Fast and Accurate Maximum-Likelihood Estimation of Multi-Type Birth-Death Epidemiological Models from Phylogenetic Trees

Multi-type birth-death (MTBD) models are phylodynamic analogies of compartmental models in classical epidemiology. They serve to infer such epidemiological parameters as the average number of secondary infections Re and the infectious time from a phylogenetic tree (a genealogy of pathogen sequences). The representatives of this model family focus on various aspects of pathogen epidemics. For instance, the birth-death exposed-infectious (BDEI) model describes the transmission of pathogens featuring an incubation period (when there is a delay between the moment of infection and becoming infectious, as for Ebola and SARS-CoV-2), and permits its estimation along with other parameters. With constantly growing sequencing data, MTBD models should be extremely useful for unravelling information on pathogen epidemics. However, existing implementations of these models in a phylodynamic framework have not yet caught up with the sequencing speed. Computing time and numerical instability issues limit their applicability to medium data sets (≤ 500 samples), while the accuracy of estimations should increase with more data. We propose a new highly parallelizable formulation of ordinary differential equations for MTBD models. We also extend them to forests to represent situations when a (sub-)epidemic started from several cases (e.g., multiple introductions to a country). We implemented it for the BDEI model in a maximum likelihood framework using a combination of numerical analysis methods for efficient equation resolution. Our implementation estimates epidemiological parameter values and their confidence intervals in two minutes on a phylogenetic tree of 10,000 samples. Comparison to the existing implementations on simulated data shows that it is not only much faster but also more accurate. An application of our tool to the 2014 Ebola epidemic in Sierra-Leone is also convincing, with very fast calculation and precise estimates. As MTBD models are closely related to Cladogenetic State Speciation and Extinction (ClaSSE)-like models, our findings could also be easily transferred to the macroevolution domain.

Numerical simulations of granular dam break: Comparison between discrete element, Navier-Stokes, and thin-layer models

Granular flows occur in various contexts, including laboratory experiments, industrial processes, and natural geophysical flows. To investigate their dynamics, different kinds of physically based models have been developed. These models can be characterized by the length scale at which dynamic processes are described. Discrete models use a microscopic scale to individually model each grain, Navier-Stokes models use a mesoscopic scale to consider elementary volumes of grains, and thin-layer models use a macroscopic scale to model the dynamics of elementary columns of fluids. In each case, the derivation of the associated equations is well-known. However, few studies focus on the extent to which these modeling solutions yield mutually coherent results. In this article, we compare the simulations of a granular dam break on a horizontal or inclined planes for the discrete model convex optimization contact dynamics (COCD), the Navier-Stokes model Basilisk, and the thin-layer depth-averaged model SHALTOP. We show that, although all three models allow reproducing the temporal evolution of the free surface in the horizontal case (except for SHALTOP at the initiation), the modeled flow dynamics are significantly different, and, in particular, during the stopping phase. The stresses measured at the flow's bottom, reflecting the flow dynamics, are in relatively good agreement, but significant variations are obtained with the COCD model due to complex and fast-varying granular lattices. Similar conclusions are drawn using the same rheological parameters to model a granular dam break on an inclined plane. This comparison exercise is essential for assessing the limits and uncertainties of granular flow modeling.

Extension of the Trotterized Unitary Coupled Cluster to Triple Excitations

The Trotterized Unitary Coupled Cluster Single and Double (UCCSD) ansatz has recently attracted interest due to its use in Variation Quantum Eigensolver (VQE) molecular simulations on quantum computers. However, when the size of molecules increases, UCCSD becomes less interesting as it cannot achieve sufficient accuracy. Including higher-order excitations is therefore mandatory to recover the UCC's missing correlation effects. Here, we extend the Trotterized UCC approach via the addition of (true) Triple T excitations introducing UCCSDT. We also include both spin and orbital symmetries. Indeed, in practice, the latter help to reduce unnecessary circuit excitations and thus accelerate the optimization process enabling researchers to tackle larger molecules. Our initial numerical tests (12-14 qubits) show that UCCSDT improves the overall accuracy by at least two orders of magnitude with respect to standard UCCSD. Overall, the UCCSDT ansatz is shown to reach chemical accuracy and to be competitive with the CCSD(T) gold-standard classical method of quantum chemistry.

