Synergistic effects of inhaled aztreonam plus tobramycin on hypermutable cystic fibrosis Pseudomonas aeruginosa isolates in a dynamic biofilm model evaluated by mechanism-based modeling and whole genome sequencing.

Hypermutable Pseudomonas aeruginosa strains are highly prevalent in chronic lung infections of patients with cystic fibrosis (CF). Acute exacerbations of these infections have limited treatment options. This study aimed to investigate inhaled aztreonam and tobramycin against clinical hypermutable P. aeruginosa strains using the CDC dynamic in vitro biofilm reactor (CBR), mechanism-based mathematical modeling (MBM) and genomic studies. Two CF multidrug-resistant strains were investigated in a 168h CBR (n=2 biological replicates). Regimens were inhaled aztreonam (75 mg 8-hourly) and tobramycin (300 mg 12-hourly) in monotherapies and combination. The simulated pharmacokinetic profiles of aztreonam and tobramycin (t1/2=3h) were based on published lung fluid concentrations in patients with CF. Total viable and resistant counts were determined for planktonic and biofilm bacteria. MBM of total and resistant bacterial counts, and whole genome sequencing were completed. Both isolates showed reproducible bacterial regrowth and resistance amplification for the monotherapies by 168h. The combination performed synergistically, with minimal resistant subpopulations compared to the respective monotherapies at 168h. Mechanistic synergy appropriately described the antibacterial effects of the combination regimen in the MBM. Genomic analysis of colonies recovered from monotherapy regimens indicated noncanonical resistance mechanisms were likely responsible for treatment failure. The combination of aztreonam and tobramycin was required to suppress regrowth and resistance of planktonic and biofilm bacteria in all biological replicates of both hypermutable multidrug-resistant P. aeruginosa CF isolates. The developed MBM could be utilized for future investigations of this promising inhaled combination.

Translational modeling-based evidence for enhanced efficacy of standard-of-care drugs in combination with anti-microRNA-155 in non-small-cell lung cancer.

Elevated microRNA-155 (miR-155) expression in non-small-cell lung cancer (NSCLC) promotes cisplatin resistance and negatively impacts treatment outcomes. However, miR-155 can also boost anti-tumor immunity by suppressing PD-L1 expression. We developed a multiscale mechanistic model, calibrated with in vivo data and then extrapolated to humans, to investigate the therapeutic effects of nanoparticle-delivered anti-miR-155 in NSCLC, alone or in combination with standard-of-care drugs. Model simulations and analyses of the clinical scenario revealed that monotherapy with anti-miR-155 at a dose of 2.5 mg/kg administered once every three weeks has substantial anti-cancer activity. It led to a median progression-free survival (PFS) of 6.7 months, which compared favorably to cisplatin and immune checkpoint inhibitors. Further, we explored the combinations of anti-miR-155 with standard-of-care drugs, and found strongly synergistic two- and three-drug combinations. A three-drug combination of anti-miR-155, cisplatin, and pembrolizumab resulted in a median PFS of 13.1 months, while a two-drug combination of anti-miR-155 and cisplatin resulted in a median PFS of 11.3 months, which emerged as a more practical option due to its simple design and cost-effectiveness. Our analyses also provided valuable insights into unfavorable dose ratios for drug combinations, highlighting the need for optimizing dose regimen to prevent antagonistic effects. Thus, this work bridges the gap between preclinical development and clinical translation of anti-miR-155 and unravels the potential of anti-miR-155 combination therapies in NSCLC.

A Refined Thin-Film Model for Drug Dissolution Considering Radial Diffusion - Simulating Powder Dissolution.

