Multi-scale computational modelling in biology and physiology

Uncertainty quantification and sensitivity analysis of neuron models with ion concentration dynamics

This paper provides a comprehensive and computationally efficient case study for uncertainty quantification (UQ) and global sensitivity analysis (GSA) in a neuron model incorporating ion concentration dynamics. We address how challenges with UQ and GSA in this context can be approached and solved, including challenges related to computational cost, parameters affecting the system's resting state, and the presence of both fast and slow dynamics. Specifically, we analyze the electrodiffusive neuron-extracellular-glia (edNEG) model, which captures electrical potentials, ion concentrations (Na+, K+, Ca2+, and Cl-), and volume changes across six compartments. Our methodology includes a UQ procedure assessing the model's reliability and susceptibility to input uncertainty and a variance-based GSA identifying the most influential input parameters. To mitigate computational costs, we employ surrogate modeling techniques, optimized using efficient numerical integration methods. We propose a strategy for isolating parameters affecting the resting state and analyze the edNEG model dynamics under both physiological and pathological conditions. The influence of uncertain parameters on model outputs, particularly during spiking dynamics, is systematically explored. Rapid dynamics of membrane potentials necessitate a focus on informative spiking features, while slower variations in ion concentrations allow a meaningful study at each time point. Our study offers valuable guidelines for future UQ and GSA investigations on neuron models with ion concentration dynamics, contributing to the broader application of such models in computational neuroscience.

Effects of void defects on the mechanical properties of biphasic calcium phosphate nanoparticles: A molecular dynamics investigation

Porous biphasic calcium phosphate (BCP) ceramics are widely used in bone tissue engineering, and the mechanical properties of BCP implants must be reliable. However, the effects of pore structure (e.g., shape and size) on the mechanical properties are not well understood. In this study, we used molecular dynamics simulations to investigate the influence of pore shape and size on the mechanical behavior of BCP nanoparticles. BCP void models with cylindrical and cuboid pores ranging from 2 to 16 nm in diameter were constructed, and the elastic moduli were calculated. In addition, uniaxial tensile and compressive tests were performed on the models. We found that the pore size had a more significant impact on the mechanical properties of BCP than pore shape. Further, the elastic moduli decreased nonlinearly with increasing pore size. In addition, the tensile and compressive strength also decreased with the increase in pore size, but the ductility improved. Furthermore, deformation and fracture were more likely to occur near the pores and at the phase interfaces as a result of high atomic local strain in the calcium-deficient hydroxyapatite area. The results of this work reveal the effects of pore parameters on the mechanical properties of porous BCP at the nanometer level, which may aid the design of improved porous and multiphase CaP-based biomaterials for bone regeneration.

A multiscale computational framework for the development of spines in molluscan shells

From mathematical models of growth to computer simulations of pigmentation, the study of shell formation has given rise to an abundant number of models, working at various scales. Yet, attempts to combine those models have remained sparse, due to the challenge of combining categorically different approaches. In this paper, we propose a framework to streamline the process of combining the molecular and tissue scales of shell formation. We choose these levels as a proxy to link the genotype level, which is better described by molecular models, and the phenotype level, which is better described by tissue-level mechanics. We also show how to connect observations on shell populations to the approach, resulting in collections of molecular parameters that may be associated with different populations of real shell specimens. The approach is as follows: we use a Quality-Diversity algorithm, a type of black-box optimization algorithm, to explore the range of concentration profiles emerging as solutions of a molecular model, and that define growth patterns for the mechanical model. At the same time, the mechanical model is simulated over a wide range of growth patterns, resulting in a variety of spine shapes. While time-consuming, these steps only need to be performed once and then function as look-up tables. Actual pictures of shell spines can then be matched against the list of existing spine shapes, yielding a potential growth pattern which, in turn, gives us matching molecular parameters. The framework is modular, such that models can be easily swapped without changing the overall working of the method. As a demonstration of the approach, we solve specific molecular and mechanical models, adapted from available theoretical studies on molluscan shells, and apply the multiscale framework to evaluate the characteristics of spines from three distinct populations of Turbo sazae.

Engineering innovations in medicine and biology: Revolutionizing patient care through mechanical solutions

The overlap between mechanical engineering and medicine is expanding more and more over the years. Engineers are now using their expertise to design and create functional biomaterials and are continually collaborating with physicians to improve patient health. In this review, we explore the state of scientific knowledge in the areas of biomaterials, biomechanics, nanomechanics, and computational fluid dynamics (CFD) in relation to the pharmaceutical and medical industry. Focusing on current research and breakthroughs, we provide an overview of how these fields are being used to create new technologies for medical treatments of human patients. Barriers and constraints in these fields, as well as ways to overcome them, are also described in this review. Finally, the potential for future advances in biomaterials to fundamentally change the current approach to medicine and biology is also discussed.

