Rate-limiting recovery processes in neurotransmission under sustained stimulation.

At active zones of chemical synapses, an arriving electric signal induces the fusion of vesicles with the presynaptic membrane, thereby releasing neurotransmitters into the synaptic cleft. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. Of central interest is the question which of the two restoration steps acts as the limiting factor during neurotransmission under high-frequency sustained stimulation. In order to investigate this problem, we introduce a non-linear reaction network which involves explicit recovery steps for both the vesicles and the release sites, and includes the induced time-dependent output current. The associated reaction dynamics are formulated by means of ordinary differential equations (ODEs), as well as via the associated stochastic jump process. While the stochastic jump model describes the dynamics at a single active zone, the average over many active zones is close to the ODE solution and shares its periodic structure. The reason for this can be traced back to the insight that recovery dynamics of vesicles and release sites are statistically almost independent. A sensitivity analysis on the recovery rates based on the ODE formulation reveals that neither the vesicle nor the release site recovery step can be identified as the essential rate-limiting step but that the rate-limiting feature changes over the course of stimulation. Under sustained stimulation, the dynamics given by the ODEs exhibit transient changes leading from an initial depression of the postsynaptic response to an asymptotic periodic orbit, while the individual trajectories of the stochastic jump model lack the oscillatory behavior and asymptotic periodicity of the ODE-solution.

The Effect of Time Spent With Participants on Program Outcomes.

PURPOSE OF STUDY: Little research exists on the correlation between time spent with participants in Critical Time Intervention-modeled programs, such as Coordinated Behavioral Care's (CBC) Pathway Home, and successful completion of the programs. This study explored associations between the total amount of time spent with participants in the initial 3 months of the program and positive program outcomes. METHODOLOGY AND SAMPLE: Data on total time spent with participants in their initial phase of the program were gathered from Pathway Home participants who were enrolled in the program from 2016 to 2019 and then were compared with program outcomes. RESULTS: The study found positive correlations between amount of time spent with participants and the attendance of a behavioral health appointment within 1 month of community entry, and positive disenrollment outcomes. This study did not find predictive significance of time spent. IMPLICATIONS FOR CASE MANAGEMENT PRACTICE: Time spent with participants is a significant variable to study, yet more research is needed on its relationship to positive outcomes.

Variance of filtered signals: Characterization for linear reaction networks and application to neurotransmission dynamics.

Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance of the synaptic vesicle to the calcium channels determines the release probability and consequently 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.

Neural tube patterning: from a minimal model for rostrocaudal patterning toward an integrated 3D model.

Rostrocaudal patterning of the neural tube is a defining event in vertebrate brain development. This process is driven by morphogen gradients which specify the fate of neural progenitor cells, leading to the partitioning of the tube. Although this is extensively studied experimentally, an integrated view of the genetic circuitry is lacking. Here, we present a minimal gene regulatory model for rostrocaudal patterning, whose tristable topology was determined in a data-driven way. Using this model, we identified the repression of hindbrain fate as promising strategy for the improvement of current protocols for the generation of dopaminergic neurons. Furthermore, we combined our model with an established minimal model for dorsoventral patterning on a realistic 3D neural tube and found that key features of neural tube patterning could be recapitulated. Doing so, we demonstrate how data and models from different sources can be combined to simulate complex in vivo processes.