Search Time for a Small Ribbon and Application to Vesicular Release at Neuronal Synapses (original) (raw)
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A comparison of deterministic and stochastic simulations of neuronal vesicle release models
Physical Biology, 2010
We study the calcium-induced vesicle release into the synaptic cleft using a deterministic algorithm and MCell, a Monte Carlo algorithm that tracks individual molecules. We compare the average vesicle release probability obtained using both algorithms and investigate the effect of the three main sources of noise: diffusion, sensor kinetics and fluctuations from the voltage-dependent calcium channels (VDCCs). We find that the stochastic opening kinetics of the VDCCs are the main contributors to differences in the release probability. Our results show that the deterministic calculations lead to reliable results, with an error of less than 20%, when the sensor is located at least 50 nm from the VDCCs, corresponding to microdomain signaling. For smaller distances, i.e. nanodomain signaling, the error becomes larger and a stochastic algorithm is necessary.
2018
Calcium diffusion in the thin one hundred nanometers layer located between the plasma membrane and docked vesicles in the pre-synaptic terminal of neuronal cells mediates vesicular fusion and synaptic transmission. Accounting for the narrow-cusp geometry located underneath the vesicle is a key ingredient that defines the probability and the time scale of calcium diffusion to bind calcium sensors for the initiation of vesicular release. We study here the time scale, the calcium binding dynamics and the consequences for asynchronous versus synchronous release. To conclude, threedimensional modeling approaches and the associated coarse-grained simulations can now account efficiently for the precise co-organization of vesicles and Voltage-Gated-Calcium-Channel (VGCC). This co-organization is a key determinant of short-term plasticity and it shapes asynchronous release. Moreover, changing the location of VGCC from few nanometers underneath the vesicle modifies significantly the release p...
Scientific reports, 2016
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation. This process relies on rare stochastic events where a particle located in a large bulk has to find small and often hidden targets. We present here a hybrid discrete-continuum model that takes into account a stochastic regime governed by rare events and a continuous regime in the bulk. The rare discrete binding events are modeled by a Markov chain for the encounter of small targets by few Brownian particles, for which the arrival time is Poissonian. The large ensemble of particles is described by mass action laws. We use this novel model to predict the time distribution of vesicular release at neuronal synapses. Vesicular release is triggered by the binding of few calcium ions that can originate either from the synaptic bulk or from the entry through calcium channels. We report here that the distribution of release time is bimodal although it is triggered by a single fast action potenti...
Multi-scale modeling and asymptotic analysis for neuronal synapses and networks
2015
In the present PhD thesis, we study neuronal structures at different scales, from synapses to neural networks. Our goal is to develop mathematical models and their analysis, in order to determine how the properties of synapses at the molecular level shape their activity and propagate to the network level. This change of scale can be formulated and analyzed using several tools such as partial differential equations, stochastic processes and numerical simulations. In the first part, we compute 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 Mobius conformal transformation applied to the Laplace equation. We also estimate, 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 develop model equations and the...
The First 100 nm Inside the Pre-synaptic Terminal Where Calcium Diffusion Triggers Vesicular Release
Frontiers in Synaptic Neuroscience
Calcium diffusion in the thin 100 nm layer located between the plasma membrane and docked vesicles in the pre-synaptic terminal of neuronal cells mediates vesicular fusion and synaptic transmission. Accounting for the narrow-cusp geometry located underneath the vesicle is a key ingredient that defines the probability and the time scale of calcium diffusion to bind calcium sensors for the initiation of vesicular release. We review here the time scale, the calcium binding dynamics and the consequences for asynchronous versus synchronous release. To conclude, three-dimensional modeling approaches and the associated coarse-grained simulations can now account efficiently for the precise co-organization of vesicles and Voltage-Gated-Calcium-Channel (VGCC). This co-organization is a key determinant of short-term plasticity and it shapes asynchronous release. Moreover, changing the location of VGCC from few nanometers underneath the vesicle modifies significantly the release probability. Finally, by modifying the calcium buffer concentration, a single synapse can switch from facilitation to depression.
Modélisation multi-échelle et analyse asymptotique pour les synapses et les réseaux neuronaux
2015
In the present PhD thesis, we study neuronal structures at different scales, from synapses to neural networks. Our goal is to develop mathematical models and their analysis, in order to determine how the properties of synapses at the molecular level shape their activity and propagate to the network level. This change of scale can be formulated and analyzed using several tools such as partial differential equations, stochastic processes and numerical simulations. In the first part, we compute 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 estimate, 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 develop model equations and the...
A Semiquantitative Theory of Synaptic Vesicle Movements
Biophysical Journal, 1973
Under the assumption that vesicles are the anatomic correlate of quantal release, the forces governing the movement of synaptic vesicles inside neurons are analyzed. Semiquantitative calculations are presented to show that a diffuse layer field penetrates a few Debye lengths into the axoplasm. This field binds tightly a monolayer of water to the membrane forming the potential barrier for miniature end-plate potential (mepp) release. The action potential destroys the monolayer and pulls the vesicle to the membrane. The vesicles are brought to the synaptic zone and held there by a Na+ leak in the synaptic membrane. A stochastic theory of synaptic vesicle release is presented to explain experimental results. The rate of vesicle release is fractionated into a rate of membrane contacts by a vesicle and a rate of vesicle discharge per contact. I would like to express my appreciation to Dr. Motoy Kuno for his help and advice. The development of the compound probability from Vere-Jones was shown to me by Dr. Robert Zucker. I thank him for this and a very helpful critical reading.
S1 Finite Time Bias for Symmetric vs. Standard Normalization A finite integration time T leads to a bias in the autocorrelation function both using the standard normalization/subtraction byĪ 2 T (defined by Eq. 1 in the main text) and with the symmetric normalization/subtraction (Eq. 4). See references (14-16). The bias for the two cases are given by Eq. 2 and Eq. 5 in the main text respectively. Figure S1 shows the symmetrically and asymmetrically normalized autocorrelation functions for free diffusion with T = 200 s and τ D = 5 s along with the infinite integration time result for comparison.
JSIR Vol.79(04) [April 2020], 2020
When a postsynaptic neuron receives a spike from the axon, its synapse releases neurotransmitters to the synaptic cleft. The probability of vesicle release depends on the amount of calcium ions. The concentration of calcium ions keeps on changing with time. The opening and closing of these channels is controlled by the calcium ion gates operating at different rates. Similarly, the binding of neurotransmitters to the membrane depends on the number of receptors. The existing literature considers probabilities of vesicle release and binding of neurotransmitters as constants. In practice, these two probabilities are time-dependent. This issue is addressed in this paper and new derivations of the time-varying nature of these two probabilities are obtained from simulation study and analysis. The present investigation of estimation of these two time-dependent probabilities will help to develop improved nanoscale neuronal communication models.