Ab initio generalized Langevin equation.

We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables (CVs) in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multiscale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of CVs by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency.

Efficient models of cortical activity via local dynamic equilibria and coarse-grained interactions.

Biologically detailed models of brain circuitry are challenging to build and simulate due to the large number of neurons, their complex interactions, and the many unknown physiological parameters. Simplified mathematical models are more tractable, but harder to evaluate when too far removed from neuroanatomy/physiology. We propose that a multiscale model, coarse-grained (CG) while preserving local biological details, offers the best balance between biological realism and computability. This paper presents such a model. Generally, CG models focus on the interaction between groups of neurons-here termed "pixels"-rather than individual cells. In our case, dynamics are alternately updated at intra- and interpixel scales, with one informing the other, until convergence to equilibrium is achieved on both scales. An innovation is how we exploit the underlying biology: Taking advantage of the similarity in local anatomical structures across large regions of the cortex, we model intrapixel dynamics as a single dynamical system driven by "external" inputs. These inputs vary with events external to the pixel, but their ranges can be estimated a priori. Precomputing and tabulating all potential local responses speed up the updating procedure significantly compared to direct multiscale simulation. We illustrate our methodology using a model of the primate visual cortex. Except for local neuron-to-neuron variability (necessarily lost in any CG approximation) our model reproduces various features of large-scale network models at a tiny fraction of the computational cost. These include neuronal responses as a consequence of their orientation selectivity, a primary function of visual neurons.

Multiscale modeling shows how 2'-deoxy-ATP rescues ventricular function in heart failure.

2'-deoxy-ATP (dATP) improves cardiac function by increasing the rate of crossbridge cycling and Ca[Formula: see text] transient decay. However, the mechanisms of these effects and how therapeutic responses to dATP are achieved when dATP is only a small fraction of the total ATP pool remain poorly understood. Here, we used a multiscale computational modeling approach to analyze the mechanisms by which dATP improves ventricular function. We integrated atomistic simulations of prepowerstroke myosin and actomyosin association, filament-scale Markov state modeling of sarcomere mechanics, cell-scale analysis of myocyte Ca[Formula: see text] dynamics and contraction, organ-scale modeling of biventricular mechanoenergetics, and systems level modeling of circulatory dynamics. Molecular and Brownian dynamics simulations showed that dATP increases the actomyosin association rate by 1.9 fold. Markov state models predicted that dATP increases the pool of myosin heads available for crossbridge cycling, increasing steady-state force development at low dATP fractions by 1.3 fold due to mechanosensing and nearest-neighbor cooperativity. This was found to be the dominant mechanism by which small amounts of dATP can improve contractile function at myofilament to organ scales. Together with faster myocyte Ca[Formula: see text] handling, this led to improved ventricular contractility, especially in a failing heart model in which dATP increased ejection fraction by 16% and the energy efficiency of cardiac contraction by 1%. This work represents a complete multiscale model analysis of a small molecule myosin modulator from single molecule to organ system biophysics and elucidates how the molecular mechanisms of dATP may improve cardiovascular function in heart failure with reduced ejection fraction.

Structure prediction of linear and cyclic peptides using CABS-flex.

The structural modeling of peptides can be a useful aid in the discovery of new drugs and a deeper understanding of the molecular mechanisms of life. Here we present a novel multiscale protocol for the structure prediction of linear and cyclic peptides. The protocol combines two main stages: coarse-grained simulations using the CABS-flex standalone package and an all-atom reconstruction-optimization process using the Modeller program. We evaluated the protocol on a set of linear peptides and two sets of cyclic peptides, with cyclization through the backbone and disulfide bonds. A comparison with other state-of-the-art tools (APPTEST, PEP-FOLD, ESMFold and AlphaFold implementation in ColabFold) shows that for most cases, AlphaFold offers the highest resolution. However, CABS-flex is competitive, particularly when it comes to short linear peptides. As demonstrated, the protocol performance can be further improved by combination with the residue-residue contact prediction method or more efficient scoring. The protocol is included in the CABS-flex standalone package along with online documentation to aid users in predicting the structure of peptides and mini-proteins.

