Claire Guerrier | Universté Rennes 2 (original) (raw)
Papers by Claire Guerrier
Journal of Open Source Software
In the present PhD thesis, we study neuronal structures at different scales, from synapses to neu... more 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...
Claire Guerrier - Mathematical modeling and multiscale simulations for vesicular release at neuro... more 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 n...
2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2018
Determining how a neuron computes requires an understanding of the complex spatiotemporal relatio... more Determining how a neuron computes requires an understanding of the complex spatiotemporal relationship between its input (e.g. synaptic input as a result of external stimuli) and action potential output. Recent advances in in vivo, laser-scanning multiphoton technology, known as random-access microscopy (RAM), can capture this relationship by imaging fluorescent light, emitted from calcium-sensitive biosensors responding to synaptic and action potential firing in a neuron’s full dendritic arbor and cell body. Ideally, a continuous output of fluorescent intensities from the neuron would be converted to a binary output (`event’, ‘or no-event’). These binary events can be used to correlate temporal and spatial associations between the input and output. However, neurons contain hundreds-to-thousands of synapses on the dendritic arbors generating an enormous quantity of data composed of physiological signals, which vary greatly in shape and size. Thus, automating data-processing tasks is essential to support high-throughput analysis for real-time/post-processing operations and to improve operators’ comprehension of the data used to decipher neuron computations. Here, we describe an automated software algorithm to detect brain neuron events in real-time using an acousto-optic, multiphoton, laser scanning RAM developed in our laboratory. The fluorescent light intensities, from a genetically encoded, calcium biosensor (GCAMP 6m), are measured by our RAM system and are input to our ‘event-detector’, which converts them to a binary output meant for real-time applications. We evaluate three algorithms for this purpose: exponentially weighted moving average, cumulative sum, and template matching; present each algorithm’s performance; and discuss user-feasibility of each. We validated our system in vivo, using the visual circuit of the Xenopus laevis.
In the present PhD thesis, we study neuronal structures at different scales, from synapses to neu... more 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...
Calcium diffusion in the thin one hundred nanometers layer located between the plasma membrane an... more 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...
Journal of Computational Physics, 2017
models and stochastic simulation methods for computing rare but key binding events in cell biology,
Multiscale Modeling & Simulation, 2015
The arrival of a Brownian particle at a narrow cusp located underneath a ball is a model of vesic... more The arrival of a Brownian particle at a narrow cusp located underneath a ball is a model of vesicular release at neuronal synapses, triggered by calcium ions. The asymptotic computation of the arrival time presents several difficulties that can be overcome using conformal mappings and asymptotic analysis of the model equations. Using a regular expansion of the solution of the Laplace equation in the mapped domain, we compute the solution involving both small and large spatial scales. We derive novel asymptotic formulas for Brownian escape through cusps in both two and three dimensions. The range of validity of the asymptotic formulas is challenged by stochastic simulations. Finally, we apply the analysis to estimate the vesicular release probability at presynaptic terminals and, in particular, we suggest that vesicular organization imposes a severe constraint on calcium channel localization: diffusing calcium ions can trigger vesicular release only in a specific range of positions that we provide.
Encyclopedia of Computational Neuroscience, 2014
The European Physical Journal Special Topics
ABSTRACT We report here recent progress in computing the search time for a stochastic particle to... more ABSTRACT We report here recent progress in computing the search time for a stochastic particle to find a small target hidden in cusp-like pockets. The target is a small segment in dimension two, a small hole or a narrow ribbon in dimension three, placed at the end of a cusp. The asymptotic analysis of the diffusion equation reveals the role of the local geometry, and a mathematical difficulty comes from the boundary layer near the target. The methods are conformal mapping and matching asymptotic. We present applications in cell biology where cellular activation occurs when a diffusing particle finds a hidden site. This is the case during vesicular fusion initiated after a protein located between the vesicular and cell membranes binds to several diffusing calcium ions. Another example is a drug activation site located inside a deep molecular pocket. The analytical formulas clarify the role of small parameters
Scientific reports, Jan 18, 2016
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation... more 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...
Proceedings of the National Academy of Sciences of the United States of America, Jan 20, 2015
How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address th... more How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrop...
Frontiers in Synaptic Neuroscience
Calcium diffusion in the thin 100 nm layer located between the plasma membrane and docked vesicle... more 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.
Journal of Open Source Software
In the present PhD thesis, we study neuronal structures at different scales, from synapses to neu... more 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...
Claire Guerrier - Mathematical modeling and multiscale simulations for vesicular release at neuro... more 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 n...