Projection Based Semi-Implicit Partitioned Reduced Basis Method for Fluid-Structure Interaction Problems

In this manuscript a POD-Galerkin based Reduced Order Model for unsteady Fluid-Structure Interaction problems is presented. The model is based on a partitioned algorithm, with semi-implicit treatment of the coupling conditions. A Chorin-Temam projection scheme is applied to the incompressible Navier-Stokes problem, and a Robin coupling condition is used for the coupling between the fluid and the solid. The coupled problem is based on an Arbitrary Lagrangian Eulerian formulation, and the Proper Orthogonal Decomposition procedure is used for the generation of the reduced basis. We extend existing works on a segregated Reduced Order Model for Fluid-Structure Interaction to unsteady problems that couple an incompressible, Newtonian fluid with a linear elastic solid, in two spatial dimensions. We consider three test cases to assess the overall capabilities of the method: an unsteady, non-parametrized problem, a problem that presents a geometrical parametrization of the solid domain, and finally, a problem where a parametrization of the solid's shear modulus is taken into account.

[The French Armed Forces Biomedical Research Institute (IRBA) and wastewater-based epidemiology: Applicability and relevance in armed forces]

The French Armed Forces Biomedical Research Institute (IRBA) deeply involved in research on SARS-COV-2, participated in the creation of the Obépine sentinel network in charge of detecting, qualifying and quantifying the virus genome in wastewater in France. During this pandemic, wastewater-based epidemiology has proven to be a first class public health tool for assessing viral dynamics in populations and environment. Obépine has also conducted research demonstrating the low infectivity of faeces and wastewater and allowed for early detection of epidemic waves linked to new variants. The IRBA has adapted this powerful tool to the monitoring of viral infections on board the aircraft carrier Charles-de-Gaulle in order to get an operational system for anticipation after the first local outbreak in 2020. The presence of this surveillance and anticipation tool has allowed a better management of SARS-CoV-2 contingent introductions on board during stopovers or crewmembers entries. The combination of a mandatory vaccination protocol and the surveillance of viral circulation in black waters has made it possible to identify and locate cases, and thus to continue the operational mission in the COVID-19 environment while limiting the spread and preserving the health of the crew. This innovative tool can easily be redirected to the search for any other pathogens in blackwater or even, in the long term, to ensure health surveillance of any military establishment, at sea or on land, in France or on overseas bases.

Reduction in SARS-CoV-2 Virus Infectivity in Human and Hamster Feces

Objective: There is extensive evidence that SARS-CoV-2 replicates in the gastrointestinal tract. However, the infectivity of virions in feces is poorly documented. Although the primary mode of transmission is airborne, the risk of transmission from contaminated feces remains to be assessed. Design: The persistence of SARS-CoV-2 (infectivity and RNA) in human and animal feces was evaluated by virus isolation on cell culture and RT-qPCR, respectively. The exposure of golden Syrian hamsters to experimentally contaminated feces through intranasal inoculation has also been tested to assess the fecal-oral transmission route. Results: For periods that are compatible with average intestinal transit, the SARS-CoV-2 genome was noticeably stable in human and animal feces, contrary to the virus infectivity that was reduced in a time- and temperature-dependent manner. In human stools, this reduction was variable depending on the donors. Viral RNA was excreted in the feces of infected hamsters, but exposure of naïve hamsters to feces of infected animals did not lead to any productive infection. Conversely, hamsters could be experimentally infected following exposure to spiked fresh feces. Conclusion: Infection following exposure to naturally contaminated feces has been suspected but has not been established so far. The present work demonstrates that SARS-CoV-2 rapidly lost infectivity in spiked or naturally infected feces. Although the possibility of persistent viral particles in human or animal feces cannot be fully ruled out, SARS-CoV-2 transmission after exposure to contaminated feces is unlikely.

SARS-CoV-2 genome quantification in wastewaters at regional and city scale allows precise monitoring of the whole outbreaks dynamics and variants spreading in the population

SARS-CoV-2 is a coronavirus causing a globalized outbreak called COVID-19. SARS-CoV-2 transmission is associated with inhalation of contaminated respiratory droplets and could causes severe complications. Until today several "waves" of infections have been observed despite implementation of strict health policies. Decisions for such sanitary measures are based on population health monitoring. Unfortunately, for COVID-19, a significant proportion of individuals are asymptomatic but play a role in the virus transmission. To overcome these limitations, several strategies were developed including genome quantification in wastewater that could allow monitoring of the health status of population, since shedding of SARS-CoV-2 in patient stool is frequent. Wastewater-based epidemiology (WBE) was established and several countries implemented this approach to allow COVID-19 outbreak monitoring. In France, the OBEPINE project performed a quantitative analysis of SARS-CoV-2 in raw wastewater samples collected from major wastewater treatment plants (WWTP) since March 2020. In the greater Paris area 1101 samples (507 for five WWTP and 594 for sewer) were collected. This 16 months monitoring allows us to observe the outbreak dynamics. Comparison of WBE indicators with health data lead to several important observation; the good level of correlation with incidence rates, the average 3 days lead time, and the sensitivity (WBE change when incidence is > to 7/100000 inhabitants). We also compared the local monitoring (city level) with the regional monitoring, to help cluster identification. Moreover, variants of concern (VOC) emerged due to the selection pressure. We developed a specific RT-qPCR method targeting the deletion H69-V70 in the spike protein, using this deletion as a proxy of the B.1.1.7 presence in the wastewater. With this data we demonstrate the predominant role played by this strain in the third wave. All these results allow a better description and understanding of the pandemic and highlight the role of such WBE indicators.