PURPOSE: We aim to present a refined thin-film model describing the drug particle dissolution considering radial diffusion in spherical boundary layer, and to demonstrate the ability of the model to describe the dissolution behavior of bulk drug powders. METHODS: The dissolution model introduced in this study was refined from a radial diffusion-based model previously published by our laboratory (So et al. in Pharm Res. 39:907-17, 2022). The refined model was created to simulate the dissolution of bulk powders, and to account for the evolution of particle size and diffusion layer thickness during dissolution. In vitro dissolution testing, using fractionated hydrochlorothiazide powders, was employed to assess the performance of the model. RESULTS: Overall, there was a good agreement between the experimental dissolution data and the predicted dissolution profiles using the proposed model across all size fractions of hydrochlorothiazide. The model over-predicted the dissolution rate when the particles became smaller. Notably, the classic Nernst-Brunner formalism led to an under-estimation of the dissolution rate. Additionally, calculation based on the equivalent particle size derived from the specific surface area substantially over-predicted the dissolution rate. CONCLUSION: The study demonstrated the potential of the radial diffusion-based model to describe dissolution of drug powders. In contrast, the classic Nernst-Brunner equation could under-estimate drug dissolution rate, largely due to the underlying assumption of translational diffusion. Moreover, the study indicated that not all surfaces on a drug particle contribute to dissolution. Therefore, relying on the experimentally-determined specific surface area for predicting drug dissolution is not advisable.

Cracking the code: Spatial heterogeneity as the missing piece for modeling granular fluidized bed drying.

Pharmaceutical twin-screw wet granulation is a multifaceted and intricate process pivotal to drug product development. Accurate modeling of this process is indispensable for optimizing manufacturing parameters and ensuring product quality. The fluid bed dryer, an integral component of this granulation process, significantly influences the granular critical quality attributes. This study builds upon prior research by integrating experimental findings on granule segregation during fluid bed drying into an existing compartmental model, enhancing its predictive capabilities. An additional model layer on granule segregation behavior is composed and integrated into the existing model structure in this study. The added model compartment describes probability distributions on the vertical position of granules within each granule size class considered. To beware of overfitting, predictions of both the moisture content after drying and the granule bed temperature throughout drying are discussed in this study relative to experimental data from earlier published studies. These independent analyses demonstrated a marked improvement in prediction accuracy compared to earlier published model structures. The refined model accurately predicts the residual moisture content after drying for an untrained formulation. Moreover, it simultaneously makes accurate predictions of the granular bed temperature, which emboldens its structural correctness. This advancement makes it a powerful tool for predicting the behavior of the pharmaceutical fluid bed drying, which holds significant promise to facilitate pharmaceutical product development.

Mathematical modelling of clonal reduction therapeutic strategies in acute myeloid leukemia.

Over the years, the overall survival of older patients diagnosed with acute myeloid leukemia (AML) has not significantly increased. Although standard cytotoxic therapies that rapidly eliminate dividing myeloblasts are used to induce remission, relapse can occur due to surviving therapy-resistant leukemic stem cells (LSCs). Hence, anti-LSC strategies have become a key target to cure AML. We have recently shown that previously approved cardiac glycosides and glucocorticoids target LSC-enriched CD34+ cells in the primary human AML 8227 model with more efficacy than normal hematopoietic stem cells (HSCs). To translate these in vitro findings into humans, we developed a mathematical model of stem cell dynamics that describes the stochastic evolution of LSCs in AML post-standard-of-care. To this, we integrated population pharmacokinetic-pharmacodynamic (PKPD) models to investigate the clonal reduction potential of several promising candidate drugs in comparison to cytarabine, which is commonly used in high doses for consolidation therapy in AML patients. Our results suggest that cardiac glycosides (proscillaridin A, digoxin and ouabain) and glucocorticoids (budesonide and mometasone) reduce the expansion of LSCs through a decrease in their viability. While our model predicts that effective doses of cardiac glycosides are potentially too toxic to use in patients, simulations show the possibility of mometasone to prevent relapse through the glucocorticoid's ability to drastically reduce LSC population size. This work therefore highlights the prospect of these treatments for anti-LSC strategies and underlines the use of quantitative approaches to preclinical drug translation in AML.

Hybridizing mechanistic mathematical modeling with deep learning methods to predict individual cancer patient survival after immune checkpoint inhibitor therapy.

