Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.
Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance to the calcium channels determines the release probability and thereby the postsynaptic signal. Suitable models of the process need to capture both the mean and the variance observed in electrophysiological measurements of the postsynaptic current. In this work, we propose a method to directly compute the exact first- and second-order moments for signals generated by a linear reaction network under convolution with an impulse response function, rendering computationally expensive numerical simulations of the underlying stochastic counting process obsolete. We show that the autocorrelation of the process is central for the calculation of the filtered signal’s second-order moments, and derive a system of PDEs for the cross-correlation functions (including the autocorrelations) of linear reaction networks with time-dependent rates. Finally, we employ our method to efficiently compare different spatial coarse graining approaches for a specific model of synaptic vesicle fusion. Beyond the application to neurotransmission processes, the developed theory can be applied to any linear reaction system that produces a filtered stochastic signal.
Background:
Synapses, as specialised cell-cell contacts, allow for a faithful and controlled signal transmission between a neuron and a target cell. Presynapses, the sites of neurotransmitter release, form de novo throughout the development of an organism. Although this process is fundamental to the development and function of synaptic circuits, how developing neurons control number and distribution of individual synapses remains poorly understood. In-vivo imaging analysis of synapse formation at the neuromuscular junction of anaesthetised Drosophila third instar larvae allows for spatial and temporal resolution of the underlying molecular processes. However, high-throughput, comprehensive analysis are hampered by the manual and time-consuming imaging analysis methods applied hitherto. Here, we focus on the early presynaptic formation steps, that is, the presynaptic seeding, initiated by the formation of transient Liprin-a/SYD1 seeding sites, either stabilised or disintegrated over a time span of 30-90 min.
Results:
To investigate the dynamics of the Liprin-a/SYD1 seeding sites, we developed an automated analysis pipeline for 3D confocal images from in-vivo imaging at distinct time points to analyse fluorescently labelled presynaptic protein dynamics during early synapse formation. The workflow is realised in the data analysis software Amira, utilising the hierarchical watershed algorithm, and was designed for automatic processing with an option for manual proofreading. Compared to the previous 2D manual quantification, this automated approach provides a higher sensitivity in single Liprin-a seeding site detection in low-intensity areas and in regions of dense seeding sites.In addition, it substantially reduces the work time. To account for possible errors occurring in the automated processing, we implemented an additional proofreading step allowing for a manual correction of Liprin-a seeding site segmentation and assignment, thus greatly improving the analysis while only marginally increasing work time by 10% to a total work time reduction of 80% compared to the 2D manual analysis paradigm.
Conclusion:
The process of synaptogenesis underlies the general principles of locomotion, learning and memory formation. The developed fast and accurate semi-automated 3D workflow provides a substantial progress in the analysis of this molecular process and its application can be easily extended to other dynamic in-vivo research approaches across species.
Background:
Synapses, as specialised cell-cell contacts, allow for a faithful and controlled signal transmission between a neuron and a target cell. Presynapses, the sites of neurotransmitter release, form de novo throughout the development of an organism. Although this process is fundamental to the development and function of synaptic circuits, how developing neurons control number and distribution of individual synapses remains poorly understood. In-vivo imaging analysis of synapse formation at the neuromuscular junction of anaesthetised Drosophila third instar larvae allows for spatial and temporal resolution of the underlying molecular processes. However, high-throughput, comprehensive analysis are hampered by the manual and time-consuming imaging analysis methods applied hitherto. Here, we focus on the early presynaptic formation steps, that is, the presynaptic seeding, initiated by the formation of transient Liprin-a/SYD1 seeding sites, either stabilised or disintegrated over a time span of 30-90 min.
Results:
To investigate the dynamics of the Liprin-a/SYD1 seeding sites, we developed an automated analysis pipeline for 3D confocal images from in-vivo imaging at distinct time points to analyse fluorescently labelled presynaptic protein dynamics during early synapse formation. The workflow is realised in the data analysis software Amira, utilising the hierarchical watershed algorithm, and was designed for automatic processing with an option for manual proofreading. Compared to the previous 2D manual quantification, this automated approach provides a higher sensitivity in single Liprin-a seeding site detection in low-intensity areas and in regions of dense seeding sites.In addition, it substantially reduces the work time. To account for possible errors occurring in the automated processing, we implemented an additional proofreading step allowing for a manual correction of Liprin-a seeding site segmentation and assignment, thus greatly improving the analysis while only marginally increasing work time by 10% to a total work time reduction of 80% compared to the 2D manual analysis paradigm.
Conclusion:
The process of synaptogenesis underlies the general principles of locomotion, learning and memory formation. The developed fast and accurate semi-automated 3D workflow provides a substantial progress in the analysis of this molecular process and its application can be easily extended to other dynamic in-vivo research approaches across species.