A nationwide indicator to smooth and normalize heterogeneous SARS-CoV-2 RNA data in wastewater

Since many infected people experience no or few symptoms, the SARS-CoV-2 epidemic is frequently monitored through massive virus testing of the population, an approach that may be biased and may be difficult to sustain in low-income countries. Since SARS-CoV-2 RNA can be detected in stool samples, quantifying SARS-CoV-2 genome by RT-qPCR in wastewater treatment plants (WWTPs) has been carried out as a complementary tool to monitor virus circulation among human populations. However, measuring SARS-CoV-2 viral load in WWTPs can be affected by many experimental and environmental factors. To circumvent these limits, we propose here a novel indicator, the wastewater indicator (WWI), that partly reduces and corrects the noise associated with the SARS-CoV-2 genome quantification in wastewater (average noise reduction of 19%). All data processing results in an average correlation gain of 18% with the incidence rate. The WWI can take into account the censorship linked to the limit of quantification (LOQ), allows the automatic detection of outliers to be integrated into the smoothing algorithm, estimates the average measurement error committed on the samples and proposes a solution for inter-laboratory normalization in the absence of inter-laboratory assays (ILA). This method has been successfully applied in the context of Obépine, a French national network that has been quantifying SARS-CoV-2 genome in a representative sample of French WWTPs since March 5th 2020. By August 26th, 2021, 168 WWTPs were monitored in the French metropolitan and overseas territories of France. We detail the process of elaboration of this indicator, show that it is strongly correlated to the incidence rate and that the optimal time lag between these two signals is only a few days, making our indicator an efficient complement to the incidence rate. This alternative approach may be especially important to evaluate SARS-CoV-2 dynamics in human populations when the testing rate is low.

Several forms of SARS-CoV-2 RNA can be detected in wastewaters: Implication for wastewater-based epidemiology and risk assessment

The ongoing global pandemic of coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been a public health emergency of international concern. Although SARS-CoV-2 is considered to be mainly transmitted by inhalation of contaminated droplets and aerosols, SARS-CoV-2 is also detected in human feces and to a less extent in urine, and in raw wastewaters (to date viral RNA only) suggesting that other routes of infection may exist. Monitoring SARS-CoV-2 genomes in wastewaters has been proposed as a complementary approach for tracing the dynamics of virus transmission within human population connected to wastewater network. The understanding on SARS-CoV-2 transmission through wastewater surveillance, the development of epidemic modeling and the evaluation of SARS-CoV-2 transmission from contaminated wastewater are largely limited by our knowledge on viral RNA genome persistence and virus infectivity preservation in such an environment. Using an integrity based RT-qPCR assay this study led to the discovery that SARS-CoV-2 RNA can persist under several forms in wastewaters, which provides important information on the presence of SARS-CoV-2 in raw wastewaters and associated risk assessment.

Several forms of SARS-CoV-2 RNA can be detected in wastewaters: Implication for wastewater-based epidemiology and risk assessment

The ongoing global pandemic of coronavirus disease 2019 (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has been a public health emergency of international concern. Although SARS-CoV-2 is considered to be mainly transmitted by inhalation of contaminated droplets and aerosols, SARS-CoV-2 is also detected in human feces and to a less extent in urine, and in raw wastewaters (to date viral RNA only) suggesting that other routes of infection may exist. Monitoring SARS-CoV-2 genomes in wastewaters has been proposed as a complementary approach for tracing the dynamics of virus transmission within human population connected to wastewater network. The understanding on SARS-CoV-2 transmission through wastewater surveillance, the development of epidemic modeling and the evaluation of SARS-CoV-2 transmission from contaminated wastewater are largely limited by our knowledge on viral RNA genome persistence and virus infectivity preservation in such an environment. Using an integrity based RT-qPCR assay this study led to the discovery that SARS-CoV-2 RNA can persist under several forms in wastewaters, which provides important information on the presence of SARS-CoV-2 in raw wastewaters and associated risk assessment.

