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.

Modeling the Development of Cellular Exhaustion and Tumor-Immune Stalemate.

Cellular exhaustion in various immune cells develops in response to prolonged stimulation and overactivation during chronic infections and in cancer. Marked by an upregulation of inhibitory receptors and diminished effector functions, exhausted immune cells are unable to fully eradicate the antigen responsible for the overexposure. In cancer settings, this results in a relatively small but constant tumor burden known as a localized tumor-immune stalemate. In recent years, studies have elucidated key aspects of the development and progression of cellular exhaustion and have re-addressed previous misconceptions. Biological publications have also provided insight into the functional capabilities of exhausted cells. Complementing these findings, the model presented here serves as a mathematical framework for the establishment of cellular exhaustion and the development of the localized stalemate against a solid tumor. Analysis of this model indicates that this stalemate is stable and can handle small perturbations. Additionally, model analysis also provides insight into potential targets of future immunotherapy efforts.

Mining Marine Metagenomes Revealed a Quorum-Quenching Lactonase with Improved Biochemical Properties That Inhibits the Food Spoilage Bacterium Pseudomonas fluorescens.

The marine environment presents great potential as a source of microorganisms that possess novel enzymes with unique activities and biochemical properties. Examples of such are the quorum-quenching (QQ) enzymes that hydrolyze bacterial quorum-sensing (QS) signaling molecules, such as N-acyl-homoserine lactones (AHLs). QS is a form of cell-to-cell communication that enables bacteria to synchronize gene expression in correlation with population density. Searching marine metagenomes for sequences homologous to an AHL lactonase from the phosphotriesterase-like lactonase (PLL) family, we identified new putative AHL lactonases (sharing 30 to 40% amino acid identity to a thermostable PLL member). Phylogenetic analysis indicated that these putative AHL lactonases comprise a new clade of marine enzymes in the PLL family. Following recombinant expression and purification, we verified the AHL lactonase activity for one of these proteins, named moLRP (marine-originated lactonase-related protein). This enzyme presented greater activity and stability at a broad range of temperatures and pH, tolerance to high salinity levels (up to 5 M NaCl), and higher durability in bacterial culture, compared to another PLL member, parathion hydrolase (PPH). The addition of purified moLRP to cultures of Pseudomonas fluorescens inhibited its extracellular protease activity, expression of the protease encoding gene, biofilm formation, and the sedimentation process in milk-based medium. These findings suggest that moLRP is adapted to the marine environment and can potentially serve as an effective QQ enzyme, inhibiting the QS process in Gram-negative bacteria involved in food spoilage. IMPORTANCE Our results emphasize the potential of sequence and structure-based identification of new QQ enzymes from environmental metagenomes, such as from the ocean, with improved stability or activity. The findings also suggest that purified QQ enzymes can present new strategies against food spoilage, in addition to their recognized involvement in inhibiting bacterial pathogen virulence factors. Future studies on the delivery and safety of enzymatic QQ strategy against bacterial food spoilage should be performed.

The Effectiveness of Case-management Rehabilitation Intervention in Facilitating Return to Work and Maintenance of Employment After Myocardial Infarction: Results of a Randomized Controlled Trial.

OBJECTIVE: To study the long-term effectiveness of case-management rehabilitation intervention on vocational reintegration of patients after myocardial infarction (MI). DESIGN: Blinded simple randomization was used to construct an intervention and control groups that were followed up for two years. SUBJECTS AND SETTING: 151 patients, aged 50.3 ± 5.9 years, who experienced uncomplicated MI and were enrolled in a cardiac rehabilitation program were recruited. INTERVENTIONS: included an early referral to an occupational physician, tailoring an occupational rehabilitation program, based on individual patient needs, coordination with relevant parties, psychosocial intervention, intensive follow-up sessions during a two-year follow-up. MAIN MEASURES: Return to work within six months of hospitalization and maintenance of employment at one and two years of follow-up. RESULTS: Return-to-work (RTW) rate in the intervention group was 89% and nearly all maintained employment at one year of follow-up (92%) and two years of follow-up (87%). Moreover, almost all of them returned to and maintained their previous jobs. The corresponding figures were: 98%, 94% and 98%, respectively. The figures for the RTW and employment maintenance for the control group were: 74%, 75%, and 72%, respectively. Only about 75%, in this group kept their previous job. The case-management intervention was associated with increased odds of maintaining employment at follow-up of one year (OR = 5.89, 95% CI 1.42-24.30) and two years (OR = 3.12, 95% CI 1.01-10.03). CONCLUSIONS: The extended case-management rehabilitation intervention had a substantial positive impact on both the RTW of MI patients and their maintenance of employment at one and two years of follow-up. TRIAL REGISTRATION: This trial is registered at US National Institutes of Health #NCT04934735.

