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To truly appreciate the myriad of events which relate synaptic function and vesicle dynamics, simulations should be done in a spatially realistic environment. This holds true in particular in order to explain as well the rather astonishing motor patterns which we observed within in vivo recordings which underlie peristaltic contractionsas well as the shape of the EPSPs at different forms of long-term stimulation, presented both here, at a well characterized synapse, the neuromuscular junction (NMJ) of the Drosophila larva (c.f. Figure 1). To this end, we have employed a reductionist approach and generated three dimensional models of single presynaptic boutons at the Drosophila larval NMJ. Vesicle dynamics are described by diffusion-like partial differential equations which are solved numerically on unstructured grids using the uG platform. In our model we varied parameters such as bouton-size, vesicle output probability (Po), stimulation frequency and number of synapses, to observe how altering these parameters effected bouton function. Hence we demonstrate that the morphologic and physiologic specialization maybe a convergent evolutionary adaptation to regulate the trade off between sustained, low output, and short term, high output, synaptic signals. There seems to be a biologically meaningful explanation for the co-existence of the two different bouton types as previously observed at the NMJ (characterized especially by the relation between size and Po), the assigning of two different tasks with respect to short- and long-time behaviour could allow for an optimized interplay of different synapse types. We can present astonishing similar results of experimental and simulation data which could be gained in particular without any data fitting, however based only on biophysical values which could be taken from different experimental results. As a side product, we demonstrate how advanced methods from numerical mathematics could help in future to resolve also other difficult experimental neurobiological issues.
The morphology of presynaptic specializations can vary greatly ranging from classical single-release-site boutons in the central nervous system to boutons of various sizes harboring multiple vesicle release sites. Multi-release-site boutons can be found in several neural contexts, for example at the neuromuscular junction (NMJ) of body wall muscles of Drosophila larvae. These NMJs are built by two motor neurons forming two types of glutamatergic multi-release-site boutons with two typical diameters. However, it is unknown why these distinct nerve terminal configurations are used on the same postsynaptic muscle fiber. To systematically dissect the biophysical properties of these boutons we developed a full three-dimensional model of such boutons, their release sites and transmitter-harboring vesicles and analyzed the local vesicle dynamics of various configurations during stimulation. Here we show that the rate of transmission of a bouton is primarily limited by diffusion-based vesicle movements and that the probability of vesicle release and the size of a bouton affect bouton-performance in distinct temporal domains allowing for an optimal transmission of the neural signals at different time scales. A comparison of our in silico simulations with in vivo recordings of the natural motor pattern of both neurons revealed that the bouton properties resemble a well-tuned cooperation of the parameters release probability and bouton size, enabling a reliable transmission of the prevailing firing-pattern at diffusion-limited boutons. Our findings indicate that the prevailing firing-pattern of a neuron may determine the physiological and morphological parameters required for its synaptic terminals.
Poster presentation from Twentieth Annual Computational Neuroscience Meeting: CNS*2011 Stockholm, Sweden. 23-28 July 2011. To truly appreciate the myriad of events which relate synaptic function and vesicle dynamics, simulations should be done in a spatially realistic environment. This holds true in particular in order to explain the rather astonishing motor patterns presented here which we observed within in vivo recordings which underlie peristaltic contractions at a well characterized synapse, the neuromuscular junction (NMJ) of the Drosophila larva. To this end, we have employed a reductionist approach and generated three dimensional models of single presynaptic boutons at the Drosophila larval NMJ. Vesicle dynamics are described by diffusion-like partial differential equations which are solved numerically on unstructured grids using the uG platform. In our model we varied parameters such as bouton-size, vesicle output probability (Po), stimulation frequency and number of synapses, to observe how altering these parameters effected bouton function. Hence we demonstrate that the morphologic and physiologic specialization maybe a convergent evolutionary adaptation to regulate the trade off between sustained, low output, and short term, high output, synaptic signals. There seems to be a biologically meaningful explanation for the co-existence of the two different bouton types as previously observed at the NMJ (characterized especially by the relation between size and Po),the assigning of two different tasks with respect to short- and long-time behaviour could allow for an optimized interplay of different synapse types. As a side product, we demonstrate how advanced methods from numerical mathematics could help in future to resolve also other difficult experimental neurobiological issues.
Mathematical models of virus dynamics have not previously acknowledged spatial resolution at the intracellular level despite substantial arguments that favor the consideration of intracellular spatial dependence. The replication of the hepatitis C virus (HCV) viral RNA (vRNA) occurs within special replication complexes formed from membranes derived from endoplasmatic reticulum (ER). These regions, termed membranous webs, are generated primarily through specific interactions between nonstructural virus-encoded proteins (NSPs) and host cellular factors. The NSPs are responsible for the replication of the vRNA and their movement is restricted to the ER surface. Therefore, in this study we developed fully spatio-temporal resolved models of the vRNA replication cycle of HCV. Our simulations are performed upon realistic reconstructed cell structures—namely the ER surface and the membranous webs—based on data derived from immunostained cells replicating HCV vRNA. We visualized 3D simulations that reproduced dynamics resulting from interplay of the different components of our models (vRNA, NSPs, and a host factor), and we present an evaluation of the concentrations for the components within different regions of the cell. Thus far, our model is restricted to an internal portion of a hepatocyte and is qualitative more than quantitative. For a quantitative adaption to complete cells, various additional parameters will have to be determined through further in vitro cell biology experiments, which can be stimulated by the results deccribed in the present study.
The hepatitis C virus (HCV) RNA replication cycle is a dynamic intracellular process occurring in three-dimensional space (3D), which is difficult both to capture experimentally and to visualize conceptually. HCV-generated replication factories are housed within virus-induced intracellular structures termed membranous webs (MW), which are derived from the Endoplasmatic Reticulum (ER). Recently, we published 3D spatiotemporal resolved diffusion–reaction models of the HCV RNA replication cycle by means of surface partial differential equation (sPDE) descriptions. We distinguished between the basic components of the HCV RNA replication cycle, namely HCV RNA, non-structural viral proteins (NSPs), and a host factor. In particular, we evaluated the sPDE models upon realistic reconstructed intracellular compartments (ER/MW). In this paper, we propose a significant extension of the model based upon two additional parameters: different aggregate states of HCV RNA and NSPs, and population dynamics inspired diffusion and reaction coefficients instead of multilinear ones. The combination of both aspects enables realistic modeling of viral replication at all scales. Specifically, we describe a replication complex state consisting of HCV RNA together with a defined amount of NSPs. As a result of the combination of spatial resolution and different aggregate states, the new model mimics a cis requirement for HCV RNA replication. We used heuristic parameters for our simulations, which were run only on a subsection of the ER. Nevertheless, this was sufficient to allow the fitting of core aspects of virus reproduction, at least qualitatively. Our findings should help stimulate new model approaches and experimental directions for virology.