Theoretical analysis of the role of chromatin interactions in long-range action of enhancers and insulators

Long-distance regulatory interactions between enhancers and their target genes are commonplace in higher eukaryotes. Interposed boundaries or insulators are able to block these long distance regulatory interactions. The mechanistic basis for insulator activity and how it relates to enhancer action-at-a-distance remains unclear. Here we explore the idea that topological loops could simultaneously account for regulatory interactions of distal enhancers and the insulating activity of boundary elements. We show that while loop formation is not in itself sufficient to explain action at a distance, incorporating transient non-specific and moderate attractive interactions between the chromatin fibers strongly enhances long-distance regulatory interactions and is sufficient to generate a euchromatin-like state. Under these same conditions, the subdivision of the loop into two topologically independent loops by insulators inhibits inter-domain interactions. The underlying cause of this effect is a suppression of crossings in the contact map at intermediate distances. Thus our model simultaneously accounts for regulatory interactions at a distance and the insulator activity of boundary elements. This unified model of the regulatory roles of chromatin loops makes several testable predictions that could be confronted with \emph{in vitro} experiments, as well as genomic chromatin conformation capture and fluorescent microscopic approaches.Comment: 10 pages, originally submitted to an (undisclosed) journal in May 201

Modelling radiation-induced cell cycle delays

Ionizing radiation is known to delay the cell cycle progression. In particular after particle exposure significant delays have been observed and it has been shown that the extent of delay affects the expression of damage such as chromosome aberrations. Thus, to predict how cells respond to ionizing radiation and to derive reliable estimates of radiation risks, information about radiation-induced cell cycle perturbations is required. In the present study we describe and apply a method for retrieval of information about the time-course of all cell cycle phases from experimental data on the mitotic index only. We study the progression of mammalian cells through the cell cycle after exposure. The analysis reveals a prolonged block of damaged cells in the G2 phase. Furthermore, by performing an error analysis on simulated data valuable information for the design of experimental studies has been obtained. The analysis showed that the number of cells analyzed in an experimental sample should be at least 100 to obtain a relative error less than 20%.Comment: 19 pages, 11 figures, accepted for publication in Radiation and Environmental Biophysic

Migration rules: tumours are conglomerates of self-metastases

Tumours are heterogeneous populations composed of different cells types: stem cells with the capacity for self-renewal and more differentiated cells lacking such ability. The overall growth behaviour of a developing neoplasm is determined largely by the combined kinetic interactions of these cells. By tracking the fate of individual cancer cells using agent-based methods in silico, we apply basic rules for cell proliferation, migration and cell death to show how these kinetic parameters interact to control, and perhaps dictate defining spatial and temporal tumour growth dynamics in tumour development. When the migration rate is small, a single cancer stem cell can only generate a small, self-limited clone because of the finite life span of progeny and spatial constraints. By contrast, a high migration rate can break this equilibrium, seeding new clones at sites outside the expanse of older clones. In this manner, the tumour continually ‘self-metastasises'. Counterintuitively, when the proliferation capacity is low and the rate of cell death is high, tumour growth is accelerated because of the freeing up of space for self-metastatic expansion. Changes to proliferation and cell death that increase the rate at which cells migrate benefit tumour growth as a whole. The dominating influence of migration on tumour growth leads to unexpected dependencies of tumour growth on proliferation capacity and cell death. These dependencies stand to inform standard therapeutic approaches, which anticipate a positive response to cell killing and mitotic arrest

Number and Size Distribution of Colorectal Adenomas under the Multistage Clonal Expansion Model of Cancer

Colorectal cancer (CRC) is believed to arise from mutant stem cells in colonic crypts that undergo a well-characterized progression involving benign adenoma, the precursor to invasive carcinoma. Although a number of (epi)genetic events have been identified as drivers of this process, little is known about the dynamics involved in the stage-wise progression from the first appearance of an adenoma to its ultimate conversion to malignant cancer. By the time adenomas become endoscopically detectable (i.e., are in the range of 1–2 mm in diameter), adenomas are already comprised of hundreds of thousands of cells and may have been in existence for several years if not decades. Thus, a large fraction of adenomas may actually remain undetected during endoscopic screening and, at least in principle, could give rise to cancer before they are detected. It is therefore of importance to establish what fraction of adenomas is detectable, both as a function of when the colon is screened for neoplasia and as a function of the achievable detection limit. To this end, we have derived mathematical expressions for the detectable adenoma number and size distributions based on a recently developed stochastic model of CRC. Our results and illustrations using these expressions suggest (1) that screening efficacy is critically dependent on the detection threshold and implicit knowledge of the relevant stem cell fraction in adenomas, (2) that a large fraction of non-extinct adenomas remains likely undetected assuming plausible detection thresholds and cell division rates, and (3), under a realistic description of adenoma initiation, growth and progression to CRC, the empirical prevalence of adenomas is likely inflated with lesions that are not on the pathway to cancer

Evolution of Resistance to Targeted Anti-Cancer Therapies during Continuous and Pulsed Administration Strategies

The discovery of small molecules targeted to specific oncogenic pathways has revolutionized anti-cancer therapy. However, such therapy often fails due to the evolution of acquired resistance. One long-standing question in clinical cancer research is the identification of optimum therapeutic administration strategies so that the risk of resistance is minimized. In this paper, we investigate optimal drug dosing schedules to prevent, or at least delay, the emergence of resistance. We design and analyze a stochastic mathematical model describing the evolutionary dynamics of a tumor cell population during therapy. We consider drug resistance emerging due to a single (epi)genetic alteration and calculate the probability of resistance arising during specific dosing strategies. We then optimize treatment protocols such that the risk of resistance is minimal while considering drug toxicity and side effects as constraints. Our methodology can be used to identify optimum drug administration schedules to avoid resistance conferred by one (epi)genetic alteration for any cancer and treatment type

On systems and control approaches to therapeutic gain

BACKGROUND: Mathematical models of cancer relevant processes are being developed at an increasing rate. Conceptual frameworks are needed to support new treatment designs based on such models. METHODS: A modern control perspective is used to formulate two therapeutic gain strategies. RESULTS: Two conceptually distinct therapeutic gain strategies are provided. The first is direct in that its goal is to kill cancer cells more so than normal cells, the second is indirect in that its goal is to achieve implicit therapeutic gains by transferring states of cancer cells of non-curable cases to a target state defined by the cancer cells of curable cases. The direct strategy requires models that connect anti-cancer agents to an endpoint that is modulated by the cause of the cancer and that correlates with cell death. It is an abstraction of a strategy for treating mismatch repair (MMR) deficient cancers with iodinated uridine (IUdR); IU-DNA correlates with radiation induced cell killing and MMR modulates the relationship between IUdR and IU-DNA because loss of MMR decreases the removal of IU from the DNA. The second strategy is indirect. It assumes that non-curable patient outcomes will improve if the states of their malignant cells are first transferred toward a state that is similar to that of a curable patient. This strategy is difficult to employ because it requires a model that relates drugs to determinants of differences in patient survival times. It is an abstraction of a strategy for treating BCR-ABL pro-B cell childhood leukemia patients using curable cases as the guides. CONCLUSION: Cancer therapeutic gain problem formulations define the purpose, and thus the scope, of cancer process modeling. Their abstractions facilitate considerations of alternative treatment strategies and support syntheses of learning experiences across different cancers