From evidence-based medicine to digital twin technology for predicting ventricular tachycardia in ischaemic cardiomyopathy

Survivors of myocardial infarction are at risk of life-threatening ventricular tachycardias (VTs) later in their lives. Current guidelines for implantable cardioverter defibrillators (ICDs) implantation to prevent VT-related sudden cardiac death is solely based on symptoms and left ventricular ejection fraction. Catheter ablation of scar-related VTs is performed following ICD therapy, reducing VTs, painful shocks, anxiety, depression and worsening heart failure. We postulate that better prediction of the occurrence and circuit of VT, will improve identification of patients at risk for VT and boost preventive ablation, reducing mortality and morbidity. For this purpose, multiple time-evolving aspects of the underlying pathophysiology, including the anatomical substrate, triggers and modulators, should be part of VT prediction models. We envision digital twins as a solution combining clinical expertise with three prediction approaches: evidence-based medicine (clinical practice), data-driven models (data science) and mechanistic models (biomedical engineering). This paper aims to create a mutual understanding between experts in the different fields by providing a comprehensive description of the clinical problem and the three approaches in an understandable manner, leveraging future collaborations and technological innovations for clinical decision support. Moreover, it defines open challenges and gains for digital twin solutions and discusses the potential of hybrid modelling.

Assessing the Effect of Incretin Hormones and Other Insulin Secretagogues on Pancreatic Beta-Cell Function: Review on Mathematical Modelling Approaches

Mathematical modelling in glucose metabolism has proven very useful for different reasons. Several models have allowed deeper understanding of the relevant physiological and pathophysiological aspects and promoted new experimental activity to reach increased knowledge of the biological and physiological systems of interest. Glucose metabolism modelling has also proven useful to identify the parameters with specific physiological meaning in single individuals, this being relevant for clinical applications in terms of precision diagnostics or therapy. Among those model-based physiological parameters, an important role resides in those for the assessment of different functional aspects of the pancreatic beta cell. This study focuses on the mathematical models of incretin hormones and other endogenous substances with known effects on insulin secretion and beta-cell function, mainly amino acids, non-esterified fatty acids, and glucagon. We found that there is a relatively large number of mathematical models for the effects on the beta cells of incretin hormones, both at the cellular/organ level or at the higher, whole-body level. In contrast, very few models were identified for the assessment of the effect of other insulin secretagogues. Given the opportunities offered by mathematical modelling, we believe that novel models in the investigated field are certainly advisable.

Genetics and neurobiology of eating disorders

Eating disorders (anorexia nervosa, bulimia nervosa and binge-eating disorder) are a heterogeneous class of complex illnesses marked by weight and appetite dysregulation coupled with distinctive behavioral and psychological features. Our understanding of their genetics and neurobiology is evolving thanks to global cooperation on genome-wide association studies, neuroimaging, and animal models. Until now, however, these approaches have advanced the field in parallel, with inadequate cross-talk. This review covers overlapping advances in these key domains and encourages greater integration of hypotheses and findings to create a more unified science of eating disorders. We highlight ongoing and future work designed to identify implicated biological pathways that will inform staging models based on biology as well as targeted prevention and tailored intervention, and will galvanize interest in the development of pharmacologic agents that target the core biology of the illnesses, for which we currently have few effective pharmacotherapeutics.

Implementing computational modeling in tissue engineering: where disciplines meet

In recent years, the mathematical and computational sciences have developed novel methodologies and insights that can aid in designing advanced bioreactors, microfluidic set-ups or organ-on-chip devices, in optimizing culture conditions, or predicting long-term behavior of engineered tissues in vivo. In this review, we introduce the concept of computational models and how they can be integrated in an interdisciplinary workflow for Tissue Engineering and Regenerative Medicine (TERM). We specifically aim this review of general concepts and examples at experimental scientists with little or no computational modeling experience. We also describe the contribution of computational models in understanding TERM processes and in advancing the TERM field by providing novel insights.

Multivalue Collocation Methods for Ordinary and Fractional Differential Equations

The present paper illustrates some classes of multivalue methods for the numerical solution of ordinary and fractional differential equations. In particular, it focuses on two-step and mixed collocation methods, Nordsieck GLM collocation methods for ordinary differential equations, and on two-step spline collocation methods for fractional differential equations. The construction of the methods together with the convergence and stability analysis are reported and some numerical experiments are carried out to show the efficiency of the proposed methods.

