Paired turbulence and light do not produce a supralinear calcium increase in Hermissenda

Reaction-diffusion models in weighted and directed connectomes

Connectomes represent comprehensive descriptions of neural connections in a nervous system to better understand and model central brain function and peripheral processing of afferent and efferent neural signals. Connectomes can be considered as a distinctive and necessary structural component alongside glial, vascular, neurochemical, and metabolic networks of the nervous systems of higher organisms that are required for the control of body functions and interaction with the environment. They are carriers of functional epiphenomena such as planning behavior and cognition, which are based on the processing of highly dynamic neural signaling patterns. In this study, we examine more detailed connectomes with edge weighting and orientation properties, in which reciprocal neuronal connections are also considered. Diffusion processes are a further necessary condition for generating dynamic bioelectric patterns in connectomes. Based on our high-precision connectome data, we investigate different diffusion-reaction models to study the propagation of dynamic concentration patterns in control and lesioned connectomes. Therefore, differential equations for modeling diffusion were combined with well-known reaction terms to allow the use of connection weights, connectivity orientation and spatial distances.

Three reaction-diffusion systems Gray-Scott, Gierer-Meinhardt and Mimura-Murray were investigated. For this purpose, implicit solvers were implemented in a numerically stable reaction-diffusion system within the framework of neuroVIISAS. The implemented reaction-diffusion systems were applied to a subconnectome which shapes the mechanosensitive pathway that is strongly affected in the multiple sclerosis demyelination disease. It was found that demyelination modeling by connectivity weight modulation changes the oscillations of the target region, i.e. the primary somatosensory cortex, of the mechanosensitive pathway.

In conclusion, a new application of reaction-diffusion systems to weighted and directed connectomes has been realized. Because the implementation were performed in the neuroVIISAS framework many possibilities for the study of dynamic reaction-diffusion processes in empirical connectomes as well as specific randomized network models are available now.

Approaches and tools for modeling signaling pathways and calcium dynamics in neurons

Signaling pathways are cascades of intracellular biochemical reactions that are activated by transmembrane receptors, and ultimately lead to transcription in the nucleus. In neurons, both calcium permeable synaptic and ionic channels as well as G protein coupled receptors initiate activation of signaling pathway molecules that interact with electrical activity at multiple spatial and time scales. At small temporal and spatial scales, calcium modifies the properties of ionic channels, whereas at larger temporal and spatial scales, various kinases and phosphatases modify the properties of ionic channels, producing phenomena such as synaptic plasticity and homeostatic plasticity. The elongated structure of neuronal dendrites and the organization of multi-protein complexes by anchoring proteins imply that the spatial dimension must be explicit. Therefore, modeling signaling pathways in neurons utilizes algorithms for both diffusion and reactions. The small size of spines coupled with small concentrations of some molecules implies that some reactions occur stochastically. The need for stochastic simulation of many reaction and diffusion events coupled with the multiple temporal and spatial scales makes modeling of signaling pathways a difficult problem. Several different software programs have achieved different aspects of these capabilities. This review explains some of the mathematical formulas used for modeling reactions and diffusion. In addition, it briefly presents the simulators used for modeling reaction-diffusion systems in neurons, together with scientific problems addressed.

The role of type 4 phosphodiesterases in generating microdomains of cAMP: large scale stochastic simulations

Cyclic AMP (cAMP) and its main effector Protein Kinase A (PKA) are critical for several aspects of neuronal function including synaptic plasticity. Specificity of synaptic plasticity requires that cAMP activates PKA in a highly localized manner despite the speed with which cAMP diffuses. Two mechanisms have been proposed to produce localized elevations in cAMP, known as microdomains: impeded diffusion, and high phosphodiesterase (PDE) activity. This paper investigates the mechanism of localized cAMP signaling using a computational model of the biochemical network in the HEK293 cell, which is a subset of pathways involved in PKA-dependent synaptic plasticity. This biochemical network includes cAMP production, PKA activation, and cAMP degradation by PDE activity. The model is implemented in NeuroRD: novel, computationally efficient, stochastic reaction-diffusion software, and is constrained by intracellular cAMP dynamics that were determined experimentally by real-time imaging using an Epac-based FRET sensor (H30). The model reproduces the high concentration cAMP microdomain in the submembrane region, distinct from the lower concentration of cAMP in the cytosol. Simulations further demonstrate that generation of the cAMP microdomain requires a pool of PDE4D anchored in the cytosol and also requires PKA-mediated phosphorylation of PDE4D which increases its activity. The microdomain does not require impeded diffusion of cAMP, confirming that barriers are not required for microdomains. The simulations reported here further demonstrate the utility of the new stochastic reaction-diffusion algorithm for exploring signaling pathways in spatially complex structures such as neurons.

Modelling the molecular mechanisms of synaptic plasticity using systems biology approaches

Synaptic plasticity is thought to underlie learning and memory, but the complexity of the interactions between the ion channels, enzymes and genes that are involved in synaptic plasticity impedes a deep understanding of this phenomenon. Computer modelling has been used to investigate the information processing that is performed by the signalling pathways involved in synaptic plasticity in principal neurons of the hippocampus, striatum and cerebellum. In the past few years, new software developments that combine computational neuroscience techniques with systems biology techniques have allowed large-scale, kinetic models of the molecular mechanisms underlying long-term potentiation and long-term depression. We highlight important advancements produced by these quantitative modelling efforts and introduce promising approaches that use advancements in live-cell imaging.