Epidemiological Forecasting with Model Reduction of Compartmental Models. Application to the COVID-19 Pandemic

Simple Summary

Using tools from the reduced order modeling of parametric ODEs and PDEs, including a new positivity-preserving greedy reduced basis method, we present a novel forecasting method for predicting the propagation of an epidemic. The method takes a collection of highly detailed compartmental models (with different initial conditions, initial times, epidemiological parameters and numerous compartments) and learns a model with few compartments which best fits the available health data and which is used to provide the forecasts. We illustrate the promising potential of the approach to the spread of the current COVID-19 pandemic in the case of the Paris region during the period from March to November 2020, in which two epidemic waves took place.

Abstract

We propose a forecasting method for predicting epidemiological health series on a two-week horizon at regional and interregional resolution. The approach is based on the model order reduction of parametric compartmental models and is designed to accommodate small amounts of sanitary data. The efficiency of the method is shown in the case of the prediction of the number of infected people and people removed from the collected data, either due to death or recovery, during the two pandemic waves of COVID-19 in France, which took place approximately between February and November 2020. Numerical results illustrate the promising potential of the approach.

Evaluation of lockdown effect on SARS-CoV-2 dynamics through viral genome quantification in waste water, Greater Paris, France, 5 March to 23 April 2020

IntroductionSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent of coronavirus disease (COVID-19). People infected with SARS-CoV-2 may exhibit no or mild non-specific symptoms; thus, they may contribute to silent circulation of the virus among humans. Since SARS-CoV-2 RNA can be detected in stool samples, monitoring SARS-CoV-2 RNA in waste water (WW) has been proposed as a complementary tool to investigate virus circulation in human populations.AimTo test if the quantification of SARS-CoV-2 genomes in WW correlates with the number of symptomatic or non-symptomatic carriers.MethodWe performed a time-course quantitative analysis of SARS-CoV-2 by RT-qPCR in raw WW samples collected from several major WW treatment plants in Greater Paris. The study period was 5 March to 23 April 2020, including the lockdown period in France (from 17 March).ResultsWe showed that the increase of genome units in raw WW accurately followed the increase of human COVID-19 cases observed at the regional level. Of note, the viral genome could be detected before the epidemic grew massively (around 8 March). Equally importantly, a marked decrease in the quantities of genome units was observed concomitantly with the reduction in the number of new COVID-19 cases, 29 days following the lockdown.ConclusionThis work suggests that a quantitative monitoring of SARS-CoV-2 genomes in WW could generate important additional information for improved monitoring of SARS-CoV-2 circulation at local or regional levels and emphasises the role of WW-based epidemiology.

Evaluation of lockdown effect on SARS-CoV-2 dynamics through viral genome quantification in waste water, Greater Paris, France, 5 March to 23 April 2020

IntroductionSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent of coronavirus disease (COVID-19). People infected with SARS-CoV-2 may exhibit no or mild non-specific symptoms; thus, they may contribute to silent circulation of the virus among humans. Since SARS-CoV-2 RNA can be detected in stool samples, monitoring SARS-CoV-2 RNA in waste water (WW) has been proposed as a complementary tool to investigate virus circulation in human populations.AimTo test if the quantification of SARS-CoV-2 genomes in WW correlates with the number of symptomatic or non-symptomatic carriers.MethodWe performed a time-course quantitative analysis of SARS-CoV-2 by RT-qPCR in raw WW samples collected from several major WW treatment plants in Greater Paris. The study period was 5 March to 23 April 2020, including the lockdown period in France (from 17 March).ResultsWe showed that the increase of genome units in raw WW accurately followed the increase of human COVID-19 cases observed at the regional level. Of note, the viral genome could be detected before the epidemic grew massively (around 8 March). Equally importantly, a marked decrease in the quantities of genome units was observed concomitantly with the reduction in the number of new COVID-19 cases, 29 days following the lockdown.ConclusionThis work suggests that a quantitative monitoring of SARS-CoV-2 genomes in WW could generate important additional information for improved monitoring of SARS-CoV-2 circulation at local or regional levels and emphasises the role of WW-based epidemiology.

