Toxicity Management in CAR T cell therapy for B-ALL: Mathematical modelling as a new avenue for improvement.

Shalla Hanson, David Robert Grimes, Jake P. Taylor-King, Benedikt Bauer, Pravnam I. Warman, Ziv Frankenstein, Artem Kaznatcheev, Michael J. Bonassar, Vincent L. Cannataro, Zeinab Y. Motawe, Ernesto A. B. F. Lima, Sungjune Kim, Marco L. Davila, Arturo Araujo

Abstract

Advances in genetic engineering have made it possible to reprogram individual immune cells to express receptors that recognise markers on tumour cell surfaces. The process of re-engineering T cell lymphocytes to express Chimeric Antigen Receptors (CARs), and then re-infusing the CAR-modified T cells into patients to treat various cancers is referred to as CAR T cell therapy. This therapy is being explored in clinical trials - most prominently for B Cell Acute Lymphoblastic Leukaemia (B-ALL), a common B cell malignancy, for which CAR T cell therapy has led to remission in up to 90% of patients. Despite this extraordinary response rate, however, potentially fatal inflammatory side effects occur in up to 10% of patients who have positive responses. Further, approximately 50% of patients who initially respond to the therapy relapse. Significant improvement is thus necessary before the therapy can be made widely available for use in the clinic. To inform future development, we develop a mathematical model to explore interactions between CAR T cells, inflammatory toxicity, and individual patients' tumour burdens in silico. This paper outlines the underlying system of coupled ordinary differential equations designed based on well-known immunological principles and widely accepted views on the mechanism of toxicity development in CAR T cell therapy for B-ALL - and reports in silico outcomes in relationship to standard and recently conjectured predictors of toxicity in a heterogeneous, randomly generated patient population. Our initial results and analyses are consistent with and connect immunological mechanisms to the clinically observed, counterintuitive hypothesis that initial tumour burden is a stronger predictor of toxicity than is the dose of CAR T cells administered to patients. We outline how the mechanism of action in CAR T cell therapy can give rise to such non-standard trends in toxicity development, and demonstrate the utility of mathematical modelling in understanding the relationship between predictors of toxicity, mechanism of action, and patient outcomes.

Link:http://biorxiv.org/content/early/2016/04/22/049908

Universal asymptotic clone size distribution for general population growth

Michael D. Nicholson, Tibor Antal

Deterministically growing (wild-type) populations which seed stochastically developing mutant clones have found an expanding number of applications from microbial populations to cancer. The special case of exponential wild-type population growth, usually termed as the Luria-Delbruck or Lea-Coulson model, is often assumed but seldom realistic. In this article we generalise the model to different types of wild-type population growth, with mutants evolving as a birth-death branching process. Our focus is on the size distribution of clones after some time, which can be mapped to the total number of mutants. Exact expressions are derived for exponential, power-law and logistic population growth. We prove that the large time limit of the clone size distribution has a general two-parameter form for a large class of population growth. The large time clone size distribution always has a power-law tail, and for subexponential wild-type growth the probability of a given clone size is inversely proportional to the clone size. We support our results by analysing a data-set on tumour metastasis sizes, and we find that a power-law tail is more likely than an exponential one, in agreement with our predictions.

Link: http://arxiv.org/abs/1604.04936#

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silico insights

Why one-size-fits-all vaso-modulatory interventions fail to control glioma invasion: in silica insights

J. C. L. Alfonso, A. Kohn-Luque, T. Stylianopoulos, F. Feuerhake, A. Deutsch, H. Hatzikirou

There is an ongoing debate on the therapeutic potential of vaso-modulatory interventions against glioma invasion. Prominent vasculature-targeting therapies involve functional tumour-associated blood vessel deterioration and normalisation. The former aims at tumour infarction and nutrient deprivation medi- ated by vascular targeting agents that induce occlusion/collapse of tumour blood vessels. In contrast, the therapeutic intention of normalising the abnormal structure and function of tumour vascular net- works, e.g. via alleviating stress-induced vaso-occlusion, is to improve chemo-, immuno- and radiation therapy efficacy. Although both strategies have shown therapeutic potential, it remains unclear why they often fail to control glioma invasion into the surrounding healthy brain tissue. To shed light on this issue, we propose a mathematical model of glioma invasion focusing on the interplay between the mi- gration/proliferation dichotomy (Go-or-Grow) of glioma cells and modulations of the functional tumour vasculature. Vaso-modulatory interventions are modelled by varying the degree of vaso-occlusion. We discovered the existence of a critical cell proliferation/diffusion ratio that separates glioma invasion re- sponses to vaso-modulatory interventions into two distinct regimes. While for tumours, belonging to one regime, vascular modulations reduce the tumour front speed and increase the infiltration width, for those in the other regime the invasion speed increases and infiltration width decreases. We show how these in silico findings can be used to guide individualised approaches of vaso-modulatory treatment strategies and thereby improve success rates.