Unveiling the Morphology of Carbon-Supported Ru Nanoparticles by Multiscale Modeling.

Simulating the behavior of metal nanoparticles on supports is crucial for boosting their catalytic performance and various nanotechnology applications; however, such simulations are limited by the conflicts between accuracy and efficiency. Herein, we introduce a multiscale modeling strategy to unveil the morphology of Ru supported on pristine and N-doped graphene. Our multiscale modeling started with the electronic structures of a supported Ru single atom, revealing the strong metal-support interaction around pyridinic nitrogen sites. To determine the stable configurations of Ru2-13 clusters on three different graphene supports, global energy minimum searches were performed. The sintering of the global minimum Ru13 clusters on supports was further simulated by ab initio molecular dynamics (AIMD). The AIMD data set was then collected for deep potential molecular dynamics to study the melting of Ru nanoparticles. This study presents comprehensive descriptions of carbon-supported Ru and develops modeling approaches that bridge different scales and can be applied to various supported nanoparticle systems.

In Vitro Release from Polymeric Core/Shell Nanoparticles through the Lens of Multiscale Modeling.

The large number of studies involving nanoparticles for cancer therapy is due to their peculiar features: they protect loaded active molecules while extending circulation time and can extravasate from the blood flow to the tumor to deliver drugs directly in the target area. Mathematical modeling can provide a preliminary in silico exploration of design space to optimize an experimental activity that often relies on a trial-and-error approach. However, because of the characteristic size of these vectors (10-1000 nm), numerous phenomena of interest occur at different time and length scales, making a single modeling technique insufficient to fully characterize the system of interest. In this work we employed a multiscale modeling approach, which bridges the phenomena of interest across different scales, to study the in vitro release from polymeric core/shell nanoparticles for cancer therapy loaded with an active compound assembled as a hydrophobic ion pair. The "computational microscope" provided by molecular dynamics simulations was used to track drug molecules through the release process at an atomic scale. The outcomes suggested that the drug is mainly partitioned in the polymer and released as hydrophobic ion pair rather than a free molecule, and that the hydrophobic ion pair is preferentially partitioned in Tween 20 micelles in the release media. A model at macroscale, aimed at describing the release rate and elucidating the release mechanism, was developed according to the results from molecular simulations and validated against experimental data. The outcomes provided insights that are challenging to be obtained experimentally and which supported the development and validation of a release model at macroscale. Overall, the adopted multiscale approach corroborated the experimental findings and provided significant insights into the mechanisms of release.

NIAID/SMB Workshop on Multiscale Modeling of Infectious and Immune-Mediated Diseases.

On July 19th, 2023, the National Institute of Allergy and Infectious Diseases co-organized a workshop with the Society of Mathematical Biology, with the authors of this paper as the organizing committee. The workshop, "Bridging multiscale modeling and practical clinical applications in infectious diseases" sought to create an environment for mathematical modelers, statisticians, and infectious disease researchers and clinicians to exchange ideas and perspectives.

Comparative study of the experimentally observed and GAN-generated 3D microstructures in dual-phase steels.

In a deep-learning-based algorithm, generative adversarial networks can generate images similar to an input. Using this algorithm, an artificial three-dimensional (3D) microstructure can be reproduced from two-dimensional images. Although the generated 3D microstructure has a similar appearance, its reproducibility should be examined for practical applications. This study used an automated serial sectioning technique to compare the 3D microstructures of two dual-phase steels generated from three orthogonal surface images with their corresponding observed 3D microstructures. The mechanical behaviors were examined using the finite element analysis method for the representative volume element, in which finite element models of microstructures were directly constructed from the 3D voxel data using a voxel coarsening approach. The macroscopic material responses of the generated microstructures captured the anisotropy caused by the microscopic morphology. However, these responses did not quantitatively align with those of the observed microstructures owing to inaccuracies in reproducing the volume fraction of the ferrite/martensite phase. Additionally, the generation algorithm struggled to replicate the microscopic morphology, particularly in cases with a low volume fraction of the martensite phase where the martensite connectivity was not discernible from the input images. The results demonstrate the limitations of the generation algorithm and the necessity for 3D observations.