Modeling LSD1-Mediated Tumor Stagnation.

LSD1 (KDMA1) has gained attention in the last decade as a cancer biomarker and drug target. In particular, recent work suggests that LSD1 inhibition alone reduces tumor growth, increases T cell tumor infiltration, and complements PD1/PDL1 checkpoint inhibitor therapy. In order to elucidate the immunogenic effects of LSD1 inhibition, we develop a mathematical model of tumor growth under the influence of the adaptive immune response. In particular, we investigate the anti-tumor cytotoxicity of LSD1-mediated T cell dynamics, in order to better understand the synergistic potential of LSD1 inhibition in combination immunotherapies, including checkpoint inhibitors. To that end, we formulate a non-spatial delay differential equation model and fit to the B16 mouse model data from Sheng et al. (Cell 174(3):549-563, 2018. https://doi.org/10.1016/j.cell.2018.05.052 ). Our results suggest that the immunogenic effect of LSD1 inhibition accelerates anti-tumor cytotoxicity. However, cytotoxicity does not seem to account for the slower growth observed in LSD1-inhibited tumors, despite evidence suggesting immune-mediation of this effect.

Study of dose-dependent combination immunotherapy using engineered T cells and IL-2 in cervical cancer.

Adoptive T cell based immunotherapy is gaining significant traction in cancer treatment. Despite its limited efficacy so far in treating solid tumors compared to hematologic cancers, recent advances in T cell engineering render this treatment increasingly more successful in solid tumors, demonstrating its broader therapeutic potential. In this paper we develop a mathematical model to study the efficacy of engineered T cell receptor (TCR) T cell therapy targeting the E7 antigen in cervical cancer cell lines. We consider a dynamical system that follows the population of cancer cells, TCR T cells, and IL-2 treatment concentration. We demonstrate that there exists a TCR T cell dosage window for a successful cancer elimination that can be expressed in terms of the initial tumor size. We obtain the TCR T cell dose for two cervical cancer cell lines: 4050 and CaSki. Finally, a combination therapy of TCR T cell and IL-2 treatment is studied. We show that certain treatment protocols can improve therapy responses in the 4050 cell line, but not in the CaSki cell line.

Modeling the Effect of Memory in the Adaptive Immune Response.

It is well understood that there are key differences between a primary immune response and subsequent responses. Specifically, memory T cells that remain after a primary response drive the clearance of antigen in later encounters. While the existence of memory T cells is widely accepted, the specific mechanisms that govern their function are generally debated. In this paper, we develop a mathematical model of the immune response. This model follows the creation, activation, and regulation of memory T cells, which allows us to explore the differences between the primary and secondary immune responses. Through the incorporation of memory T cells, we demonstrate how the immune system can mount a faster and more effective secondary response. This mathematical model provides a quantitative framework for studying chronic infections and auto-immune diseases.

Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia.

We describe here a simple model for the interaction between leukemic cells and the autologous immune response in chronic phase chronic myelogenous leukemia (CML). This model is a simplified version of the model we proposed in Clapp et al. (Cancer Res 75:4053-4062, 2015). Our simplification is based on the observation that certain key characteristics of the dynamics of CML can be captured with a three-compartment model: two for the leukemic cells (stem cells and mature cells) and one for the immune response. We characterize the existence of steady states and their stability for generic forms of immunosuppressive effects of leukemic cells. We provide a complete co-dimension one bifurcation analysis. Our results show how clinical response to tyrosine kinase inhibitors treatment is compatible with the existence of a stable low disease, treatment-free steady state.

Modeling the Transfer of Drug Resistance in Solid Tumors.

