Mathematical Models of Cell Migration and Proliferation in Scratch Assays

Scratch assays are standard in-vitro experimental procedures for studying cell migration. In these experiments, a scratch is made on a cell monolayer. By imaging the recolonisation process of the scratched region, we are able to quantify cell migration rates. This experimental technique is commonly used in the pharmaceutical industry to identify new compounds that target cell migration, and to evaluate the efficacy of potential drugs that inhibit cancer invasion. Given the key role this method plays in assessing the potential of new compounds for clinical use, it is important to develop robust quantification frameworks that accurately describe the movement of the front of migrating cells. We develop a migration quantification method that fits experimental data more closely than existing methods, provides a more accurate statistical classification of the migration rate between different assays and is able to cope with experimental data of lower quality than the classic quantification methods can handle. The robustness of our new method is validated using both in-vitro and in-silico data. Developing robust quantification methods allows the validation of mathematical models that can be used to test hypotheses about the physical and biological mechanisms that govern cell migration. Typically scratch assays are modelled by continuum reaction-diffusion equations depicting cell migration by diffusion and carrying capacity-limited proliferation by a logistic source term. An age-structured population model is presented that aims to explain the two phases of proliferation in scratch assays previously observed experimentally: where an initial phase is observed where proliferation is not logistic, followed by a second phase where proliferation appears to be logistic. The cell population is modelled by a McKendrick-von Foerster partial differential equation. The conditions under which the model captures this two-phase behaviour are presented. Finally, an important aspect of modelling biological systems is the development of efficient algorithms. The scratch assay is a classical example of a system in which there is low cell number in some regions of the spatial domain and high cell number in others. When the cell number is sufficiently high, mean-field models, like partial differential equations, can capture the relevant dynamics. However, when the cell number is low, such models are not appropriate and stochastic representations must be employed. Hybrid algorithms allow multiple modelling frameworks for the same species in different parts of the spatial domain. Typically hybrid algorithms consider heuristic methods based on the cell density for determining which compartments will be updated deterministically or stochastically. We introduce a hybrid algorithm that couples the mesoscopic description of a reaction-diffusion system with its mean-field analogue. We consider a natural indicator of when the mean-field approximation is valid: the system variance. We estimate the system variance using the intrinsic noise approximation and use this estimate to determine the regions in which the system is updated stochastically or deterministically over time. We apply the hybrid algorithm to the stochastic Fisher-Kolmogorov-Petrovsky-Piscounov model, a typical model of scratch assays. We analyse systematically how good is the approximation to the stochastic process and compare its performance to another hybrid algorithm

A level-set approach for a multi-scale cancer invasion model

The quest for a deeper understanding of the cancer growth and spread process focuses on the naturally multiscale nature of cancer invasion, which requires an appropriate multiscale modeling and analysis approach. The cross-talk between the dynamics of the cancer cell population on the tissue scale (macroscale) and the proteolytic molecular processes along the tumor border on the cell scale (microscale) plays a particularly important role within the invasion processes, leading to dramatic changes in tumor morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new  formulation of this process involving a novel derivation of the macro scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells

Local migration quantification method for scratch assays

The scratch assay is an in vitro technique used to assess the contribution of molecular and cellular mechanisms to cell migration. The assay can also be used to evaluate therapeutic compounds before clinical use. Current quantification methods of scratch assays deal poorly with irregular cell-free areas and crooked leading edges which are features typically present in the experimental data. We introduce a new migration quantification method, called 'monolayer edge velocimetry', that permits analysis of low-quality experimental data and better statistical classification of migration rates than standard quantification methods. The new method relies on quantifying the horizontal component of the cell monolayer velocity across the leading edge. By performing a classification test on in silico data, we show that the method exhibits significantly lower statistical errors than standard methods. When applied to in vitro data, our method outperforms standard methods by detecting differences in the migration rates between different cell groups that the other methods could not detect. Application of this new method will enable quantification of migration rates from in vitro scratch assay data that cannot be analysed using existing methods

Quantitative frameworks for understanding cancer cell invasion through in-vitro scratch assays