This study provided the comparison between experimentally observed and computationally generated 3D microstructures of dual-phase steels in the macro- and microscopic material behaviors with finite element analysis method for periodic microstructure.

ezAlign: A Tool for Converting Coarse-Grained Molecular Dynamics Structures to Atomistic Resolution for Multiscale Modeling.

Soft condensed matter is challenging to study due to the vast time and length scales that are necessary to accurately represent complex systems and capture their underlying physics. Multiscale simulations are necessary to study processes that have disparate time and/or length scales, which abound throughout biology and other complex systems. Herein we present ezAlign, an open-source software for converting coarse-grained molecular dynamics structures to atomistic representation, allowing multiscale modeling of biomolecular systems. The ezAlign v1.1 software package is publicly available for download at github.com/LLNL/ezAlign. Its underlying methodology is based on a simple alignment of an atomistic template molecule, followed by position-restraint energy minimization, which forces the atomistic molecule to adopt a conformation consistent with the coarse-grained molecule. The molecules are then combined, solvated, minimized, and equilibrated with position restraints. Validation of the process was conducted on a pure POPC membrane and compared with other popular methods to construct atomistic membranes. Additional examples, including surfactant self-assembly, membrane proteins, and more complex bacterial and human plasma membrane models, are also presented. By providing these examples, parameter files, code, and an easy-to-follow recipe to add new molecules, this work will aid future multiscale modeling efforts.

Unambiguous Models and Machine Learning Strategies for Anomalous Extreme Events in Turbulent Dynamical System.

Data-driven modeling methods are studied for turbulent dynamical systems with extreme events under an unambiguous model framework. New neural network architectures are proposed to effectively learn the key dynamical mechanisms including the multiscale coupling and strong instability, and gain robust skill for long-time prediction resistive to the accumulated model errors from the data-driven approximation. The machine learning model overcomes the inherent limitations in traditional long short-time memory networks by exploiting a conditional Gaussian structure informed of the essential physical dynamics. The model performance is demonstrated under a prototype model from idealized geophysical flow and passive tracers, which exhibits analytical solutions with representative statistical features. Many attractive properties are found in the trained model in recovering the hidden dynamics using a limited dataset and sparse observation time, showing uniformly high skill with persistent numerical stability in predicting both the trajectory and statistical solutions among different statistical regimes away from the training regime. The model framework is promising to be applied to a wider class of turbulent systems with complex structures.

Multi-scale simulations of pulmonary airflow based on a coupled 3D-1D-0D model.

Pulmonary airflow simulation is a valuable tool for studying respiratory function and disease. However, the respiratory system is a complex multiscale system that involves various physical and biological processes across different spatial and temporal scales. In this study, we propose a 3D-1D-0D multiscale method for simulating pulmonary airflow, which integrates different levels of detail and complexity of the respiratory system. The method consists of three components: a 3D computational fluid dynamics model for the airflow in the trachea and bronchus, a 1D pipe model for the airflow in the terminal bronchioles, and a 0D biphasic mixture model for the airflow in the respiratory bronchioles and alveoli coupled with the lung deformation. The coupling between the different components is achieved by satisfying the mass and momentum conservation law and the pressure continuity condition at the interfaces. We demonstrate the validity and applicability of our method by comparing the results with data of previous models. We also investigate the reduction in inhaled air volume due to the pulmonary fibrosis using the developed multiscale model. Our method provides a comprehensive and realistic framework for simulating pulmonary airflow and can potentially facilitate the diagnosis and treatment of respiratory diseases.

