Cancer-associated mutations in healthy individuals: assessing the risk of carcinogenesis

Luminescent Analysis of Blood Serum for Diagnostics of Pathological and Pre-Pathological States of Cancer Patients

This study is devoted to the development of a methodological approach to mathematical analysis and data interpretation of blood serum phosphorescence intensity in cancer patients for determining the pathological states and differential diagnostics of oncological process stages. The purpose of the study is blood serum phosphorescence research in patients with colorectal cancer (CRC) and stomach adenocarcinoma (SAC) and determination of the ultraweak luminescence role for diagnostics of the disease, determining its stages, control of pathogenetic therapy efficiency and forecast of recovery. The values of phosphorescence intensity of blood serum films in patients with CRC and SAC are significantly higher than the corresponding values for the control group. Contrary to the absolute intensity, the relative intensity increase compared to the control group is much more informative for oncoprocess diagnostics, since it exhibits three times increase even at the first stage of tumoral process. Serum phosphorescence intensity continues to increase with progressing of the disease. As the result of our study, the relative intensity increase compared to the first stage can be recommended as an informative indicator for differential diagnostics of oncological process stages. As a conclusion, determination of blood serum phosphorescence intensity can be considered as a sensitive and specific diagnostic method in oncology. With a correct methodological approach to data processing and interpretation, this method can be used in clinical practice for determining the oncopathological states, differential diagnostics of oncoprocess stages and diagnostics of precancer changes, which precede tumoral process development.

Agent-based modelling reveals strategies to reduce the fitness and metastatic potential of circulating tumour cell clusters

Metastasis-the ability of cancer cells to disperse throughout the body and establish new tumours at distant locations-is responsible for most cancer-related deaths. Although both single and clusters of circulating tumour cells (CTCs) have been isolated from cancer patients, CTC clusters are generally associated with higher metastatic potential and worse prognosis. From an evolutionary perspective, being part of a cluster can provide cells with several benefits both in terms of survival (e.g. protection) and reproduction (group dispersal). Thus, strategies aimed at inducing cluster dissociation could decrease the metastatic potential of CTCs. However, finding agents or conditions that induce the dissociation of CTC clusters is hampered by the fact that their detection, isolation and propagation remain challenging. Here, we used a mechanistic agent-based model to (a) investigate the response of CTC clusters of various sizes and densities to different challenges-in terms of cell survival and cluster stability, and (b) make predictions as to the combination of factors and parameter values that could decrease the fitness and metastatic potential of CTC clusters. Our model shows that the resilience and stability of CTC clusters are dependent on both their size and density. Also, CTC clusters of distinct sizes and densities respond differently to changes in resource availability, with high-density clusters being least affected. In terms of responses to microenvironmental threats (such as drugs), increasing their intensity is, generally, least effective on high-density clusters. Lastly, we found that combining various levels of resource availability and threat intensity can be more effective at decreasing the survival of CTC clusters than each factor alone. We suggest that the complex effects that cluster density and size showed on both the resilience and stability of the CTC clusters are likely to have significant consequences for their metastatic potential and responses to therapies.

A dynamical systems model for the measurement of cellular senescence

Senescent cells provide a good in vitro model to study ageing. However, cultures of ‘senescent’ cells consist of a mix of cell subtypes (proliferative, senescent, growth-arrested and apoptotic). Determining the proportion of senescent cells is crucial for studying ageing and developing new anti-degenerative therapies. Commonly used markers such as doubling population, senescence-associated β-galactosidase, Ki-67, γH2AX and TUNEL assays capture diverse and overlapping cellular populations and are not purely specific to senescence. A newly developed dynamical systems model follows the transition of an initial culture to senescence tracking population doubling, and the proportion of cells in proliferating, growth-arrested, apoptotic and senescent states. Our model provides a parsimonious description of transitions between these states accruing towards a predominantly senescent population. Using a genetic algorithm, these model parameters are well constrained by an in vitro human primary fibroblast dataset recording five markers at 16 time points. The computational model accurately fits to the data and translates these joint markers into the first complete description of the proportion of cells in different states over the lifetime. The high temporal resolution of the dataset demonstrates the efficacy of strategies for reconstructing the trajectory towards replicative senescence with a minimal number of experimental recordings.

