Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

No abstract

Models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations from exponential growth only at higher densities due to limited resources such as space and nutrients. However, recent pre-clinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models however, tumor growth data is limited by the lower limit of detection (i.e. a measurable lesion) and confounding variables, such as tumor microenvironment and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to consider the small number of cells in this low-density regime and use the moment approach for stochastic parameter estimation to calibrate the stochastic growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells depends on cell number. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging tumors and relapse. Author SummaryThe growth kinetics of cancer cells at very low cell densities are of utmost clinical importance as the ability of a small number of newly transformed or surviving cells to grow exponentially and thus, to "take off" underlies tumor formation and relapse after treatment. Mathematical models of stochastic tumor cell growth typically assume a stochastic birth-death process of cells impacted by limited nutrients and space when cells reach high density, resulting in the widely accepted logistic growth model. Here we present an in-depth investigation of alternate growth models adopted from ecology to describe potential deviations from a simple cell autonomous birth-death model at low cell densities. We show that our stochastic modeling framework is robust and can be used to identify the underlying structure of stochastic growth trajectories from both simulated and experimental data taken from a controlled in vitro setting in which we can capture data from the relevant low cell density regime. This work suggests that the assumption of cell autonomous proliferation via a constant exponential growth rate at low cell densities may not be appropriate for all cancer cell growth dynamics. Consideration of cooperative behavior amongst tumor cells in this regime is critical for elucidating strategies for controll...

The development of resistance to chemotherapy is a major cause of treatment failure in breast cancer. While mathematical models describing the dynamics of resistant cancer cell subpopulations have been proposed, experimental validation has been difficult due to the complex nature of resistance that limits the ability of a single phenotypic marker to sufficiently identify the drug resistant subpopulations. We address this problem with a coupled experimental/modeling approach to reveal the composition of drug resistant subpopulations changing in time following drug exposure. We calibrate time-resolved drug sensitivity assays to three mathematical models to interrogate the models’ ability to capture drug response dynamics. The Akaike information criterion was employed to evaluate the three models, and it identified a multi-state model incorporating the role of population heterogeneity and cellular plasticity as the optimal model. To validate the model’s ability to identify subpopulation composition, we mixed different proportions of wild-type MCF-7 and MCF-7/ADR resistant cells and evaluated the corresponding model output. Our blinded two-state model was able to estimate the proportions of cell types with an R-squared value of 0.857. To the best of our knowledge, this is the first work to combine experimental time-resolved drug sensitivity data with a mathematical model of resistance development.

Summary We provide an overview on the use of biological assays to calibrate and initialize mechanism-based models of cancer phenomena. Although artificial intelligence methods currently dominate the landscape in computational oncology, mathematical models that seek to explicitly incorporate biological mechanisms into their formalism are of increasing interest. These models can guide experimental design and provide insights into the underlying mechanisms of cancer progression. Historically, these models have included a myriad of parameters that have been difficult to quantify in biologically relevant systems, limiting their practical insights. Recently, however, there has been much interest calibrating biologically based models with the quantitative measurements available from (for example) RNA sequencing, time-resolved microscopy, and in vivo imaging. In this contribution, we summarize how a variety of experimental methods quantify tumor characteristics from the molecular to tissue scales and describe how such data can be directly integrated with mechanism-based models to improve predictions of tumor growth and treatment response.

Background Factors that lead to successful SARS-CoV-2 transmission are still not well described. We investigated the association between a case’s viral load and the risk of transmission to contacts in the context of other exposure-related factors. Methods Data were generated through routine testing and contact tracing at a large university. Case viral loads were obtained from cycle threshold values associated with a positive polymerase chain reaction test result from October 1, 2020 to April 15, 2021. Cases were included if they had at least one contact who tested 3–14 days after the exposure. Case-contact pairs were formed by linking index cases with contacts. Chi-square tests were used to evaluate differences in proportions of contacts testing positive. Generalized estimating equation models with a log link were used to evaluate whether viral load and other exposure-related factors were associated with a contact testing positive. Results Median viral load among the 212 cases included in the study was 5.6 (1.8–10.4) log10 RNA copies per mL of saliva. Among 365 contacts, 70 (19%) tested positive following their exposure; 36 (51%) were exposed to a case that was asymptomatic or pre-symptomatic on the day of exposure. The proportion of contacts that tested positive increased monotonically with index case viral load (12%, 23% and 25% corresponding to < 5, 5–8 and > 8 log10 copies per mL, respectively; X2 = 7.18, df = 2, p = 0.03). Adjusting for cough, time between test and exposure, and physical contact, the risk of transmission to a close contact was significantly associated with viral load (RR = 1.27, 95% CI 1.22–1.32). Conclusions Further research is needed to understand whether these relationships persist for newer variants. For those variants whose transmission advantage is mediated through a high viral load, public health measures could be scaled accordingly. Index cases with higher viral loads could be prioritized for contact tracing and recommendations to quarantine contacts could be made according to the likelihood of transmission based on risk factors such as viral load.

As the ongoing COVID-19 pandemic passes from an acute to a chronic situation, countries and territories are grappling with the issue of how to reopen safely. The unique kinetics of infectivity of SARS-CoV-2, with its significant presymptomatic transmission, presents an unprecedented challenge to our intuitions. In this context, a generalizable quantitative understanding of the impact of SARS-CoV-2 infectivity on disease control strategies is vital. We used a previously published time-dependent model of SARS-CoV-2 infectivity (He et al., 2020) to parameterize an epidemiological model of transmission, which was then used to explore the effect of various disease control measures. Our analysis suggests that using symptom-based isolation alone as a control strategy is ineffective in limiting the spread of COVID-19, in contrast to its effectiveness in other diseases, such as SARS and influenza. Additionally, timeliness of testing and tracing strategies to reduce time to isolation, along with widespread adoption of measures to limit transmission are critical for any containment strategy. Our findings suggest that for symptom-based isolation and testing strategies to be effective, reduced transmission is required, reinforcing the importance of measures to limit transmission. From a public health strategy perspective, our findings lend support to the idea that symptomatic isolation should not form the primary basis for COVID-19 disease control.

19: Prolonged viral shedding in an HIV patient with literature review of risk factors for prolonged viral shedding and its implications for isolation strategies.