The Energy Homeostasis Principle: A Naturalistic Approach to Explain the Emergence of Behavior

It is still elusive to explain the emergence of behavior and understanding based on its neural mechanisms. One renowned proposal is the Free Energy Principle (FEP), which uses an information-theoretic framework derived from thermodynamic considerations to describe how behavior and understanding emerge. FEP starts from a whole-organism approach, based on mental states and phenomena, mapping them into the neuronal substrate. An alternative approach, the Energy Homeostasis Principle (EHP), initiates a similar explanatory effort but starts from single-neuron phenomena and builds up to whole-organism behavior and understanding. In this work, we further develop the EHP as a distinct but complementary vision to FEP and try to explain how behavior and understanding would emerge from the local requirements of the neurons. Based on EHP and a strict naturalist approach that sees living beings as physical and deterministic systems, we explain scenarios where learning would emerge without the need for volition or goals. Given these starting points, we state several considerations of how we see the nervous system, particularly the role of the function, purpose, and conception of goal-oriented behavior. We problematize these conceptions, giving an alternative teleology-free framework in which behavior and, ultimately, understanding would still emerge. We reinterpret neural processing by explaining basic learning scenarios up to simple anticipatory behavior. Finally, we end the article with an evolutionary perspective of how this non-goal-oriented behavior appeared. We acknowledge that our proposal, in its current form, is still far from explaining the emergence of understanding. Nonetheless, we set the ground for an alternative neuron-based framework to ultimately explain understanding.

A mathematical model of cardiovascular dynamics for the diagnosis and prognosis of hemorrhagic shock

A variety of mathematical models of the cardiovascular system have been suggested over several years in order to describe the time-course of a series of physiological variables (i.e. heart rate, cardiac output, arterial pressure) relevant for the compensation mechanisms to perturbations, such as severe haemorrhage. The current study provides a simple but realistic mathematical description of cardiovascular dynamics that may be useful in the assessment and prognosis of hemorrhagic shock. The present work proposes a first version of a differential-algebraic equations model, the model dynamical ODE model for haemorrhage (dODEg). The model consists of 10 differential and 14 algebraic equations, incorporating 61 model parameters. This model is capable of replicating the changes in heart rate, mean arterial pressure and cardiac output after the onset of bleeding observed in four experimental animal preparations and fits well to the experimental data. By predicting the time-course of the physiological response after haemorrhage, the dODEg model presented here may be of significant value for the quantitative assessment of conventional or novel therapeutic regimens. The model may be applied to the prediction of survivability and to the determination of the urgency of evacuation towards definitive surgical treatment in the operational setting.

Ten steps to investigate a cellular system with mathematical modeling

Cellular and intracellular processes are inherently complex due to the large number of components and interactions, which are often nonlinear and occur at different spatiotemporal scales. Because of this complexity, mathematical modeling is increasingly used to simulate such systems and perform experiments in silico, many orders of magnitude faster than real experiments and often at a higher spatiotemporal resolution. In this article, we will focus on the generic modeling process and illustrate it with an example model of membrane lipid turnover.

Multiscale modeling meets machine learning: What can we learn?

Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

High-Throughput Methods in the Discovery and Study of Biomaterials and Materiobiology

The complex interaction of cells with biomaterials (i.e., materiobiology) plays an increasingly pivotal role in the development of novel implants, biomedical devices, and tissue engineering scaffolds to treat diseases, aid in the restoration of bodily functions, construct healthy tissues, or regenerate diseased ones. However, the conventional approaches are incapable of screening the huge amount of potential material parameter combinations to identify the optimal cell responses and involve a combination of serendipity and many series of trial-and-error experiments. For advanced tissue engineering and regenerative medicine, highly efficient and complex bioanalysis platforms are expected to explore the complex interaction of cells with biomaterials using combinatorial approaches that offer desired complex microenvironments during healing, development, and homeostasis. In this review, we first introduce materiobiology and its high-throughput screening (HTS). Then we present an in-depth of the recent progress of 2D/3D HTS platforms (i.e., gradient and microarray) in the principle, preparation, screening for materiobiology, and combination with other advanced technologies. The Compendium for Biomaterial Transcriptomics and high content imaging, computational simulations, and their translation toward commercial and clinical uses are highlighted. In the final section, current challenges and future perspectives are discussed. High-throughput experimentation within the field of materiobiology enables the elucidation of the relationships between biomaterial properties and biological behavior and thereby serves as a potential tool for accelerating the development of high-performance biomaterials.

Spiral Wave Propagation in Communities with Spatially Correlated Heterogeneity

Many multicellular communities propagate signals in a directed manner via excitable waves. Cell-to-cell heterogeneity is a ubiquitous feature of multicellular communities, but the effects of heterogeneity on wave propagation are still unclear. Here, we use a minimal FitzHugh-Nagumo-type model to investigate excitable wave propagation in a two-dimensional heterogeneous community. The model shows three dynamic regimes in which waves either propagate directionally, die out, or spiral indefinitely, and we characterize how these regimes depend on the heterogeneity parameters. We find that in some parameter regimes, spatial correlations in the heterogeneity enhance directional propagation and suppress spiraling. However, in other regimes, spatial correlations promote spiraling, a surprising feature that we explain by demonstrating that these spirals form by a second, distinct mechanism. Finally, we characterize the dynamics using techniques from percolation theory. Despite the fact that percolation theory does not completely describe the dynamics quantitatively because it neglects the details of the excitable propagation, we find that it accounts for the transitions between the dynamic regimes and the general dependency of the spiral period on the heterogeneity and thus provides important insights. Our results reveal that the spatial structure of cell-to-cell heterogeneity can have important consequences for signal propagation in cellular communities.

Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences

Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved.

Opportunities and Challenges of Whole-Cell and -Tissue Simulations of the Outer Retina in Health and Disease

Visual processing starts in the outer retina, where photoreceptor cells sense photons that trigger electrical responses. Retinal pigment epithelial cells are located external to the photoreceptor layer and have critical functions in supporting cell and tissue homeostasis and thus sustaining a healthy retina. The high level of specialization makes the retina vulnerable to alterations that promote retinal degeneration. In this review, we discuss opportunities and challenges in proposing whole-cell and -tissue simulations of the human outer retina. An implicit position taken throughout this review is that mapping diverse data sets onto integrative computational models is likely to be a pivotal approach to understanding complex disease and developing novel interventions.

In silico clinical trials for pediatric orphan diseases

To date poor treatment options are available for patients with congenital pseudarthrosis of the tibia (CPT), a pediatric orphan disease. In this study we have performed an in silico clinical trial on 200 virtual subjects, generated from a previously established model of murine bone regeneration, to tackle the challenges associated with the small, pediatric patient population. Each virtual subject was simulated to receive no treatment and bone morphogenetic protein (BMP) treatment. We have shown that the degree of severity of CPT is significantly reduced with BMP treatment, although the effect is highly subject-specific. Using machine learning techniques we were also able to stratify the virtual subject population in adverse responders, non-responders, responders and asymptomatic. In summary, this study shows the potential of in silico medicine technologies as well as their implications for other orphan diseases.

Modeling the multi-scale mechanisms of macromolecular resource allocation

As microbes face changing environments, they dynamically allocate macromolecular resources to produce a particular phenotypic state. Broad 'omics' data sets have revealed several interesting phenomena regarding how the proteome is allocated under differing conditions, but the functional consequences of these states and how they are achieved remain open questions. Various types of multi-scale mathematical models have been used to elucidate the genetic basis for systems-level adaptations. In this review, we outline several different strategies by which microbes accomplish resource allocation and detail how mathematical models have aided in our understanding of these processes. Ultimately, such modeling efforts have helped elucidate the principles of proteome allocation and hold promise for further discovery.

IN-SILICO MODELING OF LEFT VENTRICLE TO SIMULATE DILATED CARDIOMYOPATHY AND CF-LVAD SUPPORT

Numerical modeling of the left ventricle dynamics plays an important role in testing different physiological scenarios and treatment techniques before the in vitro and in vivo assessments. However, utilized left ventricle model becomes vital in the simulations because validity of the results depends on the response of the numerical model to the parameter changes and additional sub-models for the applied treatment techniques. In this study, it is aimed to evaluate different numerical left ventricle models describing healthy and failing ventricle dynamics as well as the response of these models under continuous flow left ventricular assist device support. Six different numerical left ventricle models which include time varying elastance and single fiber contraction approaches are selected and applied in combination with a closed loop electric analogue of the circulation to achieve this purpose. The time varying elastace models relate ventricular pressure and volume changes in a simplistic way while the single fiber contraction models combine different scales ranging from protein to organ level. Change of the hemodynamic signals at the organ level for healthy, failing and CF-LVAD supported left ventricle models shows functionality of these models and helps to understand usability of them for different purposes.

Proportional Insulin Infusion in Closed-Loop Control of Blood Glucose

A differential equation model is formulated that describes the dynamics of glucose concentration in blood circulation. The model accounts for the intake of food, expenditure of calories and the control of glucose levels by insulin and glucagon. These and other hormones affect the blood glucose level in various ways. In this study only main effects are taken into consideration. Moreover, by making a quasi-steady state approximation the model is reduced to a single nonlinear differential equation of which parameters are fit to data from healthy subjects. Feedback provided by insulin plays a key role in the control of the blood glucose level. Reduced β-cell function and insulin resistance may hamper this process. With the present model it is shown how by closed-loop control these defects, in an organic way, can be compensated with continuous infusion of exogenous insulin.

Statistical ensemble of gene regulatory networks of macrophage differentiation

BACKGROUND

Macrophages cover a major role in the immune system, being the most plastic cell yielding several key immune functions.

METHODS

Here we derived a minimalistic gene regulatory network model for the differentiation of macrophages into the two phenotypes M1 (pro-) and M2 (anti-inflammatory).

RESULTS

To test the model, we simulated a large number of such networks as in a statistical ensemble. In other words, to enable the inter-cellular crosstalk required to obtain an immune activation in which the macrophage plays its role, the simulated networks are not taken in isolation but combined with other cellular agents, thus setting up a discrete minimalistic model of the immune system at the microscopic/intracellular (i.e., genetic regulation) and mesoscopic/intercellular scale.

CONCLUSIONS

We show that within the mesoscopic level description of cellular interaction and cooperation, the gene regulatory logic is coherent and contributes to the overall dynamics of the ensembles that shows, statistically, the expected behaviour.