2018 40th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC), 2018
Determining how a neuron computes requires an understanding of the complex spatiotemporal relatio... more Determining how a neuron computes requires an understanding of the complex spatiotemporal relationship between its input (e.g. synaptic input as a result of external stimuli) and action potential output. Recent advances in in vivo, laser-scanning multiphoton technology, known as random-access microscopy (RAM), can capture this relationship by imaging fluorescent light, emitted from calcium-sensitive biosensors responding to synaptic and action potential firing in a neuron’s full dendritic arbor and cell body. Ideally, a continuous output of fluorescent intensities from the neuron would be converted to a binary output (`event’, ‘or no-event’). These binary events can be used to correlate temporal and spatial associations between the input and output. However, neurons contain hundreds-to-thousands of synapses on the dendritic arbors generating an enormous quantity of data composed of physiological signals, which vary greatly in shape and size. Thus, automating data-processing tasks is essential to support high-throughput analysis for real-time/post-processing operations and to improve operators’ comprehension of the data used to decipher neuron computations. Here, we describe an automated software algorithm to detect brain neuron events in real-time using an acousto-optic, multiphoton, laser scanning RAM developed in our laboratory. The fluorescent light intensities, from a genetically encoded, calcium biosensor (GCAMP 6m), are measured by our RAM system and are input to our ‘event-detector’, which converts them to a binary output meant for real-time applications. We evaluate three algorithms for this purpose: exponentially weighted moving average, cumulative sum, and template matching; present each algorithm’s performance; and discuss user-feasibility of each. We validated our system in vivo, using the visual circuit of the Xenopus laevis.
In the present PhD thesis, we study neuronal structures at different scales, from synapses to neu... more 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...
Calcium diffusion in the thin one hundred nanometers layer located between the plasma membrane an... more 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...
Journal of Computational Physics, 2017
models and stochastic simulation methods for computing rare but key binding events in cell biology,
Multiscale Modeling & Simulation, 2015
The arrival of a Brownian particle at a narrow cusp located underneath a ball is a model of vesic... more The arrival of a Brownian particle at a narrow cusp located underneath a ball is a model of vesicular release at neuronal synapses, triggered by calcium ions. The asymptotic computation of the arrival time presents several difficulties that can be overcome using conformal mappings and asymptotic analysis of the model equations. Using a regular expansion of the solution of the Laplace equation in the mapped domain, we compute the solution involving both small and large spatial scales. We derive novel asymptotic formulas for Brownian escape through cusps in both two and three dimensions. The range of validity of the asymptotic formulas is challenged by stochastic simulations. Finally, we apply the analysis to estimate the vesicular release probability at presynaptic terminals and, in particular, we suggest that vesicular organization imposes a severe constraint on calcium channel localization: diffusing calcium ions can trigger vesicular release only in a specific range of positions that we provide.
Encyclopedia of Computational Neuroscience, 2014
The European Physical Journal Special Topics
ABSTRACT We report here recent progress in computing the search time for a stochastic particle to... more ABSTRACT We report here recent progress in computing the search time for a stochastic particle to find a small target hidden in cusp-like pockets. The target is a small segment in dimension two, a small hole or a narrow ribbon in dimension three, placed at the end of a cusp. The asymptotic analysis of the diffusion equation reveals the role of the local geometry, and a mathematical difficulty comes from the boundary layer near the target. The methods are conformal mapping and matching asymptotic. We present applications in cell biology where cellular activation occurs when a diffusing particle finds a hidden site. This is the case during vesicular fusion initiated after a protein located between the vesicular and cell membranes binds to several diffusing calcium ions. Another example is a drug activation site located inside a deep molecular pocket. The analytical formulas clarify the role of small parameters
Scientific reports, Jan 18, 2016
Binding of molecules, ions or proteins to small target sites is a generic step of cell activation... more 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...
Proceedings of the National Academy of Sciences of the United States of America, Jan 20, 2015
How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address th... more How might synaptic dynamics generate synchronous oscillations in neuronal networks? We address this question in the preBötzinger complex (preBötC), a brainstem neural network that paces robust, yet labile, inspiration in mammals. The preBötC is composed of a few hundred neurons that alternate bursting activity with silent periods, but the mechanism underlying this vital rhythm remains elusive. Using a computational approach to model a randomly connected neuronal network that relies on short-term synaptic facilitation (SF) and depression (SD), we show that synaptic fluctuations can initiate population activities through recurrent excitation. We also show that a two-step SD process allows activity in the network to synchronize (bursts) and generate a population refractory period (silence). The model was validated against an array of experimental conditions, which recapitulate several processes the preBötC may experience. Consistent with the modeling assumptions, we reveal, by electrop...
Frontiers in Synaptic Neuroscience
Calcium diffusion in the thin 100 nm layer located between the plasma membrane and docked vesicle... more 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.