ABC efflux transporters are a key factor leading to multidrug resistance in cancer. Overexpression of these transporters significantly decreases the efficacy of anti-cancer drugs. Along with selection and induction, drug resistance may be transferred between cells, which is the focus of this paper. Specifically, we consider the intercellular transfer of P-glycoprotein (P-gp), a well-known ABC transporter that was shown to confer resistance to many common chemotherapeutic drugs. In a recent paper, Durán et al. (Bull Math Biol 78(6):1218-1237, 2016) studied the dynamics of mixed cultures of resistant and sensitive NCI-H460 (human non-small lung cancer) cell lines. As expected, the experimental data showed a gradual increase in the percentage of resistance cells and a decrease in the percentage of sensitive cells. The experimental work was accompanied with a mathematical model that assumed P-gp transfer from resistant cells to sensitive cells, rendering them temporarily resistant. The mathematical model provided a reasonable fit to the experimental data. In this paper, we develop a new mathematical model for the transfer of drug resistance between cancer cells. Our model is based on incorporating a resistance phenotype into a model of cancer growth (Greene et al. in J Theor Biol 367:262-277, 2015). The resulting model for P-gp transfer, written as a system of integro-differential equations, follows the dynamics of proliferating, quiescent, and apoptotic cells, with a varying resistance phenotype. We show that this model provides a good match to the dynamics of the experimental data of Durán et al. (2016). The mathematical model shows a better fit when resistant cancer cells have a slower division rate than the sensitive cells.

Modeling the Dynamics of Heterogeneity of Solid Tumors in Response to Chemotherapy.

In this paper, we extend the model of the dynamics of drug resistance in a solid tumor that was introduced by Lorz et al. (Bull Math Biol 77:1-22, 2015). Similarly to the original, radially symmetric model, the quantities we follow depend on a phenotype variable that corresponds to the level of drug resistance. The original model is modified in three ways: (i) We consider a more general growth term that takes into account the sensitivity of resistance level to high drug dosage. (ii) We add a diffusion term in space for the cancer cells and adjust all diffusion terms (for the nutrients and for the drugs) so that the permeability of the resource and drug is limited by the cell concentration. (iii) We add a mutation term with a mutation kernel that corresponds to mutations that occur regularly or rarely. We study the dynamics of the emerging resistance of the cancer cells under continuous infusion and on-off infusion of cytotoxic and cytostatic drugs. While the original Lorz model has an asymptotic profile in which the cancer cells are either fully resistant or fully sensitive, our model allows the emergence of partial resistance levels. We show that increased drug concentrations are correlated with delayed relapse. However, when the cancer relapses, more resistant traits are selected. We further show that an on-off drug infusion also selects for more resistant traits when compared with a continuous drug infusion of identical total drug concentrations. Under certain conditions, our model predicts the emergence of a heterogeneous tumor in which cancer cells of different resistance levels coexist in different areas in space.

[THE IMPACT OF A COMMUNITY INTERVENTION PROGRAM IN ISRAELI WORKSITES TO REDUCE THE RISK OF CARDIOVASCULAR DISEASES].

INTRODUCTION: Atherosclerosis is the main cause of cardiovascular (CV) morbidity and mortality in the western world. Detection and treatment of risk factors (such as hypertension, dyslipidemia and diabetes mellitus) reduce CV events. We have shown cost utility in reducing these CV risk factors in community clinics and community centers. AIMS: In this paper we focused on community workplaces. METHODS: We included 1011 workers in 15 worksites in the study. All workers were analyzed for CV risk factors and included in 6 months of intervention in their worksite in order to reduce the burden of CV risk factors. RESULTS: Significant reduction was noted in the percentage of high risk patients from 43.7% to 27.8% to 24.7% after 3 and 6 months respectively (p<0.05), in the percentage of workers with high weight circumference, high blood pressure, smokers, and in high body mass index (>30g/m2 ). CONCLUSIONS: Interventions in community workplaces can improve the CV risk factors profile and thus should be implemented as broadly as possible.

Modeling intrinsic heterogeneity and growth of cancer cells.