We present a study where predictive mechanistic modeling is used in combination with deep learning methods to predict individual patient survival probabilities under immune checkpoint inhibitor (ICI) therapy. This hybrid approach enables prediction based on both measures that are calculable from mechanistic models (but may not be directly measurable in the clinic) and easily measurable quantities or characteristics (that are not always readily incorporated into predictive mechanistic models). The mechanistic model we have applied here can predict tumor response from CT or MRI imaging based on key mechanisms underlying checkpoint inhibitor therapy, and in the present work, its parameters were combined with readily-available clinical measures from 93 patients into a hybrid training set for a deep learning time-to-event predictive model. Analysis revealed that training an artificial neural network with both mechanistic modeling-derived and clinical measures achieved higher per-patient predictive accuracy based on event-time concordance, Brier score, and negative binomial log-likelihood-based criteria than when only mechanistic model-derived values or only clinical data were used. Feature importance analysis revealed that both clinical and model-derived parameters play prominent roles in neural network decision making, and in increasing prediction accuracy, further supporting the advantage of our hybrid approach. We anticipate that many existing mechanistic models may be hybridized with deep learning methods in a similar manner to improve predictive accuracy through addition of additional data that may not be readily implemented in mechanistic descriptions.

Mathematical Models of Early Hepatitis B Virus Dynamics in Humanized Mice.

Analyzing the impact of the adaptive immune response during acute hepatitis B virus (HBV) infection is essential for understanding disease progression and control. Here we developed mathematical models of HBV infection which either lack terms for adaptive immune responses, or assume adaptive immune responses in the form of cytolytic immune killing, non-cytolytic immune cure, or non-cytolytic-mediated block of viral production. We validated the model that does not include immune responses against temporal serum hepatitis B DNA (sHBV) and temporal serum hepatitis B surface-antigen (HBsAg) experimental data from mice engrafted with human hepatocytes (HEP). Moreover, we validated the immune models against sHBV and HBsAg experimental data from mice engrafted with HEP and human immune system (HEP/HIS). As expected, the model that does not include adaptive immune responses matches the observed high sHBV and HBsAg concentrations in all HEP mice. By contrast, while all immune response models predict reduction in sHBV and HBsAg concentrations in HEP/HIS mice, the Akaike Information Criterion cannot discriminate between non-cytolytic cure (resulting in a class of cells refractory to reinfection) and antiviral block functions (of up to 99 % viral production 1-3 weeks following peak viral load). We can, however, reject cytolytic killing, as it can only match the sHBV and HBsAg data when we predict unrealistic levels of hepatocyte loss.

Mathematical modeling of viral infection and the immune response controlled by the circadian clock.

Time of day affects how well the immune system responds to viral or bacterial infections. While it is well known that the immune system is regulated by the circadian clock, the dynamic origin of time-of-day-dependent immunity remains unclear. In this paper, we studied the circadian control of immune response upon infection of influenza A virus through mathematical modeling. Dynamic simulation analyses revealed that the time-of-day-dependent immunity was rooted in the relative phase between the circadian clock and the pulse of viral infection. The relative phase, which depends on the time the infection occurs, plays a crucial role in the immune response. It can drive the immune system to one of two distinct bistable states, a high inflammatory state with a higher mortality rate or a safe state characterized by low inflammation. The mechanism we found here also explained why the same species infected by different viruses has different time-of-day-dependent immunities. Further, the time-of-day-dependent immunity was found to be abolished when the immune system was regulated by an impaired circadian clock with decreased oscillation amplitude or without oscillations.

Mathematical Modeling of Initial Exothermic Behavior and Thixotropic Properties in Nanoclay-Enhanced Cementitious Materials.

In the realm of cementitious materials, integrating nanoclay shows promise in enhancing properties relevant to additive manufacturing. This paper presents a novel mathematical model that combines simple empirical dissolution/nucleation Avrami-like kinetics with a thixotropic kinetics equation. To analyze the initial exothermic peak, two sets of the calculation parameter function are built to describe the exothermic rate as a function of time, following an exponential pattern. This allows for the prediction of the changes in cumulative heat and heat rate during hydration, considering different concentrations of nanoclay. In the rheological aspect, the relationship between shear stress, shear rate, and time is modeled as a combination of exponential dependencies. This enables the prediction of the variations in shear stress with one variable while holding the other constant (either time or shear rate). By integrating these aspects, this model effectively describes both the first exothermal peak and the rheological behavior during cement hydration with the inclusion of nanoclay. Validated against experimental results, these models demonstrate good accuracy (overall below 3% error), reliability, and applicability. The findings offer valuable insights into the thermal and rheological aspects of concrete printing, enabling informed design decisions for both scientific and industrial applications.