Evaluation of lockdown effect on SARS-CoV-2 dynamics through viral genome quantification in waste water, Greater Paris, France, 5 March to 23 April 2020

IntroductionSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent of coronavirus disease (COVID-19). People infected with SARS-CoV-2 may exhibit no or mild non-specific symptoms; thus, they may contribute to silent circulation of the virus among humans. Since SARS-CoV-2 RNA can be detected in stool samples, monitoring SARS-CoV-2 RNA in waste water (WW) has been proposed as a complementary tool to investigate virus circulation in human populations.AimTo test if the quantification of SARS-CoV-2 genomes in WW correlates with the number of symptomatic or non-symptomatic carriers.MethodWe performed a time-course quantitative analysis of SARS-CoV-2 by RT-qPCR in raw WW samples collected from several major WW treatment plants in Greater Paris. The study period was 5 March to 23 April 2020, including the lockdown period in France (from 17 March).ResultsWe showed that the increase of genome units in raw WW accurately followed the increase of human COVID-19 cases observed at the regional level. Of note, the viral genome could be detected before the epidemic grew massively (around 8 March). Equally importantly, a marked decrease in the quantities of genome units was observed concomitantly with the reduction in the number of new COVID-19 cases, 29 days following the lockdown.ConclusionThis work suggests that a quantitative monitoring of SARS-CoV-2 genomes in WW could generate important additional information for improved monitoring of SARS-CoV-2 circulation at local or regional levels and emphasises the role of WW-based epidemiology.

Evaluation of lockdown effect on SARS-CoV-2 dynamics through viral genome quantification in waste water, Greater Paris, France, 5 March to 23 April 2020

IntroductionSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent of coronavirus disease (COVID-19). People infected with SARS-CoV-2 may exhibit no or mild non-specific symptoms; thus, they may contribute to silent circulation of the virus among humans. Since SARS-CoV-2 RNA can be detected in stool samples, monitoring SARS-CoV-2 RNA in waste water (WW) has been proposed as a complementary tool to investigate virus circulation in human populations.AimTo test if the quantification of SARS-CoV-2 genomes in WW correlates with the number of symptomatic or non-symptomatic carriers.MethodWe performed a time-course quantitative analysis of SARS-CoV-2 by RT-qPCR in raw WW samples collected from several major WW treatment plants in Greater Paris. The study period was 5 March to 23 April 2020, including the lockdown period in France (from 17 March).ResultsWe showed that the increase of genome units in raw WW accurately followed the increase of human COVID-19 cases observed at the regional level. Of note, the viral genome could be detected before the epidemic grew massively (around 8 March). Equally importantly, a marked decrease in the quantities of genome units was observed concomitantly with the reduction in the number of new COVID-19 cases, 29 days following the lockdown.ConclusionThis work suggests that a quantitative monitoring of SARS-CoV-2 genomes in WW could generate important additional information for improved monitoring of SARS-CoV-2 circulation at local or regional levels and emphasises the role of WW-based epidemiology.

Evaluation of lockdown effect on SARS-CoV-2 dynamics through viral genome quantification in waste water, Greater Paris, France, 5 March to 23 April 2020

IntroductionSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent of coronavirus disease (COVID-19). People infected with SARS-CoV-2 may exhibit no or mild non-specific symptoms; thus, they may contribute to silent circulation of the virus among humans. Since SARS-CoV-2 RNA can be detected in stool samples, monitoring SARS-CoV-2 RNA in waste water (WW) has been proposed as a complementary tool to investigate virus circulation in human populations.AimTo test if the quantification of SARS-CoV-2 genomes in WW correlates with the number of symptomatic or non-symptomatic carriers.MethodWe performed a time-course quantitative analysis of SARS-CoV-2 by RT-qPCR in raw WW samples collected from several major WW treatment plants in Greater Paris. The study period was 5 March to 23 April 2020, including the lockdown period in France (from 17 March).ResultsWe showed that the increase of genome units in raw WW accurately followed the increase of human COVID-19 cases observed at the regional level. Of note, the viral genome could be detected before the epidemic grew massively (around 8 March). Equally importantly, a marked decrease in the quantities of genome units was observed concomitantly with the reduction in the number of new COVID-19 cases, 29 days following the lockdown.ConclusionThis work suggests that a quantitative monitoring of SARS-CoV-2 genomes in WW could generate important additional information for improved monitoring of SARS-CoV-2 circulation at local or regional levels and emphasises the role of WW-based epidemiology.

Evaluation of lockdown effect on SARS-CoV-2 dynamics through viral genome quantification in waste water, Greater Paris, France, 5 March to 23 April 2020

IntroductionSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiological agent of coronavirus disease (COVID-19). People infected with SARS-CoV-2 may exhibit no or mild non-specific symptoms; thus, they may contribute to silent circulation of the virus among humans. Since SARS-CoV-2 RNA can be detected in stool samples, monitoring SARS-CoV-2 RNA in waste water (WW) has been proposed as a complementary tool to investigate virus circulation in human populations.AimTo test if the quantification of SARS-CoV-2 genomes in WW correlates with the number of symptomatic or non-symptomatic carriers.MethodWe performed a time-course quantitative analysis of SARS-CoV-2 by RT-qPCR in raw WW samples collected from several major WW treatment plants in Greater Paris. The study period was 5 March to 23 April 2020, including the lockdown period in France (from 17 March).ResultsWe showed that the increase of genome units in raw WW accurately followed the increase of human COVID-19 cases observed at the regional level. Of note, the viral genome could be detected before the epidemic grew massively (around 8 March). Equally importantly, a marked decrease in the quantities of genome units was observed concomitantly with the reduction in the number of new COVID-19 cases, 29 days following the lockdown.ConclusionThis work suggests that a quantitative monitoring of SARS-CoV-2 genomes in WW could generate important additional information for improved monitoring of SARS-CoV-2 circulation at local or regional levels and emphasises the role of WW-based epidemiology.

An adaptive parareal algorithm

In this paper, we consider the problem of accelerating the numerical simulation of time dependent problems by time domain decomposition. The available algorithms enabling such decompositions present severe efficiency limitations and are an obstacle for the solution of large scale and high dimensional problems. Our main contribution is the improvement of the parallel efficiency of the parareal in time method. The parareal method is based on combining predictions made by a numerically inexpensive solver (with coarse physics and/or coarse resolution) with corrections coming from an expensive solver (with high-fidelity physics and high resolution). At convergence, the algorithm provides a solution that has the fine solver's high-fidelity physics and high resolution. In the classical version, the fine solver has a fixed high accuracy which is the major obstacle to achieve a competitive parallel efficiency. In this paper, we develop an adaptive variant that overcomes this obstacle by dynamically increasing the accuracy of the fine solver across the parareal iterations. We theoretically show that the parallel efficiency becomes very competitive in the ideal case where the cost of the coarse solver is small, thus proving that the only remaining factors impeding full scalability become the cost of the coarse solver and communication time. The developed theory has also the merit of setting a general framework to understand the success of several extensions of parareal based on iteratively improving the quality of the fine solver and re-using information from previous parareal steps. We illustrate the actual performance of the method in stiff ODEs, which are a challenging family of problems since the only mechanism for adaptivity is time and efficiency is affected by the cost of the coarse solver.

[Biochemical and statistical lessons from the evolution of the SARS-CoV-2 virus: paths for novel antiviral warfare]

In the fight against the spread of COVID-19 the emphasis is on vaccination or on reactivating existing drugs used for other purposes. The tight links that necessarily exist between the virus as it multiplies and the metabolism of its host are systematically ignored. Here we show that the metabolism of all cells is coordinated by the availability of a core building block of the cell's genome, cytidine triphosphate (CTP). This metabolite is also the key to the synthesis of the viral envelope and to the translation of its genome into proteins. This unique role explains why evolution has led to the early emergence in animals of an antiviral immunity enzyme, viperin, that synthesizes a toxic analogue of CTP. The constraints arising from this dependency guide the evolution of the virus. With this in mind, we explored the real-time experiment taking place before our eyes using probabilistic modelling approaches to the molecular evolution of the virus. We have thus followed, almost on a daily basis, the evolution of the composition of the viral genome to link it to the progeny produced over time, particularly in the form of blooms that sparked a firework of viral mutations. Some of those certainly increase the propagation of the virus. This led us to make out the critical role in this evolution of several proteins of the virus, such as its nucleocapsid N, and more generally to begin to understand how the virus ties up the host metabolism to its own benefit. A way for the virus to escape CTP-dependent control in cells would be to infect cells that are not expected to grow, such as neurons. This may account for unexpected body sites of viral development in the present epidemic.

NCIPLOT4: Fast, Robust, and Quantitative Analysis of Noncovalent Interactions

The NonCovalent Interaction index (NCI) enables identification of attractive and repulsive noncovalent interactions from promolecular densities in a fast manner. However, the approach remained up to now qualitative, only providing visual information. We present a new version of NCIPLOT, NCIPLOT4, which allows quantifying the properties of the NCI regions (volume, charge) in small and big systems in a fast manner. Examples are provided of how this new twist enables characterization and retrieval of local information in supramolecular chemistry and biosystems at the static and dynamic levels.

A coherent derivation of the Ewald summation for arbitrary orders of multipoles: The self-terms

In this work, we provide the mathematical elements we think essential for a proper understanding of the calculus of the electrostatic energy of point-multipoles of arbitrary order under periodic boundary conditions. The emphasis is put on the expressions of the so-called self-parts of the Ewald summation where different expressions can be found in the literature. Indeed, such expressions are of prime importance in the context of new generation polarizable force field where the self-field appears in the polarization equations. We provide a general framework, where the idea of the Ewald splitting is applied to the electric potential and, subsequently, all other quantities such as the electric field, the energy, and the forces are derived consistently thereof. Mathematical well-posedness is shown for all these contributions for any order of multipolar distribution.

