Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses


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Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses
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Guerrier, Claire
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Institut des Hautes Études Scientifiques (IHÉS)
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Claire Guerrier - Mathematical modeling and multiscale simulations for vesicular release at neuronal synapses Synaptic microdomains are underlying fundamental and yet not completely understood functions, such as learning and memory, breathing, sleeping, and many more. Motivated by understanding and analyzing these neuronal structures, we built a model to study vesicular release at synapses. As a first step, we computed the mean time for a Brownian particle to arrive at a narrow opening defined as the small cylinder joining two tangent spheres. The method relies on Möbius conformal transformation applied to the Laplace equation. We also estimated, when the particle starts inside a boundary layer near the hole, the splitting probability to reach the hole before leaving the boundary layer, which is also expressed using a mixed boundary-value Laplace equation. Using these results, we developed model equations and their corresponding stochastic simulations to study vesicular release at neuronal synapses, taking into account their specific geometry.
Logical constant Computer programming Complex (psychology) Musical ensemble Dot product Building Momentum Consistency Projective plane Algebraic structure Mathematical model Functional (mathematics) Open set Radical (chemistry) Arithmetic mean Goodness of fit Right angle Data transmission Chi-squared distribution
Classical physics Surface Computer programming Statistics Sequel Observational study Multiplication sign Time zone Sphere Infinity Tangent Grothendieck topology Number Time domain Independence (probability theory) Cylinder (geometry) Plane (geometry) Root Arithmetic mean Oval Square number Equation Length Field (mathematics) Rule of inference Reflection (mathematics) Projective plane Complex (psychology) Mathematical analysis Independence (probability theory) Division (mathematics) Prediction Cartesian coordinate system Sphere Time domain Dean number Computer animation Thermal radiation Network topology Equation Right angle Boundary value problem Coefficient Reduction of order Arc (geometry)
Area Point (geometry) Process (computing) Multiplication sign Mathematical analysis Similarity (geometry) Line (geometry) Mathematical model Time domain Sphere Independence (probability theory) Computer animation Green's function Mathematical singularity Differential equation Circle Absolute value Boundary value problem
Geometry Computer programming Reflection (mathematics) Thermal expansion Power (physics) Time domain Arithmetic mean Regular graph Computer animation Equation Differential equation Equation Boundary value problem
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Decision theory Multiplication sign Thermal expansion Parameter (computer programming) Mereology Time domain Goodness of fit Regular graph Arithmetic mean Term (mathematics) Equation Differential equation Amenable group Position operator Condition number Scaling (geometry) Reflection (mathematics) Point at infinity Division (mathematics) Volume (thermodynamics) Thermal expansion Set (mathematics) Incidence algebra Term (mathematics) Time domain Bilinear form Power (physics) Approximation Position operator Field extension Arithmetic mean Computer animation Lattice (order) Equation Condition number Game theory Boundary value problem Randbedingung <Mathematik>
Logical constant Computer programming Observational study Process (computing) Multiplication sign Time zone Mathematical model Ordinary differential equation Frequency Chain Arithmetic mean Position operator Stability theory Area Time zone Theory of relativity Process (computing) Building Forcing (mathematics) Projective plane Exponentiation Mathematical analysis Independence (probability theory) Mathematical model Term (mathematics) Markov chain Partial differential equation Pi Boundary value problem Physical system Resultant
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