Mechanistic regulation of planarian shape during growth and degrowth.

Adult planarians can grow when fed and degrow (shrink) when starved while maintaining their whole-body shape. It is unknown how the morphogens patterning the planarian axes are coordinated during feeding and starvation or how they modulate the necessary differential tissue growth or degrowth. Here we investigate the dynamics of planarian shape together with a theoretical study of the mechanisms regulating whole-body proportions and shape. We found that the planarian body proportions scale isometrically following similar linear rates during growth and degrowth, but that fed worms are significantly wider than starved worms. By combining a descriptive model of planarian shape and size with a mechanistic model of anterior-posterior and medio-lateral signaling calibrated with a novel parameter optimization methodology, we theoretically demonstrate that the feedback loop between these positional information signals and the shape they control can regulate the planarian whole-body shape during growth. Furthermore, the computational model produced the correct shape and size dynamics during degrowth due to a predicted increase in apoptosis rate and pole signal during starvation. These results offer mechanistic insights into the dynamic regulation of whole-body morphologies.

Theoretical considerations and empirical predictions of the pharmaco- and population dynamics of heteroresistance.

Antibiotics are considered one of the most important contributions to clinical medicine in the last century. Due to the use and overuse of these drugs, there have been increasing frequencies of infections with resistant pathogens. One form of resistance, heteroresistance, is particularly problematic; pathogens appear sensitive to a drug by common susceptibility tests. However, upon exposure to the antibiotic, resistance rapidly ascends, and treatment fails. To quantitatively explore the processes contributing to the emergence and ascent of resistance during treatment and the waning of resistance following cessation of treatment, we develop two distinct mathematical and computer-simulation models of heteroresistance. In our analysis of the properties of these models, we consider the factors that determine the response to antibiotic-mediated selection. In one model, heteroresistance is progressive, with each resistant state sequentially generating a higher resistance level. In the other model, heteroresistance is non-progressive, with a susceptible population directly generating populations with different resistance levels. The conditions where resistance will ascend in the progressive model are narrower than those of the non-progressive model. The rates of reversion from the resistant to the sensitive states are critically dependent on the transition rates and the fitness cost of resistance. Our results demonstrate that the standard test used to identify heteroresistance is insufficient. The predictions of our models are consistent with empirical results. Our results demand a reevaluation of the definition and criteria employed to identify heteroresistance. We recommend that the definition of heteroresistance should include a consideration of the rate of return to susceptibility.

Quantifying the integrated physiological effects of endothelin-1 on cardiovascular and renal function in healthy subjects: a mathematical modeling analysis.

Endothelin-1 (ET-1) is a potent vasoconstrictor with strong anti-natriuretic and anti-diuretic effects. While many experimental studies have elucidated the mechanisms of ET-1 through its two receptors, ETA and ETB, the complexity of responses and sometimes conflicting data make it challenging to understand the effects of ET-1, as well as potential therapeutic antagonism of ET-1 receptors, on human physiology. In this study, we aimed to develop an integrated and quantitative description of ET-1 effects on cardiovascular and renal function in healthy humans by coupling existing experimental data with a mathematical model of ET-1 kinetics and an existing mathematical model of cardiorenal function. Using a novel agnostic and iterative approach to incorporating and testing potential mechanisms, we identified a minimal set of physiological actions of endothelin-1 through ETA and ETB receptors by fitting the physiological responses (changes in blood pressure, renal blood flow, glomerular filtration rate (GFR), and sodium/water excretion) to ET-1 infusion, with and without ETA/ETB antagonism. The identified mechanisms align with previous experimental studies on ET-1 and offer novel insights into the relative magnitude and significance of endothelin's effects. This model serves as a foundation for further investigating the mechanisms of ET-1 and its antagonists.

Mathematical Modeling of Photo- and Thermomorphogenesis in Plants.

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.

Effect of the temperature and ultrasound on salt impregnation process of haddock.