Link:arXiv:1604.05082http://arxiv.org/abs/1604.05082

Population heterogeneity in mutation rate increases mean fitness and the frequency of higher order mutants

Helen Alexander, Stephanie I. Mayer, Sebastian Bonhoeffer

Abstract

Mutation rate is a crucial evolutionary parameter that has typically been treated as a constant in population genetic analyses. However, mutation rate is likely to vary among co-existing individuals within a population, due to genetic polymorphisms, heterogeneous environmental influences, and random physiological fluctuations. We explore the consequences of such mutation rate heterogeneity in a model allowing an arbitrary distribution of mutation rate among individuals, either with or without inheritance. We find that variation of mutation rate about the mean results in a higher probability of producing zero or many simultaneous mutations on a genome. Moreover, it increases the frequency of higher order mutants even under ongoing mutation and selection. We gain a quantitative understanding of how this frequency depends on moments of the mutation rate distribution and selection coefficients. In particular, in a two-locus model, heterogeneity leads to a relative increase in double mutant frequency proportional to the squared coefficient of variation of the mutation rate. Relative effect sizes increase with the number of loci. Finally, this clustering of deleterious mutations into fewer individuals results in a higher population mean fitness. Our results imply that mutation rate heterogeneity allows a population to maintain a higher level of adaptedness to its current environment, while simultaneously harboring greater genetic diversity in the standing variation, which could be crucial for future adaptation to a new environment. Our results also have implications for interpreting mutation rate estimates and mutant frequencies in data.

Subject area: genetics

doi: http://dx.doi.org/10.1101/045377

Dissecting resistance mechanisms in melanoma combination therapy

Eunjung Kim, Alexander Anderson

doi: http://dx.doi.org/10.1101/041855

This article is a preprint and has not been peer-reviewed [what does this mean?].

• Abstract
• Info/History
• Metrics
•  Preview PDF

Abstract

We present a compartment model that explains melanoma cell response and resistance to mono and combination therapies. Model parameters were estimated by utilizing an optimization algorithm to identify parameters that minimized the difference between predicted cell populations and experimentally measured cell numbers. The model was then validated with in vitro experimental data. Our simulations show that although a specific timing of the combination therapy is effective in controlling tumor cell populations over an extended period of time, the treatment eventually fails. We subsequently predict a more optimal combination therapy that incorporates an additional drug at the right moment.

http://biorxiv.org/content/early/2016/03/07/041855

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Daniel Nichol, Mark Robertson-Tessi, Peter Jeavons, Alexander RA Anderson

Abstract

For the last few decades modern biology has focused on quantifying, understanding and mapping the genetic characteristics of cells. This genotype-driven perspective has led to significant advances in our understanding and treatment of diseases such as cancer e.g. the discovery of driver mutations and the development of molecularly-targeted therapeutics. However, this perspective has largely ignored the functional outcome of genetic changes: the cellular phenotype. In part, this is simply because phenotypes are neither easy to define or measure as they critically depend on both genotype and context. Heterogeneity at the gene scale has been known for sometime, and there has been significant effort invested in trying to find patterns within it, but much less is understood about how this heterogeneity manifests itself in phenotypic change, i.e. the genotype-phenotype map (GP-map). This mapping is not one-to-one but many-to-many and is fundamentally the junction at which both genes and environment meet to produce phenotypes. Many genotypes produce similar phenotypes, and multiple phenotypes can emerge from a single genotype. To further complicate matters, genetically identical cells in uniform environments still exhibit phenotypic heterogeneity. Therefore a central open question in biology today is how can we connect the abundance of genomic data with cell phenotypic behaviour, this is especially pertinent to the issue of treatment resistance as many therapies act on cellular phenotypes. Our focus here is to tackle the GP-map question through the use of the simplest functional mapping we can define that also captures phenotypic heterogeneity: a molecular switch. Molecular switches are ubiquitous in biology, observed in many organisms and naturally map molecular components to decisions (i.e. phenotypes). Often stochastic in nature, such switches can be the difference between life or death in environments that fluctuate unpredictably, since they will ensure that at least some offspring are adapted to future environments. For convenience we use Chemical Reaction Networks (CRNs) to define the map of gene products to phenotypes, allowing us to investigate the impact of distinct mappings (CRNs) and perturbations to them. We observe that key biological properties naturally emerge, including both robustness and persistence. Robustness may explain why such bet hedging strategies are common in biology, and not readily destroyed through mutation. Whereas persistence may explain the apparent paradox of bet-hedging - why does phenotypic hedging exist in environments beneficial to only one of the phenotypes, when selection necessarily acts against it? The structure of the molecular switch, itself subject to selection, can slow the loss of hedging to ensure a survival mechanism even against environmental catastrophes which are very rare. Critically, these properties when taken together have profound and significant implications for the emergence of treatment resistance, since the timescale of extinction depends heavily on the underlying GP-map.

doi: http://dx.doi.org/10.1101/042424

Reaction-Diffusion Model of PDGF-driven Recruitment in Experimental Glioblastoma

Reaction-Diffusion Model of PDGF-driven Recruitment in Experimental Glioblastoma

Susan Christine Massey, Kristin Swanson

Abstract

Platelet-derived growth factor (PDGF) drives the formation of gliomas in an experimental animal model, which notably involves the recruitment of large numbers of glial progenitor cells (Assanah 2006). In order to understand the underlying mechanism, particularly what factors influence the degree of recruitment, and how varied amounts of PDGF would affect the gross characteristics and overall appearance of tumors in the brain, we adapted a reaction diffusion model of glioma, which has been used for analyzing clinical data, to model the interactions at play in these experimental models.

Link: http://biorxiv.org/content/early/2016/02/04/038471