Single-molecule analysis reveals agonist-specific dimer formation of µ-opioid receptors.

G-protein-coupled receptors (GPCRs) are key signaling proteins that mostly function as monomers, but for several receptors constitutive dimer formation has been described and in some cases is essential for function. Using single-molecule microscopy combined with super-resolution techniques on intact cells, we describe here a dynamic monomer-dimer equilibrium of µ-opioid receptors (µORs), where dimer formation is driven by specific agonists. The agonist DAMGO, but not morphine, induces dimer formation in a process that correlates both temporally and in its agonist- and phosphorylation-dependence with ß-arrestin2 binding to the receptors. This dimerization is independent from, but may precede, µOR internalization. These data suggest a new level of GPCR regulation that links dimer formation to specific agonists and their downstream signals.

Multiscale molecular kinetics by coupling Markov state models and reaction-diffusion dynamics.

A novel approach to simulate simple protein-ligand systems at large time and length scales is to couple Markov state models (MSMs) of molecular kinetics with particle-based reaction-diffusion (RD) simulations, MSM/RD. Currently, MSM/RD lacks a mathematical framework to derive coupling schemes, is limited to isotropic ligands in a single conformational state, and lacks multiparticle extensions. In this work, we address these needs by developing a general MSM/RD framework by coarse-graining molecular dynamics into hybrid switching diffusion processes. Given enough data to parameterize the model, it is capable of modeling protein-protein interactions over large time and length scales, and it can be extended to handle multiple molecules. We derive the MSM/RD framework, and we implement and verify it for two protein-protein benchmark systems and one multiparticle implementation to model the formation of pentameric ring molecules. To enable reproducibility, we have published our code in the MSM/RD software package.

Modeling of Drug Diffusion Based on Concentration Profiles in Healthy and Damaged Human Skin.

Based on experimental drug concentration profiles in healthy as well as tape-stripped ex vivo human skin, we model the penetration of the antiinflammatory drug dexamethasone into the skin layers by the one-dimensional generalized diffusion equation. We estimate the position-dependent free-energy and diffusivity profiles by solving the conjugated minimization problem, in which the only inputs are concentration profiles of dexamethasone in skin at three consecutive penetration times. The resulting free-energy profiles for damaged and healthy skin show only minor differences. In contrast, the drug diffusivity in the first 10 µm of the upper skin layer of damaged skin is 200-fold increased compared to healthy skin, which reflects the corrupted barrier function of tape-stripped skin. For the case of healthy skin, we examine the robustness of our method by analyzing the behavior of the extracted skin parameters when the number of input and output parameters are reduced. We also discuss techniques for the regularization of our parameter extraction method.

Role of bone morphogenetic proteins in sprouting angiogenesis: differential BMP receptor-dependent signaling pathways balance stalk vs. tip cell competence.

Before the onset of sprouting angiogenesis, the endothelium is prepatterned for the positioning of tip and stalk cells. Both cell identities are not static, as endothelial cells (ECs) constantly compete for the tip cell position in a dynamic fashion. Here, we show that both bone morphogenetic protein 2 (BMP2) and BMP6 are proangiogenic in vitro and ex vivo and that the BMP type I receptors, activin receptor-like kinase 3 (ALK3) and ALK2, play crucial and distinct roles in this process. BMP2 activates the expression of tip cell-associated genes, such as delta-like ligand 4 (DLL4) and kinase insert domain receptor (KDR), and p38-heat shock protein 27 (HSP27)-dependent cell migration, thereby generating tip cell competence. Whereas BMP6 also triggers collective cell migration via the p38-HSP27 signaling axis, BMP6 induces in addition SMAD1/5 signaling, thereby promoting the expression of stalk cell-associated genes, such as hairy and enhancer of split 1 (HES1) and fms-like tyrosine kinase 1 (FLT1). Specifically, ALK3 is required for sprouting from HUVEC spheroids, whereas ALK2 represses sprout formation. We demonstrate that expression levels and respective complex formation of BMP type I receptors in ECs determine stalk vs. tip cell identity, thus contributing to endothelial plasticity during sprouting angiogenesis. As antiangiogenic monotherapies that target the VEGF or ALK1 pathways have not fulfilled efficacy objectives in clinical trials, the selective targeting of the ALK2/3 pathways may be an attractive new approach.-Benn, A., Hiepen, C., Osterland, M., Schütte, C., Zwijsen, A., Knaus, P. Role of bone morphogenetic proteins in sprouting angiogenesis: differential BMP receptor-dependent signaling pathways balance stalk vs. tip cell competence.

