Stochastic Simulation Of Excitation-contraction Coupling

作为与Clara Franzini-Armstrong广泛合作的结果，我们获得了兔离子房结细胞中细胞器和ryanodine受体分布的广泛统计数据。这些数据表明，我们的三维随机SANC模型的参数需要大量修改。然而，EM数据不足以确定ryanodine受体在细胞表面的临界分布。我们使用超分辨率SIM显微镜进行了广泛的成像，并开发了软件，可以对ryanodine受体簇的位置和大小进行3D重建，这将直接用于模型中。我们目前正在开发软件，该软件将使用1000个处理器来模拟单个细胞的形状和Ryr分布。我们开发的软件，可以检测，分类和跟踪钙释放事件在3D+时间，无论是在模拟和实验记录。这导致了对模型中繁殖方式作为肾上腺素能刺激功能的新理解，并发现实验记录中的释放事件比以前怀疑的要多得多。我们已经开始研究窦房结内细胞的异质性，包括分离细胞和小鼠窦房结制备的高空间和时间分辨率图像。我们已经将三维随机模型扩展到多个相互作用的细胞。在下一期节目中，我们将尝试对异质相互作用的细胞产生心律的方式进行建模，使其成为一种涌现的特性。我们还发起了一项新的研究，将固态理论的统计物理方法应用于簇状ryanodine受体的相互作用。这表明，EC耦合过程涉及两种不同的相变，可以解析建模。根据科学顾问委员会的建议，我们正在着手将我们广泛的建模软件转换为其他研究人员可以使用的形式。由于模型软件是用计算机代数语言Macsyma编写的，其商业形式已不再可用，因此这一过程变得复杂。为了解决这个问题，我们与该语言的一些原始开发人员合作进行了一个为期4个月的项目，以升级免费的开源版本（出于版权原因称为Maxima），以便它可以处理我们的建模软件。这次升级现在已经被整合到最新版本的Maxima （Sourceforge.com）中，这样我们的建模套件现在就可以被其他人发布和使用了。然而，在过去6个月中，这项工作因Covid-19大流行而中断。利用流行病传播的数学结构与我们几十年来一直在研究的钙诱导的钙释放的数学结构几乎相同这一事实，我们重新利用了我们的数学和计算工具来开发Covid-19流行病学模型。这项工作提出了一个假设，即实时观察到的复杂传播模式可以用社会异质性的影响来解释，而许多预测模型通常都没有考虑到这一点。我们开发了一种通用的流行病模拟工具，它可以通过大量的子群体来代表一个群体，其中一些代表社会而不是地理单位，并通过用户指定的互动网络连接起来。该模型是完全随机的，并考虑了超扩散效应。我们发现，无法保持社交距离的弱势亚群体可以推动疫情发展，并导致复杂和不可预测的传播模式，这实际上可以挫败主要人群保持社交距离的努力。这项工作现已发表在《物理学前沿》杂志上。

SUMMARY OF WORK As a result of extensive collaboration with Clara Franzini-Armstrong we have obtained extensive statistical data on the distribution of organelles and ryanodine receptors in rabbit siono-atrial node cells. These data indicated that the parameters of our 3D stochastic SANC model need to be extensively revised. However, the EM data are not sufficient to define the critical distribution of ryanodine receptors on the cell surface. We have done extensive imaging using ultra-resolution SIM microscopy, and have developed software that enables 3D reconstruction of the location and size of ryanodine receptor clusters, which will be used directly in the model. We are currently developing software that will use 1000 processors to model the shape and Ryr distribution of individual cells. We have developed software that can detect, classify and track calcium release event in 3D+time, both in simulations and in experimental records. This has led to new understanding of the way that propagation occurs in the model as a function of adrenergic stimulation, and to the discovery that there are many more release events in experimental records than previously suspected. We have begun studies of heterogeneity of cells within the sinus node, both in isolated cells and in high space and time resolution images of whole sinus node preparations from mouse. We have extended the 3D stochastic model to multiple, interacting cells. In the next program period we will attempt to model the way that heterogeneous interacting cells give rise to the heart rhythm as an emergent property. We have also initiated a new study that applies statistical physics methods from solid-state theory to the interactions of clustered ryanodine receptors. This has shown that the process of EC coupling involves two different phase transitions that can be modeled analytically. As advised by the Board of Scientific Counselors, we are undertaking to translate our extensive modeling software into a form that can be used by other investigators. This has been complicated because the model software in written in the computer algebra language Macsyma whose commercial form is no longer available. To solve this problem we undertook a 4 month project in collaboration with some of the original developers of the language to upgrade the free, open-source version (called Maxima for copyright reasons) so that it can process our modeling software. This upgrade has now been incorporated in the latest version of Maxima (Sourceforge.com) so that our modeling suite can now be published and used by others. However, during the past 6 months this work has been interrupted by the Covid-19 pandemic. Taking advantage of the fact that spread of an epidemic has a mathematical structure almost identical to that of the calcium-induced calcium release we have been studying for decades, we have repurposed our mathematical and computational tools to develop a model of Covid-19 epidemiology. This work addressed the hypothesis that the complex patterns of propagation being observed in real time could be explained by the effect of social heterogeneity not generally accounted for in many forecasting models. We have developed a general epidemic simulation tool that can represent a population by a large number of sub-populations, some representing social rather than geographic units, and connected by a network of interactions specified by the user. This model is fully stochastic and incorporates the effects of super-spreading. We find that vulnerable subgroups unable to socially-distance can drive the epidemic and lead to complex and unpredictable patterns of spread that can actualy defeat the efforts of social distancing in the main population. This work has now been published in Frontiers in Physics. We have updated and extended our modeling of the sino-atrial node (pacemaker) of the heart: (1) The 3D stochastic simulation of single sino-atrial node cells has been updated to include realistic gating schemes for the L-type calcium channels based on recent work at Johns Hopkins. The model now includes two types of L-type channels and different locations of the channels in the cell. (2) We have extended models based on calciun-release units to be a full model of the coupled-clock mechanism which can be run much faster than the full 3D model. This work has been recently published in Journal of General Physiology. (3) We have developed a large scale model of the multi-cellular node at a single-cell resolution that will make possible comparisons with experimental data on the structure of the node. Experimentally, we have used mice with green fluorescent protein linked to the ryanodine receptor to demonstrate that propagated local calcium releases are due to calcium sparks "jumping" in saltatory propagation by diffusion of calcium. This finally confirms experimentally the paradigm that underlies all of our simulations of sinus node cells over the past 7 years.