The Multiscale Ernwin/SPQR RNA Structure Prediction Pipeline.

Aside from the well-known role in protein synthesis, RNA can perform catalytic, regulatory, and other essential biological functions which are determined by its three-dimensional structure. In this regard, a great effort has been made during the past decade to develop computational tools for the prediction of the structure of RNAs from the knowledge of their sequence, incorporating experimental data to refine or guide the modeling process. Nevertheless, this task can become exceptionally challenging when dealing with long noncoding RNAs, constituted by more than 200 nucleotides, due to their large size and the specific interactions involved. In this chapter, we describe a multiscale approach to predict such structures, incorporating SAXS experimental data into a hierarchical procedure which couples two coarse-grained representations: Ernwin, a helix-based approach, which deals with the global arrangement of secondary structure elements, and SPQR, a nucleotide-centered coarse-grained model, which corrects and refines the structures predicted at the coarser level.We describe the methodology through its application on the Braveheart long noncoding RNA, starting from the SAXS and secondary structure data to propose a refined, all-atom structure.

Asymmetric crowders and membrane morphology at the nexus of intracellular trafficking and oncology.

A definitive understanding of the interplay between protein binding/migration and membrane curvature evolution is emerging but needs further study. The mechanisms defining such phenomena are critical to intracellular transport and trafficking of proteins. Among trafficking modalities, exosomes have drawn attention in cancer research as these nano-sized naturally occurring vehicles are implicated in intercellular communication in the tumor microenvironment, suppressing anti-tumor immunity and preparing the metastatic niche for progression. A significant question in the field is how the release and composition of tumor exosomes are regulated. In this perspective article, we explore how physical factors such as geometry and tissue mechanics regulate cell cortical tension to influence exosome production by co-opting the biophysics as well as the signaling dynamics of intracellular trafficking pathways and how these exosomes contribute to the suppression of anti-tumor immunity and promote metastasis. We describe a multiscale modeling approach whose impact goes beyond the fundamental investigation of specific cellular processes toward actual clinical translation. Exosomal mechanisms are critical to developing and approving liquid biopsy technologies, poised to transform future non-invasive, longitudinal profiling of evolving tumors and resistance to cancer therapies to bring us one step closer to the promise of personalized medicine.

Cell signaling and tissue remodeling in the pulmonary autograft after the Ross procedure: A computational study.

In the Ross procedure, a patient's pulmonary valve is transplanted in the aortic position. Despite advantages of this surgery, reoperation is still needed in many cases due to excessive dilatation of the pulmonary autograft. To further understand the failure mechanisms, we propose a multiscale model predicting adaptive processes in the autograft at the cell and tissue scale. The cell-scale model consists of a network model, that includes important signaling pathways and relations between relevant transcription factors and their target genes. The resulting gene activity leads to changes in the mechanical properties of the tissue, modeled as a constrained mixture of collagen, elastin and smooth muscle. The multiscale model is calibrated with findings from experiments in which seven sheep underwent the Ross procedure. The model is then validated against a different set of sheep experiments, for which a qualitative agreement between model and experiment is found. Model outcomes at the cell scale, including the activity of genes and transcription factors, also match experimentally obtained transcriptomics data.

Building multiscale models with PhysiBoSS, an agent-based modeling tool.