Data-driven computation of molecular reaction coordinates.

The identification of meaningful reaction coordinates plays a key role in the study of complex molecular systems whose essential dynamics are characterized by rare or slow transition events. In a recent publication, precise defining characteristics of such reaction coordinates were identified and linked to the existence of a so-called transition manifold. This theory gives rise to a novel numerical method for the pointwise computation of reaction coordinates that relies on short parallel MD simulations only, but yields accurate approximation of the long time behavior of the system under consideration. This article presents an extension of the method towards practical applicability in computational chemistry. It links the newly defined reaction coordinates to concepts from transition path theory and Markov state model building. The main result is an alternative computational scheme that allows for a global computation of reaction coordinates based on commonly available types of simulation data, such as single long molecular trajectories or the push-forward of arbitrary canonically distributed point clouds. It is based on a Galerkin approximation of the transition manifold reaction coordinates that can be tuned to individual requirements by the choice of the Galerkin ansatz functions. Moreover, we propose a ready-to-implement variant of the new scheme, which computes data-fitted, mesh-free ansatz functions directly from the available simulation data. The efficacy of the new method is demonstrated on a small protein system.

A kernel-based approach to molecular conformation analysis.

We present a novel machine learning approach to understand conformation dynamics of biomolecules. The approach combines kernel-based techniques that are popular in the machine learning community with transfer operator theory for analyzing dynamical systems in order to identify conformation dynamics based on molecular dynamics simulation data. We show that many of the prominent methods like Markov state models, extended dynamic mode decomposition (EDMD), and time-lagged independent component analysis (TICA) can be regarded as special cases of this approach and that new efficient algorithms can be constructed based on this derivation. The results of these new powerful methods will be illustrated with several examples, in particular, the alanine dipeptide and the protein NTL9.

MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations.

Molecular dynamics (MD) simulations can model the interactions between macromolecules with high spatiotemporal resolution but at a high computational cost. By combining high-throughput MD with Markov state models (MSMs), it is now possible to obtain long time-scale behavior of small to intermediate biomolecules and complexes. To model the interactions of many molecules at large length scales, particle-based reaction-diffusion (RD) simulations are more suitable but lack molecular detail. Thus, coupling MSMs and RD simulations (MSM/RD) would be highly desirable, as they could efficiently produce simulations at large time and length scales, while still conserving the characteristic features of the interactions observed at atomic detail. While such a coupling seems straightforward, fundamental questions are still open: Which definition of MSM states is suitable? Which protocol to merge and split RD particles in an association/dissociation reaction will conserve the correct bimolecular kinetics and thermodynamics? In this paper, we make the first step toward MSM/RD by laying out a general theory of coupling and proposing a first implementation for association/dissociation of a protein with a small ligand (A + B ⇌ C). Applications on a toy model and CO diffusion into the heme cavity of myoglobin are reported.

Sparse Proteomics Analysis - a compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data.

BACKGROUND: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often interested in how mass spectra differ between patients of different classes, for example spectra from healthy patients vs. spectra from patients having a particular disease. Machine learning algorithms are needed to (a) identify these discriminating features and (b) classify unknown spectra based on this feature set. Since the acquired data is usually noisy, the algorithms should be robust against noise and outliers, while the identified feature set should be as small as possible. RESULTS: We present a new algorithm, Sparse Proteomics Analysis (SPA), based on the theory of compressed sensing that allows us to identify a minimal discriminating set of features from mass spectrometry data-sets. We show (1) how our method performs on artificial and real-world data-sets, (2) that its performance is competitive with standard (and widely used) algorithms for analyzing proteomics data, and (3) that it is robust against random and systematic noise. We further demonstrate the applicability of our algorithm to two previously published clinical data-sets.