Genetic variants in Alzheimer disease - molecular and brain network approaches

Genetic studies in late-onset Alzheimer disease (LOAD) are aimed at identifying core disease mechanisms and providing potential biomarkers and drug candidates to improve clinical care of AD. However, owing to the complexity of LOAD, including pathological heterogeneity and disease polygenicity, extraction of actionable guidance from LOAD genetics has been challenging. Past attempts to summarize the effects of LOAD-associated genetic variants have used pathway analysis and collections of small-scale experiments to hypothesize functional convergence across several variants. In this Review, we discuss how the study of molecular, cellular and brain networks provides additional information on the effects of LOAD-associated genetic variants. We then discuss emerging combinations of these omic data sets into multiscale models, which provide a more comprehensive representation of the effects of LOAD-associated genetic variants at multiple biophysical scales. Furthermore, we highlight the clinical potential of mechanistically coupling genetic variants and disease phenotypes with multiscale brain models.

Computerized techniques pave the way for drug-drug interaction prediction and interpretation

INTRODUCTION

Health care industry also patients penalized by medical errors that are inevitable but highly preventable. Vast majority of medical errors are related to adverse drug reactions, while drug-drug interactions (DDIs) are the main cause of adverse drug reactions (ADRs). DDIs and ADRs have mainly been reported by haphazard case studies. Experimental in vivo and in vitro researches also reveals DDI pairs. Laboratory and experimental researches are valuable but also expensive and in some cases researchers may suffer from limitations.

METHODS

In the current investigation, the latest published works were studied to analyze the trend and pattern of the DDI modelling and the impacts of machine learning methods. Applications of computerized techniques were also investigated for the prediction and interpretation of DDIs.

RESULTS

Computerized data-mining in pharmaceutical sciences and related databases provide new key transformative paradigms that can revolutionize the treatment of diseases and hence medical care. Given that various aspects of drug discovery and pharmacotherapy are closely related to the clinical and molecular/biological information, the scientifically sound databases (e.g., DDIs, ADRs) can be of importance for the success of pharmacotherapy modalities.

CONCLUSION

A better understanding of DDIs not only provides a robust means for designing more effective medicines but also grantees patient safety.

A Novel Method to Verify Multilevel Computational Models of Biological Systems Using Multiscale Spatio-Temporal Meta Model Checking

Insights gained from multilevel computational models of biological systems can be translated into real-life applications only if the model correctness has been verified first. One of the most frequently employed in silico techniques for computational model verification is model checking. Traditional model checking approaches only consider the evolution of numeric values, such as concentrations, over time and are appropriate for computational models of small scale systems (e.g. intracellular networks). However for gaining a systems level understanding of how biological organisms function it is essential to consider more complex large scale biological systems (e.g. organs). Verifying computational models of such systems requires capturing both how numeric values and properties of (emergent) spatial structures (e.g. area of multicellular population) change over time and across multiple levels of organization, which are not considered by existing model checking approaches. To address this limitation we have developed a novel approximate probabilistic multiscale spatio-temporal meta model checking methodology for verifying multilevel computational models relative to specifications describing the desired/expected system behaviour. The methodology is generic and supports computational models encoded using various high-level modelling formalisms because it is defined relative to time series data and not the models used to generate it. In addition, the methodology can be automatically adapted to case study specific types of spatial structures and properties using the spatio-temporal meta model checking concept. To automate the computational model verification process we have implemented the model checking approach in the software tool Mule (http://mule.modelchecking.org). Its applicability is illustrated against four systems biology computational models previously published in the literature encoding the rat cardiovascular system dynamics, the uterine contractions of labour, the Xenopus laevis cell cycle and the acute inflammation of the gut and lung. Our methodology and software will enable computational biologists to efficiently develop reliable multilevel computational models of biological systems.

Use of nanoscale mechanical stimulation for control and manipulation of cell behaviour

The ability to control cell behaviour, cell fate and simulate reliable tissue models in vitro remains a significant challenge yet is crucial for various applications of high throughput screening e.g. drug discovery. Mechanotransduction (the ability of cells to convert mechanical forces in their environment to biochemical signalling) represents an alternative mechanism to attain this control with such studies developing techniques to reproducibly control the mechanical environment in techniques which have potential to be scaled. In this review, the use of techniques such as finite element modelling and precision interferometric measurement are examined to provide context for a novel technique based on nanoscale vibration, also known as "nanokicking". Studies have shown this stimulus to alter cellular responses in both endothelial and mesenchymal stem cells (MSCs), particularly in increased proliferation rate and induced osteogenesis respectively. Endothelial cell lines were exposed to nanoscale vibration amplitudes across a frequency range of 1-100 Hz, and MSCs primarily at 1 kHz. This technique provides significant potential benefits over existing technologies, as cellular responses can be initiated without the use of expensive engineering techniques and/or chemical induction factors. Due to the reproducible and scalable nature of the apparatus it is conceivable that nanokicking could be used for controlling cell behaviour within a wide array of high throughput procedures in the research environment, within drug discovery, and for clinical/therapeutic applications.