Multiscale models provide a unique tool for studying complex processes that study events occurring at different scales across space and time. In the context of biological systems, such models can simulate mechanisms happening at the intracellular level such as signaling, and at the extracellular level where cells communicate and coordinate with other cells. They aim to understand the impact of genetic or environmental deregulation observed in complex diseases, describe the interplay between a pathological tissue and the immune system, and suggest strategies to revert the diseased phenotypes. The construction of these multiscale models remains a very complex task, including the choice of the components to consider, the level of details of the processes to simulate, or the fitting of the parameters to the data. One additional difficulty is the expert knowledge needed to program these models in languages such as C++ or Python, which may discourage the participation of non-experts. Simplifying this process through structured description formalisms - coupled with a graphical interface - is crucial in making modeling more accessible to the broader scientific community, as well as streamlining the process for advanced users. This article introduces three examples of multiscale models which rely on the framework PhysiBoSS, an add-on of PhysiCell that includes intracellular descriptions as continuous time Boolean models to the agent-based approach. The article demonstrates how to easily construct such models, relying on PhysiCell Studio, the PhysiCell Graphical User Interface. A step-by-step tutorial is provided as a Supplementary Material and all models are provided at: https://physiboss.github.io/tutorial/.

Multiscale Modeling and Characterization of Graphene Epoxy Nanocomposite.

This study aims to characterize graphene epoxy nanocomposite properties using multiscale modeling. Molecular dynamics was used to study the nanocomposite at the nanoscale and finite element analysis at the macroscale to complete the multiscale modeling. The coupling of these two scales was carried out using the Irving-Kirkwood averaging method. First, the functionalization of graphene was carried and 6% grafted graphene was selected based on Young's modulus and the tensile strength of the grafted graphene sheet. Functionalized graphene with weight fractions of 1.8, 3.7, and 5.6 wt.% were reinforced with epoxy polymer to form a graphene epoxy nanocomposite. The results showed that the graphene with 3.7 wt.% achieved the highest modulus. Subsequently, a functionalized graphene sheet with an epoxy matrix was developed to obtain the interphase properties using the MD modeling technique. The normal and shear forces at the interphase region of the graphene epoxy nanocomposite were investigated using a traction-separation test to analyze the mechanical properties including Young's modulus and traction forces. The mean stiffness of numerically tested samples with 1.8, 3.7, and 5.6 wt.% graphene and the stiffness obtained from experimental results from the literature were compared. The experimental results are lower than the multiscale model results because the experiments cannot replicate the molecular-scale behavior. However, a similar trend could be observed for the addition of up to 3.7 wt.% graphene. This demonstrated that the graphene with 3.7 wt.% shows improved interphase properties. The macroscale properties of the graphene epoxy nanocomposite models with 1.8 and 3.7 wt.% were comparatively higher.

Prelude to a Compositional Systems Biology.

Composition is a powerful principle for systems biology, focused on the interfaces, interconnections, and orchestration of distributed processes. Whereas most systems biology models focus on the structure or dynamics of specific subsystems in controlled conditions, compositional systems biology aims to connect such models into integrative multiscale simulations. This emphasizes the space between models-a compositional perspective asks what variables should be exposed through a submodel's interface? How do coupled models connect and translate across scales? How can we connect domain-specific models across biological and physical research areas to drive the synthesis of new knowledge? What is required of software that integrates diverse datasets and submodels into unified multiscale simulations? How can the resulting integrative models be accessed, flexibly recombined into new forms, and iteratively refined by a community of researchers? This essay offers a high-level overview of the key components for compositional systems biology, including: 1) a conceptual framework and corresponding graphical framework to represent interfaces, composition patterns, and orchestration patterns; 2) standardized composition schemas that offer consistent formats for composable data types and models, fostering robust infrastructure for a registry of simulation modules that can be flexibly assembled; 3) a foundational set of biological templates-schemas for cellular and molecular interfaces, which can be filled with detailed submodels and datasets, and are designed to integrate knowledge that sheds light on the molecular emergence of cells; and 4) scientific collaboration facilitated by user-friendly interfaces for connecting researchers with datasets and models, and which allows a community of researchers to effectively build integrative multiscale models of cellular systems.

A Multiscale Closed-Loop Neurotoxicity Model of Alzheimer's Disease Progression Explains Functional Connectivity Alterations.