Scratch assays are standard in-vitro experimental methods for studying cell migration. In these experiments, a scratch is made on a cell monolayer and imaging of the recolonisation of the scratched region is performed to quantify cell migration rates. This experimental technique is commonly used in the pharmaceutical industry to identify new compounds that may promote cell migration in wound healing; and to evaluate the efficacy of potential drugs that inhibit cancer invasion. Two mathematical frameworks will be presented that analyse the dynamics of these experiments. First, a new migration quantification method will be presented that fits experimental data more closely than existing quantification methods, as well as providing a more accurate statistical classification of the migration rate between different assays. Moreover, it is also able to analyse experimental data of lower quality. The methodâs robustness is validated using in-vitro and in-silico data. Then, an age-structured population model will be presented that aims to explain the two phases of proliferation in scratch assays previously observed experimentally. The cell population is modelled by a McKendrick-von Foerster partial differential equation. The conditions under which the model captures this two-phase behaviour are presented.Non UBCUnreviewedAuthor affiliation: University of HeidelbergGraduat

A level-set approach for a multi-scale cancer invasion model

The quest for a deeper understanding of the cancer growth and spread process focuses on the naturally multiscale nature of cancer invasion, which requires an appropriate multiscale modeling and analysis approach. The cross-talk between the dynamics of the cancer cell population on the tissue scale (macroscale) and the proteolytic molecular processes along the tumor border on the cell scale (microscale) plays a particularly important role within the invasion processes, leading to dramatic changes in tumor morphology and influencing the overall pattern of cancer spread. Building on the multiscale moving boundary framework proposed in Trucu et al. (Multiscale Model. Simul 11(1): 309-335), in this work we propose a new  formulation of this process involving a novel derivation of the macro scale boundary movement law based on micro-dynamics, involving a transport equation combined with the level-set method. This is explored numerically in a novel finite element macro-micro framework based on cut-cells

Drug resistance phenotypes and genotypes in Mexico in representative gram-negative species: Results from the infivar network.

AimThis report presents phenotypic and genetic data on the prevalence and characteristics of extended-spectrum β-lactamases (ESBLs) and representative carbapenemases-producing Gram-negative species in Mexico.Material and methodsA total of 52 centers participated, 43 hospital-based laboratories and 9 external laboratories. The distribution of antimicrobial resistance data for Escherichia coli, Klebsiella pneumoniae, Enterobacter cloacae complex, Acinetobacter baumannii complex, and Pseudomonas aeruginosa in selected clinical specimens from January 1 to March 31, 2020 was analyzed using the WHONET 5.6 platform. The following clinical isolates recovered from selected specimens were included: carbapenem-resistant Enterobacteriaceae, ESBL or carbapenem-resistant E. coli, and K. pneumoniae, carbapenem-resistant A. baumannii complex, and P. aeruginosa. Strains were genotyped to detect ESBL and/or carbapenemase-encoding genes.ResultsAmong blood isolates, A. baumannii complex showed more than 68% resistance for all antibiotics tested, and among Enterobacteria, E. cloacae complex showed higher resistance to carbapenems. A. baumannii complex showed a higher resistance pattern for respiratory specimens, with only amikacin having a resistance lower than 70%. Among K. pneumoniae isolates, blaTEM, blaSHV, and blaCTX were detected in 68.79%, 72.3%, and 91.9% of isolates, respectively. Among E. coli isolates, blaTEM, blaSHV, and blaCTX were detected in 20.8%, 4.53%, and 85.7% isolates, respectively. For both species, the most frequent genotype was blaCTX-M-15. Among Enterobacteriaceae, the most frequently detected carbapenemase-encoding gene was blaNDM-1 (81.5%), followed by blaOXA-232 (14.8%) and blaoxa-181(7.4%), in A. baumannii was blaOXA-24 (76%) and in P. aeruginosa, was blaIMP (25.3%), followed by blaGES and blaVIM (13.1% each).ConclusionOur study reports that NDM-1 is the most frequent carbapenemase-encoding gene in Mexico in Enterobacteriaceae with the circulation of the oxacillinase genes 181 and 232. KPC, in contrast to other countries in Latin America and the USA, is a rare occurrence. Additionally, a high circulation of ESBL blaCTX-M-15 exists in both E. coli and K. pneumoniae