Sub-membrane actin rings compartmentalize the plasma membrane

The compartmentalization of the plasma membrane (PM) is a fundamental feature of cells. The diffusivity of membrane proteins is significantly lower in biological than in artificial membranes. This is likely due to actin filaments, but assays to prove a direct dependence remain elusive. We recently showed that periodic actin rings in the neuronal axon initial segment (AIS) confine membrane protein motion between them. Still, the local enrichment of ion channels offers an alternative explanation. Here we show, using computational modeling, that in contrast to actin rings, ion channels in the AIS cannot mediate confinement. Furthermore, we show, employing a combinatorial approach of single particle tracking and super-resolution microscopy, that actin rings are close to the PM and that they confine membrane proteins in several neuronal cell types. Finally, we show that actin disruption leads to loss of compartmentalization. Taken together, we here develop a system for the investigation of membrane compartmentalization and show that actin rings compartmentalize the PM

Learning Koopman eigenfunctions of stochastic diffusions with optimal importance sampling and ISOKANN

The dominant eigenfunctions of the Koopman operator characterize the metastabilities and slow-timescale dynamics of stochastic diffusion processes. In the context of molecular dynamics and Markov state modeling, they allow for a description of the location and frequencies of rare transitions, which are hard to obtain by direct simulation alone. In this article, we reformulate the eigenproblem in terms of the ISOKANN framework, an iterative algorithm that learns the eigenfunctions by alternating between short burst simulations and a mixture of machine learning and classical numerics, which naturally leads to a proof of convergence. We furthermore show how the intermediate iterates can be used to reduce the sampling variance by importance sampling and optimal control (enhanced sampling), as well as to select locations for further training (adaptive sampling). We demonstrate the usage of our proposed method in experiments, increasing the approximation accuracy by several orders of magnitude

Clinical Effectiveness of Ritonavir-Boosted Nirmatrelvir—A Literature Review

Nirmatrelvir/Ritonavir is an oral treatment for mild to moderate COVID-19 cases with a high risk for a severe course of the disease. For this paper, a comprehensive literature review was performed, leading to a summary of currently available data on Nirmatrelvir/Ritonavir’s ability to reduce the risk of progressing to a severe disease state. Herein, the focus lies on publications that include comparisons between patients receiving Nirmatrelvir/Ritonavir and a control group. The findings can be summarized as follows: Data from the time when the Delta-variant was dominant show that Nirmatrelvir/Ritonavir reduced the risk of hospitalization or death by 88.9% for unvaccinated, non-hospitalized high-risk individuals. Data from the time when the Omicron variant was dominant found decreased relative risk reductions for various vaccination statuses: between 26% and 65% for hospitalization. The presented papers that differentiate between unvaccinated and vaccinated individuals agree that unvaccinated patients benefit more from treatment with Nirmatrelvir/Ritonavir. However, when it comes to the dependency of potential on age and comorbidities, further studies are necessary. From the available data, one can conclude that Nirmatrelvir/Ritonavir cannot substitute vaccinations; however, its low manufacturing cost and easy administration make it a valuable tool in fighting COVID-19, especially for countries with low vaccination rates

Explicit Modelling of Antibody Levels for Infectious Disease Simulations in the Context of SARS-CoV-2

Measurable levels of immunoglobulin G antibodies develop after infections with and vaccinations against severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). These antibody levels are dynamic: due to waning, antibody levels will drop over time. During the COVID-19 pandemic, multiple models predicting infection dynamics were used by policymakers to support the planning of public health policies. Explicitly integrating antibody and waning effects into the models is crucial for reliable calculations of individual infection risk. However, only few approaches have been suggested that explicitly treat these effects. This paper presents a methodology that explicitly models antibody levels and the resulting protection against infection for individuals within an agent-based model. The model was developed in response to the complexity of different immunization sequences and types and is based on neutralization titer studies. This approach allows complex population studies with explicit antibody and waning effects. We demonstrate the usefulness of our model in two use cases

Canards in modified equations for Euler discretizations

Canards are a well-studied phenomenon in fast-slow ordinary differential equations implying the delayed loss of stability after the slow passage through a singularity. Recent studies have shown that the corresponding maps stemming from explicit Runge-Kutta discretizations, in particular the forward Euler scheme, exhibit significant distinctions to the continuous-time behavior: for folds, the delay in loss of stability is typically shortened whereas, for transcritical singularities, it is arbitrarily prolonged. We employ the method of modified equations, which correspond with the fixed discretization schemes up to higher order, to understand and quantify these effects directly from a fast-slow ODE, yielding consistent results with the discrete-time behavior and opening a new perspective on the wide range of (de-)stabilization phenomena along canards

Nonnegative matrix factorization for coherent set identification by direct low rank maximum likelihood estimation

We analyze connections between two low rank modeling approaches from the last decade for treating dynamical data. The first one is the coherence problem (or coherent set approach), where groups of states are sought that evolve under the action of a stochastic matrix in a way maximally distinguishable from other groups. The second one is a low rank factorization approach for stochastic matrices, called Direct Bayesian Model Reduction (DBMR), which estimates the low rank factors directly from observed data. We show that DBMR results in a low rank model that is a projection of the full model, and exploit this insight to infer bounds on a quantitative measure of coherence within the reduced model. Both approaches can be formulated as optimization problems, and we also prove a bound between their respective objectives. On a broader scope, this work relates the two classical loss functions of nonnegative matrix factorization, namely the Frobenius norm and the generalized Kullback–Leibler divergence, and suggests new links between likelihood- based and projection-based estimation of probabilistic models

Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics

Coarse-grained (CG) molecular dynamics enables the study of biological processes at temporal and spatial scales that would be intractable at an atomistic resolution. However, accurately learning a CG force field remains a challenge. In this work, we leverage connections between score-based generative models, force fields and molecular dynamics to learn a CG force field without requiring any force inputs during training. Specifically, we train a diffusion generative model on protein structures from molecular dynamics simulations, and we show that its score function approximates a force field that can directly be used to simulate CG molecular dynamics. While having a vastly simplified training setup compared to previous work, we demonstrate that our approach leads to improved performance across several small- to medium-sized protein simulations, reproducing the CG equilibrium distribution, and preserving dynamics of all-atom simulations such as protein folding events

Workshop Report 21w5167 Optimization under Uncertainty: Learning and Decision Making in 2021

This workshop brought together researchers in optimization under uncertainty and uncertainty quantification, whose work stands to benefit from cutting-edge machine learning techniques for data-driven differential equations. The workshop focused on mathematical challenges at the interface of applied mathematics, optimization, probability and statistics, and machine learning. Through eleven scientific talks, three panel discussions, and unstructured interactions, the workshop facilitated an exchange of ideas towards new, powerful methods for optimization under uncertainty. In what follows, we give an overview of the presentations, discussions, and outcomes