Non-stationary filtered shot noise processes and applications to neuronal membranes

Filtered shot noise processes have proven to be very effective in modelling the evolution of systems exposed to stochastic shot noise sources, and have been applied to a wide variety of fields ranging from electronics through biology. In particular, they can model the membrane potential Vm of neurons driven by stochastic input, where these filtered processes are able to capture the non-stationary characteristics of Vm fluctuations in response to pre-synaptic input with variable rate. In this paper, we apply the general framework of Poisson Point Processes transformations to analyse these systems in the general case of variable input rate. We obtain exact analytic expressions, and very accurate approximations, for the joint cumulants of filtered shot noise processes with multiplicative noise. These general results are then applied to a model of neuronal membranes subject to conductance shot noise with continuously variable rate of pre-synaptic spikes. We propose very effective approximations for the time evolution of Vm distribution and simple method to estimate the pre-synaptic rate from a small number of Vm traces. This work opens the perspective of obtaining analytic access to important statistical properties of conductance-based neuronal models such as the the first passage time.Comment: 18 pages, 13 figure

Dynamique stochastique non-stationnaire de la membrane neuronale

Neurons interact through their membrane potential that generally has a complex time evolution due to numerous irregular synaptic inputs received. This complex time evolution is best described in probabilistic terms due to this irregular or "noisy" activity. The time evolution of the membrane potential is therefore both stochastic and deterministic: it is stochastic since it is driven by random input arrival times, but also deterministic, since subjecting a biological neuron to the same sequence of input arrival times often results in very similar membrane potential traces. In this thesis, we investigated key statistical properties of a simplified neuron model under nonstationary input from other neurons that results in nonstationary evolution of membrane potential statistics. We considered a passive neuron model without spiking mechanism that is driven by input currents or conductances in the form of shot noise processes. Under such input, membrane potential fluctuations can be modeled as filtered shot noise currents or conductances. We analyzed the statistical properties of these filtered processes in the framework of Poisson Point Processes transformations. The key idea is to express filtered shot noise as a transformation of random input arrival times and to apply the properties of these transformations to derive its nonstationary statistics. Using this formalism we derive exact analytical expressions, and useful approximations, for the mean and joint cumulants of the filtered process in the general case of variable input rate. This work opens many perspectives for analyzing neurons under in vivo conditions, in the presence of intense and noisy synaptic inputs.Les neurones interagissent à travers leur potentiel de membrane qui a en général une évolution temporelle complexe due aux nombreuses entrées synaptiques irrégulières reçues. Cette évolution est mieux décrite en termes probabilistes, en raison de ces entrées irrégulières ou «bruit synaptique». L'évolution temporelle du potentiel de membrane est stochastique mais aussi déterministe: stochastique, car conduite par des entrées synaptiques qui arrivent de façon aléatoire dans le temps, et déterministe, car un neurone biologique a une évolution temporelle très similaire quand soumis à une même séquence d'entrées synaptiques. Nous étudions les propriétés statistiques d'un modèle simplifié de neurone soumis à des entrées à taux variable d'où en résulte l'évolution non-stationnaire du potentiel de membrane. Nous considérons un modèle passif de membrane neuronale, sans mécanisme de décharge neuronale, soumis à des entrées à courant ou à conductance sous la forme d'un processus de «shot noise». Les fluctuations du potentiel de membrane sont aussi modélisées par un processus stochastique similaire, de «shot noise» filtré. Nous avons analysé les propriétés statistiques de ces processus dans le cadre des transformations de processus ponctuels de Poisson. Des propriétés de ces transformations sont dérivées les statistiques non-stationnaires du processus. Nous obtenons ainsi des expressions analytiques exactes pour les moments et cumulants du processus filtré dans le cas général des taux d'entrée variables. Ce travail ouvre de nombreuses perspectives pour l'analyse de neurones dans les conditions in vivo, en présence d'entrées synaptiques intenses et bruitées

Neuromatch Academy: a 3-week, online summer school in computational neuroscience

Neuromatch Academy (https://academy.neuromatch.io; (van Viegen et al., 2021)) was designed as an online summer school to cover the basics of computational neuroscience in three weeks. The materials cover dominant and emerging computational neuroscience tools, how they complement one another, and specifically focus on how they can help us to better understand how the brain functions. An original component of the materials is its focus on modeling choices, i.e. how do we choose the right approach, how do we build models, and how can we evaluate models to determine if they provide real (meaningful) insight. This meta-modeling component of the instructional materials asks what questions can be answered by different techniques, and how to apply them meaningfully to get insight about brain function