STATEMENT OF SIGNIFICANCE

The results discussed within this article summarise the potential benefits of using nanoscale vibration protocols for controlling cell behaviour. There is a significant need for reliable tissue models within the clinical and pharma industries, and the control of cell behaviour and stem cell differentiation would be highly beneficial. The full potential of this method of controlling cell behaviour has not yet been realised.

Integrating Multiscale Modeling with Drug Effects for Cancer Treatment

In this paper, we review multiscale modeling for cancer treatment with the incorporation of drug effects from an applied system's pharmacology perspective. Both the classical pharmacology and systems biology are inherently quantitative; however, systems biology focuses more on networks and multi factorial controls over biological processes rather than on drugs and targets in isolation, whereas systems pharmacology has a strong focus on studying drugs with regard to the pharmacokinetic (PK) and pharmacodynamic (PD) relations accompanying drug interactions with multiscale physiology as well as the prediction of dosage-exposure responses and economic potentials of drugs. Thus, it requires multiscale methods to address the need for integrating models from the molecular levels to the cellular, tissue, and organism levels. It is a common belief that tumorigenesis and tumor growth can be best understood and tackled by employing and integrating a multifaceted approach that includes in vivo and in vitro experiments, in silico models, multiscale tumor modeling, continuous/discrete modeling, agent-based modeling, and multiscale modeling with PK/PD drug effect inputs. We provide an example application of multiscale modeling employing stochastic hybrid system for a colon cancer cell line HCT-116 with the application of Lapatinib drug. It is observed that the simulation results are similar to those observed from the setup of the wet-lab experiments at the Translational Genomics Research Institute.

Force Field Development for Lipid Membrane Simulations

With the rapid development of computer power and wide availability of modelling software computer simulations of realistic models of lipid membranes, including their interactions with various molecular species, polypeptides and membrane proteins have become feasible for many research groups. The crucial issue of the reliability of such simulations is the quality of the force field, and many efforts, especially in the latest several years, have been devoted to parametrization and optimization of the force fields for biomembrane modelling. In this review, we give account of the recent development in this area, covering different classes of force fields, principles of the force field parametrization, comparison of the force fields, and their experimental validation. This article is part of a Special Issue entitled: Biosimulations edited by Ilpo Vattulainen and Tomasz Róg.

From molecular systems to continuum solids: A multiscale structure and dynamics

We propose a concurrent multiscale molecular dynamics for molecular systems in order to apply macroscale mechanical boundary conditions such as traction and average displacement for solid state materials, which is difficult to do in traditional molecular dynamics where boundary conditions are applied in terms of forces and displacements on selected particles. The multiscale model is systematically constructed in terms of multiscale structures of kinematics, force field, and dynamical equations. The idea is to extend the Anderson-Parrinello-Rahman molecular dynamics to the cases that have arbitrary finite domain and boundary, thus the model is capable of solving inhomogeneous, non-equilibrium problems. The macroscale stress loading on a representative volume element with periodic boundary condition is generalized to all kinds of macroscale mechanical boundary conditions. Unlike most multiscale techniques, our theory is aimed at understanding fundamental physics rather than achieving computing efficiency. Examples of problems with prescribed average displacements and surface tractions are presented to demonstrate the validity of the proposed multiscale molecular dynamics.

On the effect of preload and pre-stretch on hemodynamic simulations: an integrative approach

In this work, we address the simulation of three-dimensional arterial blood flow and its effect on the stress state of arterial walls. The novel contribution is the unprecedented combination of several modeling techniques to account for (1) the fact that known configurations for the arterial wall are in a preloaded state, (2) the compliance of the vessel segments, (3) proper boundary data over the non-physical interfaces resulting from the isolation of an arterial district from the rest of the arterial tree, (4) the presence of surrounding tissues in which the vessel is embedded and (5) residual stress state due to pre-stretch. Firstly, we formulate both the forward mechanical problem when the reference (zero-load) configuration is assumed to be known and, the preload problem arising when the known domain is a configuration at equilibrium with a certain load state (typically due to internal pressure and tethering forces). Then, two additional complexities are faced: the fluid-structure interaction problem that follows when the compliant vessels are coupled with the blood flow, and the introduction of non-physical boundaries coming from the artificial isolation of the arterial district from the original vessel. This, in turn, posses the problem of coupling dimensionally heterogeneous models to incorporate the effect of upstream and downstream systemic impedances. Additionally, a viscoelastic support on the external surface of the vessel is also incorporated. Two examples are presented to quantify in a physiologically consistent scenario the differences in simulation results when either considering or not the preload state of arterial walls. These computational simulations shed light on the validity of simplifying hypotheses in most hemodynamic models.