Intratumoral heterogeneity has been found to be a major cause of drug resistance. Cell-to-cell variation increases as a result of cancer-related alterations, which are acquired by stochastic events and further induced by environmental signals. However, most cellular mechanisms include natural fluctuations that are closely regulated, and thus lead to asynchronization of the cells, which causes intrinsic heterogeneity in a given population. Here, we derive two novel mathematical models, a stochastic agent-based model and an integro-differential equation model, each of which describes the growth of cancer cells as a dynamic transition between proliferative and quiescent states. These models are designed to predict variations in growth as a function of the intrinsic heterogeneity emerging from the durations of the cell-cycle and apoptosis, and also include cellular density dependencies. By examining the role all parameters play in the evolution of intrinsic tumor heterogeneity, and the sensitivity of the population growth to parameter values, we show that the cell-cycle length has the most significant effect on the growth dynamics. In addition, we demonstrate that the agent-based model can be approximated well by the more computationally efficient integro-differential equations when the number of cells is large. This essential step in cancer growth modeling will allow us to revisit the mechanisms of multidrug resistance by examining spatiotemporal differences of cell growth while administering a drug among the different sub-populations in a single tumor, as well as the evolution of those mechanisms as a function of the resistance level.

A Review of Mathematical Models for Leukemia and Lymphoma.

Recently, there has been significant activity in the mathematical community, aimed at developing quantitative tools for studying leukemia and lymphoma. Mathematical models have been applied to evaluate existing therapies and to suggest novel therapies. This article reviews the recent contributions of mathematical modeling to leukemia and lymphoma research. These developments suggest that mathematical modeling has great potential in this field. Collaboration between mathematicians, clinicians, and experimentalists can significantly improve leukemia and lymphoma therapy.

The impact of cell density and mutations in a model of multidrug resistance in solid tumors.

In this paper we develop a mathematical framework for describing multidrug resistance in cancer. To reflect the complexity of the underlying interplay between cancer cells and the therapeutic agent, we assume that the resistance level is a continuous parameter. Our model is written as a system of integro-differential equations that are parameterized by the resistance level. This model incorporates the cell density and mutation dependence. Analysis and simulations of the model demonstrate how the dynamics evolves to a selection of one or more traits corresponding to different levels of resistance. The emerging limit distribution with nonzero variance is the desirable modeling outcome as it represents tumor heterogeneity.

Modeling Selective Local Interactions with Memory: Motion on a 2D Lattice.

We consider a system of particles that simultaneously move on a two-dimensional periodic lattice at discrete times steps. Particles remember their last direction of movement and may either choose to continue moving in this direction, remain stationary, or move toward one of their neighbors. The form of motion is chosen based on predetermined stationary probabilities. Simulations of this model reveal a connection between these probabilities and the emerging patterns and size of aggregates. In addition, we develop a reaction diffusion master equation from which we derive a system of ODEs describing the dynamics of the particles on the lattice. Simulations demonstrate that solutions of the ODEs may replicate the aggregation patterns produced by the stochastic particle model. We investigate conditions on the parameters that influence the locations at which particles prefer to aggregate. This work is a two-dimensional generalization of [Galante & Levy, Physica D, http://dx.doi.org/10.1016/j.physd.2012.10.010], in which the corresponding one-dimensional problem was studied.

Characterization of tumor evolution by functional clonality and phylogenetics in hepatocellular carcinoma.

Hepatocellular carcinoma (HCC) is a molecularly heterogeneous solid malignancy, and its fitness may be shaped by how its tumor cells evolve. However, ability to monitor tumor cell evolution is hampered by the presence of numerous passenger mutations that do not provide any biological consequences. Here we develop a strategy to determine the tumor clonality of three independent HCC cohorts of 524 patients with diverse etiologies and race/ethnicity by utilizing somatic mutations in cancer driver genes. We identify two main types of tumor evolution, i.e., linear, and non-linear models where non-linear type could be further divided into classes, which we call shallow branching and deep branching. We find that linear evolving HCC is less aggressive than other types. GTF2IRD2B mutations are enriched in HCC with linear evolution, while TP53 mutations are the most frequent genetic alterations in HCC with non-linear models. Furthermore, we observe significant B cell enrichment in linear trees compared to non-linear trees suggesting the need for further research to uncover potential variations in immune cell types within genomically determined phylogeny types. These results hint at the possibility that tumor cells and their microenvironment may collectively influence the tumor evolution process.

Functional switching and stability of regulatory T cells.