The influence of different brine temperatures (5, 15 and 25 °C) and ultrasound on the salt gain (SG) and water gain (WG) kinetics of haddock cubes during vacuum impregnation (VI) process was evaluated. Samples were taken from salt solution (4 g NaCl/ 100 g solution) after 0, 20, 40, 60, 100, 140 and 180 min of brining process for salt and moisture analysis. Ultrasound assisted VI and increasing temperature in the salt solution increased (P < 0.05) the salt content, and SG value in the haddock cubes. Furthermore, ultrasound assisted VI enhanced the water diffusion into the cubes and resulted in an increase in WG value. The ultrasound process increased the salt effective diffusion coefficient (Ds) and the highest Ds was found at 25 °C brine temperature. Azuara, Diffusive, Peleg, Weibull, Z and L models were tested to predicting SG and WG kinetics and Azuara was the best model during brining process of haddock cubes.

Emergence of Orchestrated and Dynamic Metabolism of Saccharomyces cerevisiae.

Microbial metabolism is a fundamental cellular process that involves many biochemical events and is distinguished by its emergent properties. While the molecular details of individual reactions have been increasingly elucidated, it is not well understood how these reactions are quantitatively orchestrated to produce collective cellular behaviors. Here we developed a coarse-grained, systems, and dynamic mathematical framework, which integrates metabolic reactions with signal transduction and gene regulation to dissect the emergent metabolic traits of Saccharomyces cerevisiae. Our framework mechanistically captures a set of characteristic cellular behaviors, including the Crabtree effect, diauxic shift, diauxic lag time, and differential growth under nutrient-altered environments. It also allows modular expansion for zooming in on specific pathways for detailed metabolic profiles. This study provides a systems mathematical framework for yeast metabolic behaviors, providing insights into yeast physiology and metabolic engineering.

Modeling and experimental analysis of CO2 methanation reaction using Ni/CeO2 monolithic catalyst.

In this study, the effect of the cell density of monolithic catalysts was investigated and further mathematically modeled on cordierite supports used in CO2 methanation. Commercial cordierite monoliths with 200, 400, and 500 cpsi cell densities were coated by immersion into an ethanolic suspension of Ni/CeO2 active phase. SEM-EDS analysis confirmed that, owing to the low porosity of cordierite (surface area < 1 m2 g-1), the Ni/CeO2 diffusion into the walls was limited, especially in the case of low and intermediate cell density monoliths; thus, active phase was predominantly loaded onto the channels' external surface. Nevertheless, despite the larger exposed surface area in the monolith with high cell density, which would allow for better distribution and accessibility of Ni/CeO2, its higher macro-pore volume resulted in some introduction of the active phase into the walls. As a result, the catalytic evaluation showed that it was more influenced by increments in volumetric flow rates. The low cell density monolith displayed diffusional control at flow rates below 500 mL min-1. In contrast, intermediate and high cell density monoliths presented this behavior up to 300 mL min-1. These findings suggest that the interaction reactants-catalyst is considerably more affected by a forced non-uniform flow when increasing the injection rate. This condition reduced the transport of reactants and products within the catalyst channels and, in turn, increased the minimum temperature required for the reaction. Moreover, a slight diminution of selectivity to CH4 was observed and ascribed to the possible formation of hot spots that activate the reverse water-gas shift reaction. Finally, a mathematical model based on fundamental momentum and mass transfer equations coupled with the kinetics of CO2 methanation was successfully derived and solved to analyze the fluid dynamics of the monolithic support. The results showed a radial profile with maximum fluid velocity located at the center of the channel. A reactive zone close to the inlet was obtained, and maximum methane production (4.5 mol m-3) throughout the monolith was attained at 350 °C. Then, linear streamlines of the chemical species were developed along the channel.

A Mathematical Model for the Impact of 3HP and Social Programme Implementation on the Incidence and Mortality of Tuberculosis: Study in Brazil.