CoGNaC: A Chaste Plugin for the Multiscale Simulation of Gene Regulatory Networks Driving the Spatial Dynamics of Tissues and Cancer

We introduce a Chaste plugin for the generation and the simulation of Gene Regulatory Networks (GRNs) in multiscale models of multicellular systems. Chaste is a widely used and versatile computational framework for the multiscale modeling and simulation of multicellular biological systems. The plugin, named CoGNaC (Chaste and Gene Networks for Cancer), allows the linking of the regulatory dynamics to key properties of the cell cycle and of the differentiation process in populations of cells, which can subsequently be modeled using different spatial modeling scenarios. The approach of CoGNaC focuses on the emergent dynamical behavior of gene networks, in terms of gene activation patterns characterizing the different cellular phenotypes of real cells and, especially, on the overall robustness to perturbations and biological noise. The integration of this approach within Chaste’s modular simulation framework provides a powerful tool to model multicellular systems, possibly allowing for the formulation of novel hypotheses on gene regulation, cell differentiation, and, in particular, cancer emergence and development. In order to demonstrate the usefulness of CoGNaC over a range of modeling paradigms, two example applications are presented. The first of these concerns the characterization of the gene activation patterns of human T-helper cells. The second example is a multiscale simulation of a simplified intestinal crypt, in which, given certain conditions, tumor cells can emerge and colonize the tissue.

Automatising the analysis of stochastic biochemical time-series

BACKGROUND

Mathematical and computational modelling of biochemical systems has seen a lot of effort devoted to the definition and implementation of high-performance mechanistic simulation frameworks. Within these frameworks it is possible to analyse complex models under a variety of configurations, eventually selecting the best setting of, e.g., parameters for a target system.

MOTIVATION

This operational pipeline relies on the ability to interpret the predictions of a model, often represented as simulation time-series. Thus, an efficient data analysis pipeline is crucial to automatise time-series analyses, bearing in mind that errors in this phase might mislead the modeller's conclusions.

RESULTS

For this reason we have developed an intuitive framework-independent Python tool to automate analyses common to a variety of modelling approaches. These include assessment of useful non-trivial statistics for simulation ensembles, e.g., estimation of master equations. Intuitive and domain-independent batch scripts will allow the researcher to automatically prepare reports, thus speeding up the usual model-definition, testing and refinement pipeline.

Modeling oscillations and spiral waves in Dictyostelium populations

Unicellular organisms exhibit elaborate collective behaviors in response to environmental cues. These behaviors are controlled by complex biochemical networks within individual cells and coordinated through cell-to-cell communication. Describing these behaviors requires new mathematical models that can bridge scales-from biochemical networks within individual cells to spatially structured cellular populations. Here we present a family of "multiscale" models for the emergence of spiral waves in the social amoeba Dictyostelium discoideum. Our models exploit new experimental advances that allow for the direct measurement and manipulation of the small signaling molecule cyclic adenosine monophosphate (cAMP) used by Dictyostelium cells to coordinate behavior in cellular populations. Inspired by recent experiments, we model the Dictyostelium signaling network as an excitable system coupled to various preprocessing modules. We use this family of models to study spatially unstructured populations of "fixed" cells by constructing phase diagrams that relate the properties of population-level oscillations to parameters in the underlying biochemical network. We then briefly discuss an extension of our model that includes spatial structure and show how this naturally gives rise to spiral waves. Our models exhibit a wide range of novel phenomena. including a density-dependent frequency change, bistability, and dynamic death due to slow cAMP dynamics. Our modeling approach provides a powerful tool for bridging scales in modeling of Dictyostelium populations.

Multiscale Modeling of Gene-Behavior Associations in an Artificial Neural Network Model of Cognitive Development

In the multidisciplinary field of developmental cognitive neuroscience, statistical associations between levels of description play an increasingly important role. One example of such associations is the observation of correlations between relatively common gene variants and individual differences in behavior. It is perhaps surprising that such associations can be detected despite the remoteness of these levels of description, and the fact that behavior is the outcome of an extended developmental process involving interaction of the whole organism with a variable environment. Given that they have been detected, how do such associations inform cognitive-level theories? To investigate this question, we employed a multiscale computational model of development, using a sample domain drawn from the field of language acquisition. The model comprised an artificial neural network model of past-tense acquisition trained using the backpropagation learning algorithm, extended to incorporate population modeling and genetic algorithms. It included five levels of description-four internal: genetic, network, neurocomputation, behavior; and one external: environment. Since the mechanistic assumptions of the model were known and its operation was relatively transparent, we could evaluate whether cross-level associations gave an accurate picture of causal processes. We established that associations could be detected between artificial genes and behavioral variation, even under polygenic assumptions of a many-to-one relationship between genes and neurocomputational parameters, and when an experience-dependent developmental process interceded between the action of genes and the emergence of behavior. We evaluated these associations with respect to their specificity (to different behaviors, to function vs. structure), to their developmental stability, and to their replicability, as well as considering issues of missing heritability and gene-environment interactions. We argue that gene-behavior associations can inform cognitive theory with respect to effect size, specificity, and timing. The model demonstrates a means by which researchers can undertake multiscale modeling with respect to cognition and develop highly specific and complex hypotheses across multiple levels of description.

