Particle-based Monte-Carlo simulations are an important tool for the analysis of microscopic molecular physiology. One of the major challenges in the field is how to accurately simulate molecular diffusion, interaction, and multi-protein complex assembly in the cellular environment. Here we present a novel event-driven simulation scheme (Cellular Dynamics Simulator, CDS) that can address how volume exclusion and molecular crowding impact signaling cascades in small subcellular compartments such as dendritic spines. We contend that the exact molecular collision detection scheme used in this simulator is essential to understand the spatio-temporal pattern of Ca2+-CaM activation during synaptic stimulations.
Combining this novel simulator and a detailed kinetic model of Ca2+-CaM-CaMKII interactions, we investigate how the rate of Ca2+ injection and the spatial localization of Ca2+ channels impact the spatio-temporal patterns of Ca2+/CaM and CaMKII activations in a simplified dendritic spine. The activation of CaM requires a rapid and successive binding of Ca2+ ions. For this successive binding to happen, the CaM molecule must collide into the second Ca2+ ion before the first one dissociates from it. Thus, at a relatively low Ca2+ injection rate (0.01 ~0.1Ca2+ ions per microsecond per ion channel), the number and the location of Ca2+ channels have a major impact on the spatio-temporal pattern of CaM activation. In fact, at these rates even if ten ion channels are open simultaneously, only a small number of CaM molecules become fully saturated and the Ca2+ saturation takes place only in close proximity to the Ca2+ channels (Figure 1A). On the other hand, at higher Ca2+ injection rates (1 ~10 Ca2+ ions per microsecond) with the same number of ion channels present, the Ca2+ saturation of CaM takes place throughout the spine volume (Figure. 1B). Thus, depending on the type and/or number of ion channels, the spine Ca2+ signaling system operates in different modes: one produces a highly localized nano-domain of Ca2+/CaM activation while the other produces a global and homogenous Ca2+/CaM activation.
Figure 1. Ca2+-CaM Activation domain. (A) A snapshot of a simulation showing that CaM molecules become fully Ca2+ saturated only within close proximity of ion channels with low Ca2+ injection rates. The probability of CaM entering into a fully Ca2+ saturated state depends sharply on the distance of CaM molecules from the source of Ca2+ entry. (B) A snapshot of a simulation having a higher Ca2+ injection rate. The CaM molecules become fully Ca2+ saturated throughout the entire spine. The red spots in the figures indicate fully Ca2+ saturated CaM molecules while dark blue are partially Ca2+-saturated CaM. The light brown particles represent Ca2+ channels. The small yellow particles are Ca2+ ions.