MCell4 with BioNetGen: A Monte Carlo simulator of rule-based reaction-diffusion systems with Python interface.

Biochemical signaling pathways in living cells are often highly organized into spatially segregated volumes, membranes, scaffolds, subcellular compartments, and organelles comprising small numbers of interacting molecules. At this level of granularity stochastic behavior dominates, well-mixed continuum approximations based on concentrations break down and a particle-based approach is more accurate and more efficient. We describe and validate a new version of the open-source MCell simulation program (MCell4), which supports generalized 3D Monte Carlo modeling of diffusion and chemical reaction of discrete molecules and macromolecular complexes in solution, on surfaces representing membranes, and combinations thereof. The main improvements in MCell4 compared to the previous versions, MCell3 and MCell3-R, include a Python interface and native BioNetGen reaction language (BNGL) support. MCell4's Python interface opens up completely new possibilities for interfacing with external simulators to allow creation of sophisticated event-driven multiscale/multiphysics simulations. The native BNGL support, implemented through a new open-source library libBNG (also introduced in this paper), provides the capability to run a given BNGL model spatially resolved in MCell4 and, with appropriate simplifying assumptions, also in the BioNetGen simulation environment, greatly accelerating and simplifying model validation and comparison.

Synaptic Information Storage Capacity Measured With Information Theory.

Variation in the strength of synapses can be quantified by measuring the anatomical properties of synapses. Quantifying precision of synaptic plasticity is fundamental to understanding information storage and retrieval in neural circuits. Synapses from the same axon onto the same dendrite have a common history of coactivation, making them ideal candidates for determining the precision of synaptic plasticity based on the similarity of their physical dimensions. Here, the precision and amount of information stored in synapse dimensions were quantified with Shannon information theory, expanding prior analysis that used signal detection theory (Bartol et al., 2015). The two methods were compared using dendritic spine head volumes in the middle of the stratum radiatum of hippocampal area CA1 as well-defined measures of synaptic strength. Information theory delineated the number of distinguishable synaptic strengths based on nonoverlapping bins of dendritic spine head volumes. Shannon entropy was applied to measure synaptic information storage capacity (SISC) and resulted in a lower bound of 4.1 bits and upper bound of 4.59 bits of information based on 24 distinguishable sizes. We further compared the distribution of distinguishable sizes and a uniform distribution using Kullback-Leibler divergence and discovered that there was a nearly uniform distribution of spine head volumes across the sizes, suggesting optimal use of the distinguishable values. Thus, SISC provides a new analytical measure that can be generalized to probe synaptic strengths and capacity for plasticity in different brain regions of different species and among animals raised in different conditions or during learning. How brain diseases and disorders affect the precision of synaptic plasticity can also be probed.

Computer simulations predict the impact of neuronal atrophy on the calcium dynamics in Huntington's disease.

One of the early hallmarks of Huntington's disease (HD) is neuronal cell atrophy, especially in the striatum, underlying motor dysfunction in HD. Here using a computer model, we have predicted the impact of cell shrinkage on calcium dynamics at the cellular level. Our model indicates that as cytosolic volume decreases, the amplitude of calcium transients increases and the endoplasmic reticulum (ER) becomes more leaky due to calcium-induced calcium release and a "toxic" positive feedback mechanism mediated by ryanodine receptors that greatly increases calcium release into the cytosol. The excessive calcium release from ER saturates the calcium buffering capacity of calbindin and forces further accumulation of free calcium in the cytosol and cellular compartments including mitochondria. This leads to imbalance of calcium in both cytosol and ER regions. Excessive calcium accumulation in the cytosol can damage the mitochondria resulting in metabolic dysfunction in the cell consistent with the pathology of HD. Our computational model points toward potential drug targets and can accelerate and greatly help the experimental studies of HD paving the way for treatments of patients suffering from HD.

A spatial model of autophosphorylation of Ca 2+ /calmodulin-dependent protein kinase II in a glutamatergic spine reveals dynamics of kinase activation in the first several seconds after a complex synaptic stimulus.