Hybrid models for chemical reaction networks: Multiscale theory and application to gene regulatory systems.

Well-mixed stochastic chemical kinetics are properly modeled by the chemical master equation (CME) and associated Markov jump processes in molecule number space. If the reactants are present in large amounts, however, corresponding simulations of the stochastic dynamics become computationally expensive and model reductions are demanded. The classical model reduction approach uniformly rescales the overall dynamics to obtain deterministic systems characterized by ordinary differential equations, the well-known mass action reaction rate equations. For systems with multiple scales, there exist hybrid approaches that keep parts of the system discrete while another part is approximated either using Langevin dynamics or deterministically. This paper aims at giving a coherent overview of the different hybrid approaches, focusing on their basic concepts and the relation between them. We derive a novel general description of such hybrid models that allows expressing various forms by one type of equation. We also check in how far the approaches apply to model extensions of the CME for dynamics which do not comply with the central well-mixed condition and require some spatial resolution. A simple but meaningful gene expression system with negative self-regulation is analysed to illustrate the different approximation qualities of some of the hybrid approaches discussed. Especially, we reveal the cause of error in the case of small volume approximations.

Set-free Markov state model building.

Molecular dynamics (MD) simulations face challenging problems since the time scales of interest often are much longer than what is possible to simulate; and even if sufficiently long simulations are possible the complex nature of the resulting simulation data makes interpretation difficult. Markov State Models (MSMs) help to overcome these problems by making experimentally relevant time scales accessible via coarse grained representations that also allow for convenient interpretation. However, standard set-based MSMs exhibit some caveats limiting their approximation quality and statistical significance. One of the main caveats results from the fact that typical MD trajectories repeatedly re-cross the boundary between the sets used to build the MSM which causes statistical bias in estimating the transition probabilities between these sets. In this article, we present a set-free approach to MSM building utilizing smooth overlapping ansatz functions instead of sets and an adaptive refinement approach. This kind of meshless discretization helps to overcome the recrossing problem and yields an adaptive refinement procedure that allows us to improve the quality of the model while exploring state space and inserting new ansatz functions into the MSM.

Optimal Treatment Strategies in the Context of 'Treatment for Prevention' against HIV-1 in Resource-Poor Settings.

An estimated 2.7 million new HIV-1 infections occurred in 2010. `Treatment-for-prevention' may strongly prevent HIV-1 transmission. The basic idea is that immediate treatment initiation rapidly decreases virus burden, which reduces the number of transmittable viruses and thereby the probability of infection. However, HIV inevitably develops drug resistance, which leads to virus rebound and nullifies the effect of `treatment-for-prevention' for the time it remains unrecognized. While timely conducted treatment changes may avert periods of viral rebound, necessary treatment options and diagnostics may be lacking in resource-constrained settings. Within this work, we provide a mathematical platform for comparing different treatment paradigms that can be applied to many medical phenomena. We use this platform to optimize two distinct approaches for the treatment of HIV-1: (i) a diagnostic-guided treatment strategy, based on infrequent and patient-specific diagnostic schedules and (ii) a pro-active strategy that allows treatment adaptation prior to diagnostic ascertainment. Both strategies are compared to current clinical protocols (standard of care and the HPTN052 protocol) in terms of patient health, economic means and reduction in HIV-1 onward transmission exemplarily for South Africa. All therapeutic strategies are assessed using a coarse-grained stochastic model of within-host HIV dynamics and pseudo-codes for solving the respective optimal control problems are provided. Our mathematical model suggests that both optimal strategies (i)-(ii) perform better than the current clinical protocols and no treatment in terms of economic means, life prolongation and reduction of HIV-transmission. The optimal diagnostic-guided strategy suggests rare diagnostics and performs similar to the optimal pro-active strategy. Our results suggest that 'treatment-for-prevention' may be further improved using either of the two analyzed treatment paradigms.