In this paper, we presented a mathematical model for tuberculosis with treatment for latent tuberculosis cases and incorporated social implementations based on the impact they will have on tuberculosis incidence, cure, and recovery. We incorporated two variables containing the accumulated deaths and active cases into the model in order to study the incidence and mortality rate per year with the data reported by the model. Our objective is to study the impact of social program implementations and therapies on latent tuberculosis in particular the use of once-weekly isoniazid-rifapentine for 12 weeks (3HP). The computational experimentation was performed with data from Brazil and for model calibration, we used the Markov Chain Monte Carlo method (MCMC) with a Bayesian approach. We studied the effect of increasing the coverage of social programs, the Bolsa Familia Programme (BFP) and the Family Health Strategy (FHS) and the implementation of the 3HP as a substitution therapy for two rates of diagnosis and treatment of latent at 1% and 5%. Based of the data obtained by the model in the period 2023-2035, the FHS reported better results than BFP in the case of social implementations and 3HP with a higher rate of diagnosis and treatment of latent in the reduction of incidence and mortality rate and in cases and deaths avoided. With the objective of linking the social and biomedical implementations, we constructed two different scenarios with the rate of diagnosis and treatment. We verified with results reported by the model that with the social implementations studied and the 3HP with the highest rate of diagnosis and treatment of latent, the best results were obtained in comparison with the other independent and joint implementations. A reduction of the incidence by 36.54% with respect to the model with the current strategies and coverage was achieved, and a greater number of cases and deaths from tuberculosis was avoided.

A Mathematical Model of TCR-T Cell Therapy for Cervical Cancer.

Engineered T cell receptor (TCR)-expressing T (TCR-T) cells are intended to drive strong anti-tumor responses upon recognition of the specific cancer antigen, resulting in rapid expansion in the number of TCR-T cells and enhanced cytotoxic functions, causing cancer cell death. However, although TCR-T cell therapy against cancers has shown promising results, it remains difficult to predict which patients will benefit from such therapy. We develop a mathematical model to identify mechanisms associated with an insufficient response in a mouse cancer model. We consider a dynamical system that follows the population of cancer cells, effector TCR-T cells, regulatory T cells (Tregs), and "non-cancer-killing" TCR-T cells. We demonstrate that the majority of TCR-T cells within the tumor are "non-cancer-killing" TCR-T cells, such as exhausted cells, which contribute little or no direct cytotoxicity in the tumor microenvironment (TME). We also establish two important factors influencing tumor regression: the reversal of the immunosuppressive TME following depletion of Tregs, and the increased number of effector TCR-T cells with antitumor activity. Using mathematical modeling, we show that certain parameters, such as increasing the cytotoxicity of effector TCR-T cells and modifying the number of TCR-T cells, play important roles in determining outcomes.

Numerical modeling of senile plaque development under conditions of limited diffusivity of amyloid-ß monomers.

This paper introduces a new model to simulate the progression of senile plaques, focusing on scenarios where concentrations of amyloid beta (Aß) monomers and aggregates vary between neurons. Extracellular variations in these concentrations may arise due to limited diffusivity of Aß monomers and a high rate of Aß monomer production at lipid membranes, requiring a substantial concentration gradient for diffusion-driven transport of Aß monomers. The dimensionless formulation of the model is presented, which identifies four key dimensionless parameters governing the solutions for Aß monomer and aggregate concentrations, as well as the radius of a growing Aß plaque within the control volume. These parameters include the dimensionless diffusivity of Aß monomers, the dimensionless rate of Aß monomer production, and the dimensionless half-lives of Aß monomers and aggregates. A dimensionless parameter is then introduced to evaluate the validity of the lumped capacitance approximation. An approximate solution is derived for the scenario involving large diffusivity of Aß monomers and dysfunctional protein degradation machinery, resulting in infinitely long half-lives for Aß monomers and aggregates. In this scenario, the concentrations of Aß aggregates and the radius of the Aß plaque depend solely on a single dimensionless parameter that characterizes the rate of Aß monomer production. According to the approximate solution, the concentration of Aß aggregates is linearly dependent on the rate of monomer production, and the radius of an Aß plaque is directly proportional to the cube root of the rate of monomer production. However, when departing from the conditions of the approximate solution (e.g., finite half-lives), the concentrations of Aß monomers and aggregates, along with the plaque radius, exhibit complex dependencies on all four dimensionless parameters. For instance, under physiological half-life conditions, the plaque radius reaches a maximum value and stabilizes thereafter.

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist.

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.