Dynamic simulations of many-body electrostatic self-assembly

Two experimental studies relating to electrostatic self-assembly have been the subject of dynamic computer simulations, where the consequences of changing the charge and the dielectric constant of the materials concerned have been explored. One series of calculations relates to experiments on the assembly of polymer particles that have been subjected to tribocharging and the simulations successfully reproduce many of the observed patterns of behaviour. A second study explores events observed following collisions between single particles and small clusters composed of charged particles derived from a metal oxide composite. As before, observations recorded during the course of the experiments are reproduced by the calculations. One study in particular reveals how particle polarizability can influence the assembly process.This article is part of the theme issue 'Modern theoretical chemistry'.

Tinker-HP: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields

We present Tinker-HP, a massively MPI parallel package dedicated to classical molecular dynamics (MD) and to multiscale simulations, using advanced polarizable force fields (PFF) encompassing distributed multipoles electrostatics. Tinker-HP is an evolution of the popular Tinker package code that conserves its simplicity of use and its reference double precision implementation for CPUs. Grounded on interdisciplinary efforts with applied mathematics, Tinker-HP allows for long polarizable MD simulations on large systems up to millions of atoms. We detail in the paper the newly developed extension of massively parallel 3D spatial decomposition to point dipole polarizable models as well as their coupling to efficient Krylov iterative and non-iterative polarization solvers. The design of the code allows the use of various computer systems ranging from laboratory workstations to modern petascale supercomputers with thousands of cores. Tinker-HP proposes therefore the first high-performance scalable CPU computing environment for the development of next generation point dipole PFFs and for production simulations. Strategies linking Tinker-HP to Quantum Mechanics (QM) in the framework of multiscale polarizable self-consistent QM/MD simulations are also provided. The possibilities, performances and scalability of the software are demonstrated via benchmarks calculations using the polarizable AMOEBA force field on systems ranging from large water boxes of increasing size and ionic liquids to (very) large biosystems encompassing several proteins as well as the complete satellite tobacco mosaic virus and ribosome structures. For small systems, Tinker-HP appears to be competitive with the Tinker-OpenMM GPU implementation of Tinker. As the system size grows, Tinker-HP remains operational thanks to its access to distributed memory and takes advantage of its new algorithmic enabling for stable long timescale polarizable simulations. Overall, a several thousand-fold acceleration over a single-core computation is observed for the largest systems. The extension of the present CPU implementation of Tinker-HP to other computational platforms is discussed.

Truncated Conjugate Gradient: An Optimal Strategy for the Analytical Evaluation of the Many-Body Polarization Energy and Forces in Molecular Simulations

We introduce a new class of methods, denoted as Truncated Conjugate Gradient(TCG), to solve the many-body polarization energy and its associated forces in molecular simulations (i.e. molecular dynamics (MD) and Monte Carlo). The method consists in a fixed number of Conjugate Gradient (CG) iterations. TCG approaches provide a scalable solution to the polarization problem at a user-chosen cost and a corresponding optimal accuracy. The optimality of the CG-method guarantees that the number of the required matrix-vector products are reduced to a minimum compared to other iterative methods. This family of methods is non-empirical, fully adaptive, and provides analytical gradients, avoiding therefore any energy drift in MD as compared to popular iterative solvers. Besides speed, one great advantage of this class of approximate methods is that their accuracy is systematically improvable. Indeed, as the CG-method is a Krylov subspace method, the associated error is monotonically reduced at each iteration. On top of that, two improvements can be proposed at virtually no cost: (i) the use of preconditioners can be employed, which leads to the Truncated Preconditioned Conjugate Gradient (TPCG); (ii) since the residual of the final step of the CG-method is available, one additional Picard fixed point iteration (“peek”), equivalent to one step of Jacobi Over Relaxation (JOR) with relaxation parameter ω, can be made at almost no cost. This method is denoted by TCG-n(ω). Black-box adaptive methods to find good choices of ω are provided and discussed. Results show that TPCG-3(ω) is converged to high accuracy (a few kcal/mol) for various types of systems including proteins and highly charged systems at the fixed cost of four matrix-vector products: three CG iterations plus the initial CG descent direction. Alternatively, T(P)CG-2(ω) provides robust results at a reduced cost (three matrix-vector products) and offers new perspectives for long polarizable MD as a production algorithm. The T(P)CG-1(ω) level provides less accurate solutions for inhomogeneous systems, but its applicability to well-conditioned problems such as water is remarkable, with only two matrix-vector product evaluations.