The accumulation of amyloid-ß (Aß) and hyperphosphorylated-tau (hp-tau) are two classical histopathological biomarkers in Alzheimer's disease (AD). However, their detailed interactions with the electrophysiological changes at the meso- and macroscale are not yet fully understood. We developed a mechanistic multiscale model of AD progression, linking proteinopathy to its effects on neural activity and vice-versa. We integrated a heterodimer model of prion-like protein propagation and a brain network model of Jansen-Rit neural masses derived from human neuroimaging data whose parameters varied due to neurotoxicity. Results showed that changes in inhibition guided the electrophysiological alterations found in AD, and these changes were mainly attributed to Aß effects. Additionally, we found a causal disconnection between cellular hyperactivity and interregional hypersynchrony contrary to previous beliefs. Finally, we demonstrated that early Aß and hp-tau depositions' location determine the spatiotemporal profile of the proteinopathy. The presented model combines the molecular effects of both Aß and hp-tau together with a mechanistic protein propagation model and network effects within a closed-loop model. This holds the potential to enlighten the interplay between AD mechanisms on various scales, aiming to develop and test novel hypotheses on the contribution of different AD-related variables to the disease evolution.

Uncovering the Importance of Ligand Mobility on Cellular Uptake of Nanoparticles: Insights from Experimental, Computational, and Theoretical Investigations.

The cellular uptake of nanoparticles (NPs) by biological cells is an important and fundamental process in drug delivery. Previous studies reveal that the physicochemical properties of nanoparticles as well as those of functionalized ligands can both critically affect the uptake behaviors. However, the effect of the conjugation strategy (i.e., the "bond" between the ligand and the NP) on the cellular uptake is overlooked and remains largely elusive. Here, by taking the broadly employed gold nanoparticle as an example, we comprehensively assessed the relationship between the conjugation strategy and uptake behaviors by introducing three ligands with the same functional terminal but different anchoring sites. As revealed by in vitro cell experiments and multiscale molecular simulations, the uptake efficiency of gold NPs was positively correlated with the strength of the "bond" and more specifically the ligand mobility on the NP surface. Moreover, we validated the results presented above by proposing a thermodynamic theory for the wrapping of NPs with mobile ligands. Further, we also showed that the endocytic pathway of NPs was highly dependent on ligand mobility. Overall, this study uncovered a vital role of conjugation strategy in the cellular uptake and may provide useful guidelines for tailoring the biobehaviors of nanoparticles.

Predicted Fracture Tendency of Naturally Occurring Aluminum Surface Coatings under Tensile Loading.

Naturally occurring coatings on aluminum metal, such as its oxide or hydroxide, serve to protect the material from corrosion. Understanding the conditions under which these coatings mechanically fail is therefore expected to be an important aspect of predictive models for aluminum component lifetimes. To this end, we develop and apply a molecular dynamics (MD) modeling framework for conducting tension tests that is capable of isolating factors governing the mechanical strength as a function of coating chemistry, defect morphology, and variables associated with the loading path. We consider two representative materials, including γ-Al2O3 and γ-Al(OH)3 (i.e., oxide and hydroxide), both of which form readily as aluminum surface coatings. Our results indicate that defects have a significant bearing on the strength of aluminum oxide, with grain boundaries serving to reduce the strain at failure from εzz = 0.300 to 0.219, relative to perfect single crystal. Our simulations also predict that porosity lowers the elastic stiffness and yield strength of the oxide. Relative to perfect crystal, we find porosity factors of 5%, 10% and 20% decrease the yield stress by 26%, 36% and 53%, respectively. MD predicts that perfect hydroxide and oxide single crystal have respective strains at failure of 0.08 and 0.31 under tensile uniaxial strain loading, and that the corresponding yield stresses are respectively 1.6 and 11.1 GPa. These data indicate that the hydroxide is substantially more susceptible to mechanical failure than the oxide. Our results, coupled with literature findings that indicate hot and humid conditions favor formation of hydroxide and defective oxide coatings, indicate the potential for a complicated dependence of aluminum corrosion susceptibility and stress corrosion cracking on aging history.