Effective dynamics along given reaction coordinates, and reaction rate theory.

In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: we first show that if we start with an ergodic diffusion process whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Mori-Zwanzig, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the "equation-free" approach and the "heterogeneous multiscale method" can be seen as special cases of our approach.

The spatiotemporal master equation: Approximation of reaction-diffusion dynamics via Markov state modeling.

Accurate modeling and numerical simulation of reaction kinetics is a topic of steady interest. We consider the spatiotemporal chemical master equation (ST-CME) as a model for stochastic reaction-diffusion systems that exhibit properties of metastability. The space of motion is decomposed into metastable compartments, and diffusive motion is approximated by jumps between these compartments. Treating these jumps as first-order reactions, simulation of the resulting stochastic system is possible by the Gillespie method. We present the theory of Markov state models as a theoretical foundation of this intuitive approach. By means of Markov state modeling, both the number and shape of compartments and the transition rates between them can be determined. We consider the ST-CME for two reaction-diffusion systems and compare it to more detailed models. Moreover, a rigorous formal justification of the ST-CME by Galerkin projection methods is presented.

On metastability and Markov state models for non-stationary molecular dynamics.

Unlike for systems in equilibrium, a straightforward definition of a metastable set in the non-stationary, non-equilibrium case may only be given case-by-case-and therefore it is not directly useful any more, in particular in cases where the slowest relaxation time scales are comparable to the time scales at which the external field driving the system varies. We generalize the concept of metastability by relying on the theory of coherent sets. A pair of sets A and B is called coherent with respect to the time interval [t1, t2] if (a) most of the trajectories starting in A at t1 end up in B at t2 and (b) most of the trajectories arriving in B at t2 actually started from A at t1. Based on this definition, we can show how to compute coherent sets and then derive finite-time non-stationary Markov state models. We illustrate this concept and its main differences to equilibrium Markov state modeling on simple, one-dimensional examples.

Influence of pH and sequence in peptide aggregation via molecular simulation.

We employ a recently developed coarse-grained model for peptides and proteins where the effect of pH is automatically included. We explore the effect of pH in the aggregation process of the amyloidogenic peptide KTVIIE and two related sequences, using three different pH environments. Simulations using large systems (24 peptides chains per box) allow us to describe the formation of realistic peptide aggregates. We evaluate the thermodynamic and kinetic implications of changes in sequence and pH upon peptide aggregation, and we discuss how a minimalistic coarse-grained model can account for these details.

Chemical potential of liquids and mixtures via adaptive resolution simulation.

We employ the adaptive resolution approach AdResS, in its recently developed Grand Canonical-like version (GC-AdResS) [H. Wang, C. Hartmann, C. Schütte, and L. Delle Site, Phys. Rev. X 3, 011018 (2013)], to calculate the excess chemical potential, µ(ex), of various liquids and mixtures. We compare our results with those obtained from full atomistic simulations using the technique of thermodynamic integration and show a satisfactory agreement. In GC-AdResS, the procedure to calculate µ(ex) corresponds to the process of standard initial equilibration of the system; this implies that, independently of the specific aim of the study, µ(ex), for each molecular species, is automatically calculated every time a GC-AdResS simulation is performed.

Partial mean-field model for neurotransmission dynamics.

This article addresses reaction networks in which spatial and stochastic effects are of crucial importance. For such systems, particle-based models allow us to describe all microscopic details with high accuracy. However, they suffer from computational inefficiency if particle numbers and density get too large. Alternative coarse-grained-resolution models reduce computational effort tremendously, e.g., by replacing the particle distribution by a continuous concentration field governed by reaction-diffusion PDEs. We demonstrate how models on the different resolution levels can be combined into hybrid models that seamlessly combine the best of both worlds, describing molecular species with large copy numbers by macroscopic equations with spatial resolution while keeping the spatial-stochastic particle-based resolution level for the species with low copy numbers. To this end, we introduce a simple particle-based model for the binding dynamics of ions and vesicles at the heart of the neurotransmission process. Within this framework, we derive a novel hybrid model and present results from numerical experiments which demonstrate that the hybrid model allows for an accurate approximation of the full particle-based model in realistic scenarios.