Long-term potentiation (LTP) is a biochemical process in excitatory glutamatergic synapses in the Central Nervous System (CNS). It is initiated by a bout of synaptic activation that is strong enough to contribute to production of an action potential in the axon of the postsynaptic neuron, and it results in an increase in the size of postsynaptic depolarization during subsequent activity. The first step leading to LTP is activation and autophosphorylation of an abundant postsynaptic enzyme, Ca 2+ /calmodulin-dependent protein kinase II (CaMKII). We use simulation of activation of CaMKII holoenzymes in a realistic spatial model of a spine synapse, created in MCell4, to test three hypotheses about how the autophosphorylation response of CaMKII is shaped during a repeated high-frequency stimulus. First, the simulation results indicate that autophosphorylation of CaMKII does not constitute a bistable switch under biologically realistic conditions. Instead, prolonged autophosphorylation of CaMKII may contribute to a biochemical "kinetic proof-reading" mechanism that controls induction of synaptic plasticity. Second, concentration of CaMKII near the postsynaptic membrane increases the local concentration of kinase activity. However, neither localization nor "Ca 2+ -calmodulin-trapping (CaM-trapping)" increase the proportion of autophosphorylated subunits in holoenzymes after a complex stimulus, as previously hypothesized. Finally, we show that, as hypothesized, the amplitude of autophosphorylation in the first 30 seconds after a stimulus is extremely sensitive to the level and location of PP1 activity when PP1 is present in biologically accurate amounts. We further show that prolonged steric hindrance of dephosphorylation of CaMKII, caused by CaM-trapping, can increase the amplitude of autophosphorylation after a complex stimulus. These simulation results sharpen our quantitative understanding of the early events leading to LTP at excitatory synapses. Author Summary: Neurons in the brain are interconnected in an organized fashion by synapses that transmit neuronal activity from one neuron to another. Most of the billions of neurons in the brain have about 10,000 synapses spread over the neuronal membrane. Information is stored in the brain when the ability of specific synapses to pass along neuronal activity is strengthened resulting in formation of new networks. The increase in strength of a synapse is tightly controlled by the frequency and amplitude of its activity, and by neurohormonal signals, which, in combination, can cause long-lasting biochemical changes at the synapse that underlie learning and memory. Defects in these biochemical pathways cause mental and neurological diseases. To develop treatments, we need to understand the precise choreography of these critical biochemical changes. However, the tiny size of the synaptic compartment makes precise measurements of the biochemical reactions impossible. We have used computer simulation techniques and information gathered from experiments on purified synaptic proteins to simulate, within a single synapse, the choreography of the first biochemical step in synaptic strengthening: activation of the enzyme Ca 2+ / calmodulin-dependent protein kinase II. Our results provide insights that can be used in future studies to develop treatments for neuronal diseases.

Long-Term Potentiation Produces a Sustained Expansion of Synaptic Information Storage Capacity in Adult Rat Hippocampus.

Long-term potentiation (LTP) has become a standard model for investigating synaptic mechanisms of learning and memory. Increasingly, it is of interest to understand how LTP affects the synaptic information storage capacity of the targeted population of synapses. Here, structural synaptic plasticity during LTP was explored using three-dimensional reconstruction from serial section electron microscopy. Storage capacity was assessed by applying a new analytical approach, Shannon information theory, to delineate the number of functionally distinguishable synaptic strengths. LTP was induced by delta-burst stimulation of perforant pathway inputs to the middle molecular layer of hippocampal dentate granule cells in adult rats. Spine head volumes were measured as predictors of synaptic strength and compared between LTP and control hemispheres at 30 min and 2 hr after the induction of LTP. Synapses from the same axon onto the same dendrite were used to determine the precision of synaptic plasticity based on the similarity of their physical dimensions. Shannon entropy was measured by exploiting the frequency of spine heads in functionally distinguishable sizes to assess the degree to which LTP altered the number of bits of information storage. Outcomes from these analyses reveal that LTP expanded storage capacity; the distribution of spine head volumes was increased from 2 bits in controls to 3 bits at 30 min and 2.7 bits at 2 hr after the induction of LTP. Furthermore, the distribution of spine head volumes was more uniform across the increased number of functionally distinguishable sizes following LTP, thus achieving more efficient use of coding space across the population of synapses.