence of Ca(2+) influx, buffers influence the temporal characteristics, but not the magnitude, of [Ca(2+)] fluctuations. We derive an analytical formula describing the influence of rapid Ca(2+) buffers on [Ca(2+)] fluctuations and, importantly, identify the stochastic analog of (deterministic) effective domain volume. Our results demonstrate that Ca(2+) buffers alter the dynamics of [Ca(2+)] fluctuations in a nonintuitive manner. The finding that Ca(2+) buffers do not suppress intrinsic domain [Ca(2+)] fluctuations raises the intriguing question of whether or not [Ca(2+)] fluctuations are a physiologically significant aspect of local Ca(2+) signaling.

Exact stochastic simulation of a calcium microdomain reveals the impact of Ca²⁺ fluctuations on IP₃R gating

In this study, we numerically analyzed the nonlinear Ca(2+)-dependent gating dynamics of a single, nonconducting inositol 1,4,5-trisphosphate receptor (IP₃R) channel, using an exact and fully stochastic simulation algorithm that includes channel gating, Ca(2+) buffering, and Ca(2+) diffusion. The IP₃R is a ubiquitous intracellular Ca(2+) release channel that plays an important role in the formation of complex spatiotemporal Ca(2+) signals such as waves and oscillations. Dynamic subfemtoliter Ca(2+) microdomains reveal low copy numbers of Ca(2+) ions, buffer molecules, and IP₃Rs, and stochastic fluctuations arising from molecular interactions and diffusion do not average out. In contrast to models treating calcium dynamics deterministically, the stochastic approach accounts for this molecular noise. We varied Ca(2+) diffusion coefficients and buffer reaction rates to tune the autocorrelation properties of Ca(2+) noise and found a distinct relation between the autocorrelation time τac, the mean channel open and close times, and the resulting IP₃R open probability PO. We observed an increased PO for shorter noise autocorrelation times, caused by increasing channel open times and decreasing close times. In a pure diffusion model the effects become apparent at elevated calcium concentrations, e.g., at [Ca(2+)] = 25 μM, τac = 0.082 ms, the IP₃R open probability increased by ≈20% and mean open times increased by ≈4 ms, compared to a zero noise model. We identified the inactivating Ca(2+) binding site of IP₃R subunits as the primarily noise-susceptible element of the De Young and Keizer model. Short Ca(2+) noise autocorrelation times decrease the probability of Ca(2+) association and consequently increase IPvR activity. These results suggest a functional role of local calcium noise properties on calcium-regulated target molecules such as the ubiquitous IP₃R. This finding may stimulate novel experimental approaches analyzing the role of calcium noise properties on microdomain behavior.

Microdomain calcium fluctuations as a colored noise process

Calcium ions play a key role in subcellular signaling as localized transients of the intracellular calcium concentration modify the activity of ion channels, enzymes and transcription factors, among others. The intracellular calcium concentration is inherently noisy, as diffusion, the transient binding to and dissociation from buffer molecules and stochastically gating calcium channels contribute to the fluctuations of the local copy number of Ca²⁺ ions. We study the properties of the fluctuating calcium concentration in sub-femtoliter volumes using an exact stochastic simulation algorithm and approximations to the exact stochastic solution. It is shown that the time course of the local calcium concentration represents a colored noise process whose autocorrelation time is a function of buffer kinetics and diffusion constants. Using the chemical Langevin description and the excess buffer approximation of the process, fast approximative algorithms and theoretical connections to the Ornstein-Uhlenbeck process are obtained. In a generic example, we show how calcium noise can couple to the dynamics of a single variable moving in a double-well potential, leading to a colored noise induced transition. Our work shows how a multitude of intracellular signaling pathways may be influenced by the inherent stochasticity of calcium signals, a key messenger in virtually any cell type, and how the calcium signal can be implemented efficiently in cellular signaling models.