Comparative study of visuo-vestibular conditioning in Lymnaea stagnalis

In this review, we compare the current understanding of visuo-vestibular conditioning in Hermissenda crassicornis and Lymnaea stagnalis on the basis of behavioral, electrophysiologic, and morphologic studies. Paired presentation of a photic conditioned stimulus (CS) and an orbital rotation unconditioned stimulus (US) results in conditioned escape behavior in both species. In Hermissenda, changes in excitability of type B photoreceptors and morphologic modifications at the axon terminals follow conditioning. Caudal hair cells, which detect mechanical turbulence, have reciprocal inhibition with type B photoreceptors. In Lymnaea, the interaction between photoreceptors and hair cells is dependent on statocyst location. Furthermore, the organization of the Lymnaea eye is complex, with more than 100 photoreceptors distributed in a uniquely folded retina. Although the optimal conditions to produce long-term memory (memory persistent for >1 week) are almost identical in Hermissenda and Lymnaea, physiologic and morphologic differences suggest that the neuronal mechanisms underlying learning and memory are distinct.

An efficient stochastic diffusion algorithm for modeling second messengers in dendrites and spines

Intracellular signaling pathways, which encompass both biochemical reactions and second messenger diffusion, interact non-linearly with neuronal membrane properties in their role as essential intermediaries for synaptic plasticity and neuromodulation. Computational modeling is a productive approach for investigating these phenomena; however, most current strategies for modeling neurons exclude signaling pathways. To overcome this deficiency, a new algorithm is presented to simulate stochastic diffusion in a highly efficient manner. The gain in speed is obtained by considering collections of molecules, instead of tracking the movement of individual molecules. The probability of a molecule leaving a spatially discrete compartment is used to create a lookup table that stores the probability of k(m) molecules leaving the compartment as a function of the total number of molecules in the compartment. During the simulation, the number of molecules leaving the compartment is determined using a uniform random number as an index into the lookup table. Simulations illustrate the accuracy of this algorithm by comparing it with the theoretical solution for deterministic diffusion. Additional simulations show how spines on a dendritic branch compartmentalize diffusible molecules. The efficiency of the algorithm is sufficient to allow simulation of second messenger pathways in a multitude of spines on an entire neuron.

Ionic Currents Underlying Difference in Light Response Between Type A and Type B Photoreceptors

In Hermissenda crassicornis, the memory of light associated with turbulence is stored as changes in intrinsic and synaptic currents in both type A and type B photoreceptors. These photoreceptor types exhibit qualitatively different responses to light and current injection, and these differences shape the spatiotemporal firing patterns that control behavior. Thus the objective of the study was to identify the mechanisms underlying these differences. The approach was to develop a type B model that reproduced characteristics of type B photoreceptors recorded in vitro, and then to create a type A model by modifying a select number of ionic currents. Comparison of type A models with characteristics of type A photoreceptors recorded in vitro revealed that type A and type B photoreceptors have five main differences, three that have been characterized experimentally and two that constitute hypotheses to be tested with experiments in the future. The three differences between type A and type B photoreceptors previously characterized include the inward rectifier current, the fast sodium current, and conductance of calcium-dependent and transient potassium channels. Two additional changes were required to produce a type A photoreceptor model. The very fast firing frequency observed during the first second after light onset required a faster time constant of activation of the delayed rectifier. The fast spike adaptation required a fast, noninactivating calcium-dependent potassium current. Because these differences between type A and type B photoreceptors have not been confirmed in comparative experiments, they constitute hypotheses to be tested with future experiments.

Subcellular, cellular, and circuit mechanisms underlying classical conditioning in Hermissenda crassicornis

A breakthrough for studying the neuronal basis of learning emerged when invertebrates with simple nervous systems, such as the sea slug Hermissenda crassicornis, were shown to exhibit classical conditioning. Hermissenda learns to associate light with turbulence: prior to learning, naive animals move toward light (phototaxis) and contract their foot in response to turbulence; after learning, conditioned animals delay phototaxis in response to light. The photoreceptors of the eye, which receive monosynaptic inputs from statocyst hair cells, are both sensory neurons and the first site of sensory convergence. The memory of light associated with turbulence is stored as changes in intrinsic and synaptic currents in these photoreceptors. The subcellular mechanisms producing these changes include activation of protein kinase C and MAP kinase, which act as coincidence detectors because they are activated by convergent signaling pathways. Pathways of interneurons and motorneurons, where additional changes in excitability and synaptic connections are found, contribute to delayed phototaxis. Bursting activity recorded at several points suggest the existence of small networks that produce complex spatiotemporal firing patterns. Thus, the change in behavior may be produced by a nonlinear transformation of spatiotemporal firing patterns caused by plasticity of synaptic and intrinsic channels. The change in currents and the activation of PKC and MAPK produced by associative learning are similar to those observed in hippocampal and cerebellar neurons after rabbit classical conditioning, suggesting that these represent general mechanisms of memory storage. Thus, the knowledge gained from further study of Hermissenda will continue to illuminate mechanisms of mammalian learning.