Multiscale modelling in immunology: a review

One of the greatest challenges in biomedicine is to get a unified view of observations made from the molecular up to the organism scale. Towards this goal, multiscale models have been highly instrumental in contexts such as the cardiovascular field, angiogenesis, neurosciences and tumour biology. More recently, such models are becoming an increasingly important resource to address immunological questions as well. Systematic mining of the literature in multiscale modelling led us to identify three main fields of immunological applications: host-virus interactions, inflammatory diseases and their treatment and development of multiscale simulation platforms for immunological research and for educational purposes. Here, we review the current developments in these directions, which illustrate that multiscale models can consistently integrate immunological data generated at several scales, and can be used to describe and optimize therapeutic treatments of complex immune diseases.

Strategies for efficient numerical implementation of hybrid multi-scale agent-based models to describe biological systems

Biologically related processes operate across multiple spatiotemporal scales. For computational modeling methodologies to mimic this biological complexity, individual scale models must be linked in ways that allow for dynamic exchange of information across scales. A powerful methodology is to combine a discrete modeling approach, agent-based models (ABMs), with continuum models to form hybrid models. Hybrid multi-scale ABMs have been used to simulate emergent responses of biological systems. Here, we review two aspects of hybrid multi-scale ABMs: linking individual scale models and efficiently solving the resulting model. We discuss the computational choices associated with aspects of linking individual scale models while simultaneously maintaining model tractability. We demonstrate implementations of existing numerical methods in the context of hybrid multi-scale ABMs. Using an example model describing Mycobacterium tuberculosis infection, we show relative computational speeds of various combinations of numerical methods. Efficient linking and solution of hybrid multi-scale ABMs is key to model portability, modularity, and their use in understanding biological phenomena at a systems level.

Semantically linking in silico cancer models

Multiscale models are commonplace in cancer modeling, where individual models acting on different biological scales are combined within a single, cohesive modeling framework. However, model composition gives rise to challenges in understanding interfaces and interactions between them. Based on specific domain expertise, typically these computational models are developed by separate research groups using different methodologies, programming languages, and parameters. This paper introduces a graph-based model for semantically linking computational cancer models via domain graphs that can help us better understand and explore combinations of models spanning multiple biological scales. We take the data model encoded by TumorML, an XML-based markup language for storing cancer models in online repositories, and transpose its model description elements into a graph-based representation. By taking such an approach, we can link domain models, such as controlled vocabularies, taxonomic schemes, and ontologies, with cancer model descriptions to better understand and explore relationships between models. The union of these graphs creates a connected property graph that links cancer models by categorizations, by computational compatibility, and by semantic interoperability, yielding a framework in which opportunities for exploration and discovery of combinations of models become possible.

Unraveling liver complexity from molecular to organ level: challenges and perspectives

Biological responses are determined by information processing at multiple and highly interconnected scales. Within a tissue the individual cells respond to extracellular stimuli by regulating intracellular signaling pathways that in turn determine cell fate decisions and influence the behavior of neighboring cells. As a consequence the cellular responses critically impact tissue composition and architecture. Understanding the regulation of these mechanisms at different scales is key to unravel the emergent properties of biological systems. In this perspective, a multidisciplinary approach combining experimental data with mathematical modeling is introduced. We report the approach applied within the Virtual Liver Network to analyze processes that regulate liver functions from single cell responses to the organ level using a number of examples. By facilitating interdisciplinary collaborations, the Virtual Liver Network studies liver regeneration and inflammatory processes as well as liver metabolic functions at multiple scales, and thus provides a suitable example to identify challenges and point out potential future application of multi-scale systems biology.

Performance of distributed multiscale simulations

Multiscale simulations model phenomena across natural scales using monolithic or component-based code, running on local or distributed resources. In this work, we investigate the performance of distributed multiscale computing of component-based models, guided by six multiscale applications with different characteristics and from several disciplines. Three modes of distributed multiscale computing are identified: supplementing local dependencies with large-scale resources, load distribution over multiple resources, and load balancing of small- and large-scale resources. We find that the first mode has the apparent benefit of increasing simulation speed, and the second mode can increase simulation speed if local resources are limited. Depending on resource reservation and model coupling topology, the third mode may result in a reduction of resource consumption.

Modeling biology spanning different scales: an open challenge

It is coming nowadays more clear that in order to obtain a unified description of the different mechanisms governing the behavior and causality relations among the various parts of a living system, the development of comprehensive computational and mathematical models at different space and time scales is required. This is one of the most formidable challenges of modern biology characterized by the availability of huge amount of high throughput measurements. In this paper we draw attention to the importance of multiscale modeling in the framework of studies of biological systems in general and of the immune system in particular.