Mortality and pulmonary complications in patients undergoing surgery with perioperative SARS-CoV-2 infection: an international cohort study

Background: The impact of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) on postoperative recovery needs to be understood to inform clinical decision making during and after the COVID-19 pandemic. This study reports 30-day mortality and pulmonary complication rates in patients with perioperative SARS-CoV-2 infection. Methods: This international, multicentre, cohort study at 235 hospitals in 24 countries included all patients undergoing surgery who had SARS-CoV-2 infection confirmed within 7 days before or 30 days after surgery. The primary outcome measure was 30-day postoperative mortality and was assessed in all enrolled patients. The main secondary outcome measure was pulmonary complications, defined as pneumonia, acute respiratory distress syndrome, or unexpected postoperative ventilation. Findings: This analysis includes 1128 patients who had surgery between Jan 1 and March 31, 2020, of whom 835 (74·0%) had emergency surgery and 280 (24·8%) had elective surgery. SARS-CoV-2 infection was confirmed preoperatively in 294 (26·1%) patients. 30-day mortality was 23·8% (268 of 1128). Pulmonary complications occurred in 577 (51·2%) of 1128 patients; 30-day mortality in these patients was 38·0% (219 of 577), accounting for 81·7% (219 of 268) of all deaths. In adjusted analyses, 30-day mortality was associated with male sex (odds ratio 1·75 [95% CI 1·28–2·40], p\textless0·0001), age 70 years or older versus younger than 70 years (2·30 [1·65–3·22], p\textless0·0001), American Society of Anesthesiologists grades 3–5 versus grades 1–2 (2·35 [1·57–3·53], p\textless0·0001), malignant versus benign or obstetric diagnosis (1·55 [1·01–2·39], p=0·046), emergency versus elective surgery (1·67 [1·06–2·63], p=0·026), and major versus minor surgery (1·52 [1·01–2·31], p=0·047). Interpretation: Postoperative pulmonary complications occur in half of patients with perioperative SARS-CoV-2 infection and are associated with high mortality. Thresholds for surgery during the COVID-19 pandemic should be higher than during normal practice, particularly in men aged 70 years and older. Consideration should be given for postponing non-urgent procedures and promoting non-operative treatment to delay or avoid the need for surgery. Funding: National Institute for Health Research (NIHR), Association of Coloproctology of Great Britain and Ireland, Bowel and Cancer Research, Bowel Disease Research Foundation, Association of Upper Gastrointestinal Surgeons, British Association of Surgical Oncology, British Gynaecological Cancer Society, European Society of Coloproctology, NIHR Academy, Sarcoma UK, Vascular Society for Great Britain and Ireland, and Yorkshire Cancer Research

Inhibition of APP gamma-secretase restores Sonic Hedgehog signaling and neurogenesis in the Ts65Dn mouse model of Down syndrome

Neurogenesis impairment starting from early developmental stages is a key determinant of intellectual disability in Down syndrome (DS). Previous evidence provided a causal relationship between neurogenesis impairment and malfunctioning of the mitogenic Sonic Hedgehog (Shh) pathway. In particular, excessive levels of AICD (amyloid precursor protein intracellular domain), a cleavage product of the trisomic gene APP (amyloid precursor protein) up-regulate transcription of Ptch1 (Patched1), the Shh receptor that keeps the pathway repressed. Since AICD results from APP cleavage by \u3b3-secretase, the goal of the current study was to establish whether treatment with a \u3b3-secretase inhibitor normalizes AICD levels and restores neurogenesis in trisomic neural precursor cells. We found that treatment with a selective \u3b3-secretase inhibitor (ELND006; ELN) restores proliferation in neurospheres derived from the subventricular zone (SVZ) of the Ts65Dn mouse model of DS. This effect was accompanied by reduction of AICD and Ptch1 levels and was prevented by inhibition of the Shh pathway with cyclopamine. Treatment of Ts65Dn mice with ELN in the postnatal period P3-P15 restored neurogenesis in the SVZ and hippocampus, hippocampal granule cell number and synapse development, indicating a positive impact of treatment on brain development. In addition, in the hippocampus of treated Ts65Dn mice there was a reduction in the expression levels of various genes that are transcriptionally regulated by AICD, including APP, its origin substrate. Inhibitors of \u3b3-secretase are currently envisaged as tools for the cure of Alzheimer's disease because they lower \u3b2amyloid levels. Current results provide novel evidence that \u3b3-secretase inhibitors may represent a strategy for the rescue of neurogenesis defects in DS