Characterising information gains and losses when collecting multiple epidemic model outputs.

BACKGROUND: Collaborative comparisons and combinations of epidemic models are used as policy-relevant evidence during epidemic outbreaks. In the process of collecting multiple model projections, such collaborations may gain or lose relevant information. Typically, modellers contribute a probabilistic summary at each time-step. We compared this to directly collecting simulated trajectories. We aimed to explore information on key epidemic quantities; ensemble uncertainty; and performance against data, investigating potential to continuously gain information from a single cross-sectional collection of model results. METHODS: We compared projections from the European COVID-19 Scenario Modelling Hub. Five teams modelled incidence in Belgium, the Netherlands, and Spain. We compared July 2022 projections by incidence, peaks, and cumulative totals. We created a probabilistic ensemble drawn from all trajectories, and compared to ensembles from a median across each model's quantiles, or a linear opinion pool. We measured the predictive accuracy of individual trajectories against observations, using this in a weighted ensemble. We repeated this sequentially against increasing weeks of observed data. We evaluated these ensembles to reflect performance with varying observed data. RESULTS: By collecting modelled trajectories, we showed policy-relevant epidemic characteristics. Trajectories contained a right-skewed distribution well represented by an ensemble of trajectories or a linear opinion pool, but not models' quantile intervals. Ensembles weighted by performance typically retained the range of plausible incidence over time, and in some cases narrowed this by excluding some epidemic shapes. CONCLUSIONS: We observed several information gains from collecting modelled trajectories rather than quantile distributions, including potential for continuously updated information from a single model collection. The value of information gains and losses may vary with each collaborative effort's aims, depending on the needs of projection users. Understanding the differing information potential of methods to collect model projections can support the accuracy, sustainability, and communication of collaborative infectious disease modelling efforts.

HIV-1 polymerase inhibition by nucleoside analogs: cellular- and kinetic parameters of efficacy, susceptibility and resistance selection.

Nucleoside analogs (NAs) are used to treat numerous viral infections and cancer. They compete with endogenous nucleotides (dNTP/NTP) for incorporation into nascent DNA/RNA and inhibit replication by preventing subsequent primer extension. To date, an integrated mathematical model that could allow the analysis of their mechanism of action, of the various resistance mechanisms, and their effect on viral fitness is still lacking. We present the first mechanistic mathematical model of polymerase inhibition by NAs that takes into account the reversibility of polymerase inhibition. Analytical solutions for the model point out the cellular- and kinetic aspects of inhibition. Our model correctly predicts for HIV-1 that resistance against nucleoside analog reverse transcriptase inhibitors (NRTIs) can be conferred by decreasing their incorporation rate, increasing their excision rate, or decreasing their affinity for the polymerase enzyme. For all analyzed NRTIs and their combinations, model-predicted macroscopic parameters (efficacy, fitness and toxicity) were consistent with observations. NRTI efficacy was found to greatly vary between distinct target cells. Surprisingly, target cells with low dNTP/NTP levels may not confer hyper-susceptibility to inhibition, whereas cells with high dNTP/NTP contents are likely to confer natural resistance. Our model also allows quantification of the selective advantage of mutations by integrating their effects on viral fitness and drug susceptibility. For zidovudine triphosphate (AZT-TP), we predict that this selective advantage, as well as the minimal concentration required to select thymidine-associated mutations (TAMs) are highly cell-dependent. The developed model allows studying various resistance mechanisms, inherent fitness effects, selection forces and epistasis based on microscopic kinetic data. It can readily be embedded in extended models of the complete HIV-1 reverse transcription process, or analogous processes in other viruses and help to guide drug development and improve our understanding of the mechanisms of resistance development during treatment.