It is widely accepted that the primary immune system contains a subpopulation of cells, known as regulatory T cells whose function is to regulate the immune response. There is conflicting biological evidence regarding the ability of regulatory cells to lose their regulatory capabilities and turn into immune promoting cells. In this paper, we develop mathematical models to investigate the effects of regulatory T cell switching on the immune response. Depending on environmental conditions, regulatory T cells may transition, becoming effector T cells that are immunostimulatory rather than immunoregulatory. We consider this mechanism both in the context of a simple, ordinary differential equation (ODE) model and in the context of a more biologically detailed, delay differential equation (DDE) model of the primary immune response. It is shown that models that incorporate such a mechanism express the usual characteristics of an immune response (expansion, contraction, and memory phases), while being more robust with respect to T cell precursor frequencies. We characterize the affects of regulatory T cell switching on the peak magnitude of the immune response and identify a biologically testable range for the switching parameter. We conclude that regulatory T cell switching may play a key role in controlling immune contraction.

The dynamics of drug resistance: a mathematical perspective.

Resistance to chemotherapy is a key impediment to successful cancer treatment that has been intensively studied for the last three decades. Several central mechanisms have been identified as contributing to the resistance. In the case of multidrug resistance (MDR), the cell becomes resistant to a variety of structurally and mechanistically unrelated drugs in addition to the drug initially administered. Mathematical models of drug resistance have dealt with many of the known aspects of this field, such as pharmacologic sanctuary and location/diffusion resistance, intrinsic resistance, induced resistance and acquired resistance. In addition, there are mathematical models that take into account the kinetic/phase resistance, and models that investigate intracellular mechanisms based on specific biological functions (such as ABC transporters, apoptosis and repair mechanisms). This review covers aspects of MDR that have been mathematically studied, and explains how, from a methodological perspective, mathematics can be used to study drug resistance. We discuss quantitative approaches of mathematical analysis, and demonstrate how mathematics can be used in combination with other experimental and clinical tools. We emphasize the potential benefits of integrating analytical and mathematical methods into future clinical and experimental studies of drug resistance.

Role of symmetric and asymmetric division of stem cells in developing drug resistance.

Often, resistance to drugs is an obstacle to a successful treatment of cancer. In spite of the importance of the problem, the actual mechanisms that control the evolution of drug resistance are not fully understood. Many attempts to study drug resistance have been made in the mathematical modeling literature. Clearly, in order to understand drug resistance, it is imperative to have a good model of the underlying dynamics of cancer cells. One of the main ingredients that has been recently introduced into the rapidly growing pool of mathematical cancer models is stem cells. Surprisingly, this all-so-important subset of cells has not been fully integrated into existing mathematical models of drug resistance. In this work we incorporate the various possible ways in which a stem cell may divide into the study of drug resistance. We derive a previously undescribed estimate of the probability of developing drug resistance by the time a tumor is detected and calculate the expected number of resistant cancer stem cells at the time of tumor detection. To demonstrate the significance of this approach, we combine our previously undescribed mathematical estimates with clinical data that are taken from a recent six-year follow-up of patients receiving imatinib for the first-line treatment of chronic myelogenous leukemia. Based on our analysis we conclude that leukemia stem cells must tend to renew symmetrically as opposed to their healthy counterparts that predominantly divide asymmetrically.

Modeling selective local interactions with memory.

Recently we developed a stochastic particle system describing local interactions between cyanobacteria. We focused on the common freshwater cyanobacteria Synechocystis sp., which are coccoidal bacteria that utilize group dynamics to move toward a light source, a motion referred to as phototaxis. We were particularly interested in the local interactions between cells that were located in low to medium density areas away from the front. The simulations of our stochastic particle system in 2D replicated many experimentally observed phenomena, such as the formation of aggregations and the quasi-random motion of cells. In this paper, we seek to develop a better understanding of group dynamics produced by this model. To facilitate this study, we replace the stochastic model with a system of ordinary differential equations describing the evolution of particles in 1D. Unlike many other models, our emphasis is on particles that selectively choose one of their neighbors as the preferred direction of motion. Furthermore, we incorporate memory by allowing persistence in the motion. We conduct numerical simulations which allow us to efficiently explore the space of parameters, in order to study the stability, size, and merging of aggregations.