Polarizable molecular dynamics in a polarizable continuum solvent

We present, for the first time, scalable polarizable molecular dynamics (MD) simulations within a polarizable continuum solvent with molecular shape cavities and exact solution of the mutual polarization. The key ingredients are a very efficient algorithm for solving the equations associated with the polarizable continuum, in particular, the domain decomposition Conductor-like Screening Model (ddCOSMO), which involves a rigorous coupling of the continuum with the polarizable force field achieved through a robust variational formulation and an effective strategy to solve the coupled equations. The coupling of ddCOSMO with nonvariational force fields, including AMOEBA, is also addressed. The MD simulations are feasible, for real-life systems, on standard cluster nodes; a scalable parallel implementation allows for further acceleration in the context of a newly developed module in Tinker, named Tinker-HP. NVE simulations are stable, and long-term energy conservation can be achieved. This paper is focused on the methodological developments, the analysis of the algorithm, and the stability of the simulations; a proof-of-concept application is also presented to attest to the possibilities of this newly developed technique.

Quantum, classical, and hybrid QM/MM calculations in solution: general implementation of the ddCOSMO linear scaling strategy

We present the general theory and implementation of the Conductor-like Screening Model according to the recently developed ddCOSMO paradigm. The various quantities needed to apply ddCOSMO at different levels of theory, including quantum mechanical descriptions, are discussed in detail, with a particular focus on how to compute the integrals needed to evaluate the ddCOSMO solvation energy and its derivatives. The overall computational cost of a ddCOSMO computation is then analyzed and decomposed in the various steps: the different relative weights of such contributions are then discussed for both ddCOSMO and the fastest available alternative discretization to the COSMO equations. Finally, the scaling of the cost of the various steps with respect to the size of the solute is analyzed and discussed, showing how ddCOSMO opens significantly new possibilities when cheap or hybrid molecular mechanics/quantum mechanics methods are used to describe the solute.

Quantum Calculations in Solution for Large to Very Large Molecules: A New Linear Scaling QM/Continuum Approach

We present a new implementation of continuum solvation models for semiempirical Hamiltonians that allows the description of environmental effects on very large molecular systems. In this approach based on a domain decomposition strategy of the COSMO model (ddCOSMO), the solution to the COSMO equations is no longer the computational bottleneck but becomes a negligible part of the overall computation time. In this Letter, we analyze the computational impact of COSMO on the solution of the SCF equations for large to very large molecules, using semiempirical Hamiltonians, for both the new ddCOSMO implementation and the most recent, linear scaling one, based on the fast multipole method. A further analysis is on the simulation of the UV/visible spectrum of a light-harvesting pigment-protein complex. All of the results show how the new ddCOSMO algorithm paves the way to routine computations for large molecular systems in the condensed phase.

Scalable Evaluation of Polarization Energy and Associated Forces in Polarizable Molecular Dynamics: II.Towards Massively Parallel Computations using Smooth Particle Mesh Ewald

In this paper, we present a scalable and efficient implementation of point dipole-based polarizable force fields for molecular dynamics (MD) simulations with periodic boundary conditions (PBC). The Smooth Particle-Mesh Ewald technique is combined with two optimal iterative strategies, namely, a preconditioned conjugate gradient solver and a Jacobi solver in conjunction with the Direct Inversion in the Iterative Subspace for convergence acceleration, to solve the polarization equations. We show that both solvers exhibit very good parallel performances and overall very competitive timings in an energy-force computation needed to perform a MD step. Various tests on large systems are provided in the context of the polarizable AMOEBA force field as implemented in the newly developed Tinker-HP package which is the first implementation for a polarizable model making large scale experiments for massively parallel PBC point dipole models possible. We show that using a large number of cores offers a significant acceleration of the overall process involving the iterative methods within the context of spme and a noticeable improvement of the memory management giving access to very large systems (hundreds of thousands of atoms) as the algorithm naturally distributes the data on different cores. Coupled with advanced MD techniques, gains ranging from 2 to 3 orders of magnitude in time are now possible compared to non-optimized, sequential implementations giving new directions for polarizable molecular dynamics in periodic boundary conditions using massively parallel implementations.

Parallel-in-time molecular-dynamics simulations

While there have been many progress in the field of multiscale simulations in the space domain, in particular, due to efficient parallelization techniques, much less is known in the way to perform similar approaches in the time domain. In this paper we show on two examples that, provided we can describe in a rough but still accurate way the system under consideration, it is indeed possible to parallelize molecular dynamics simulations in time by using the recently introduced pararealalgorithm. The technique is most useful for ab initio simulations.