Estimating the number of genetic mutations (hits) required for carcinogenesis based on the distribution of somatic mutations

Individual instances of cancer are primarily a result of a combination of a small number of genetic mutations (hits). Knowing the number of such mutations is a prerequisite for identifying specific combinations of carcinogenic mutations and understanding the etiology of cancer. We present a mathematical model for estimating the number of hits based on the distribution of somatic mutations. The model is fundamentally different from previous approaches, which are based on cancer incidence by age. Our somatic mutation based model is likely to be more robust than age-based models since it does not require knowing or accounting for the highly variable mutation rate, which can vary by over three orders of magnitude. In fact, we find that the number of somatic mutations at diagnosis is weakly correlated with age at cancer diagnosis, most likely due to the extreme variability in mutation rates between individuals. Comparing the distribution of somatic mutations predicted by our model to the actual distribution from 6904 tumor samples we estimate the number of hits required for carcinogenesis for 17 cancer types. We find that different cancer types exhibit distinct somatic mutational profiles corresponding to different numbers of hits. Why might different cancer types require different numbers of hits for carcinogenesis? The answer may provide insight into the unique etiology of different cancer types.

Cancer is primarily a result of genetic mutations. Each individual instance of cancer is initiated by a specific combination of a small number of mutations (hits). In trying to identify these combinations of mutations, it is important to know how many hits to look for. However, there are conflicting estimates for the number of hits. We present a fundamentally different model for estimating the number of hits. We found that the number hits ranges from two-eight depending on cancer type. These findings may provide insight into the unique characteristics of different cancer types.

The role of telomere shortening in carcinogenesis: A hybrid stochastic-deterministic approach

Genome instability is a characteristic of most cancers, contributing to the acquisition of genetic alterations that drive tumor progression. One important source of genome instability is linked to telomere dysfunction in cells with critically short telomeres that lack p53-mediated surveillance of genomic integrity. Here we research the probability that cancer emerges through an evolutionary pathway that includes a telomere-induced phase of genome instability. To implement our models we use a hybrid stochastic-deterministic approach, which allows us to perform large numbers of simulations using biologically realistic population sizes and mutation rates, circumventing the traditional limitations of fully stochastic algorithms. The hybrid methodology should be easily adaptable to a wide range of evolutionary problems. In particular, we model telomere shortening and the acquisition of two mutations: Telomerase activation and p53 inactivation. We find that the death rate of unstable cells, and the number of cell divisions that p53 mutants can sustain beyond the normal senescence setpoint determine the likelihood that the first double mutant originates in a cell with telomere-induced instability. The model has applications to an influential telomerase-null mouse model and p16 silenced human cells. We end by discussing algorithmic performance and a measure for the accuracy of the hybrid approximation.

Optimizing homeostatic cell renewal in hierarchical tissues

In order to maintain homeostasis, mature cells removed from the top compartment of hierarchical tissues have to be replenished by means of differentiation and self-renewal events happening in the more primitive compartments. As each cell division is associated with a risk of mutation, cell division patterns have to be optimized, in order to minimize or delay the risk of malignancy generation. Here we study this optimization problem, focusing on the role of division tree length, that is, the number of layers of cells activated in response to the loss of terminally differentiated cells, which is related to the balance between differentiation and self-renewal events in the compartments. Using both analytical methods and stochastic simulations in a metapopulation-style model, we find that shorter division trees are advantageous if the objective is to minimize the total number of one-hit mutants in the cell population. Longer division trees on the other hand minimize the accumulation of two-hit mutants, which is a more likely evolutionary goal given the key role played by tumor suppressor genes in cancer initiation. While division tree length is the most important property determining mutant accumulation, we also find that increasing the size of primitive compartments helps to delay two-hit mutant generation.

Cells in multicellular organisms are organized hierarchically. A stem cell gives rise to a chain of dividing and progressively differentiating offspring. At the end of this chain (called a lineage) are terminally differentiated cells that perform their function and undergo programmed cell death, to be replaced by new divisions of less differentiated cells. Here we are interested in the design of such lineages. At one extreme, one can imagine that a loss of terminally differentiated cells only results in divisions of cells in close hierarchical proximity to them, giving rise to very short division trees. On the other hand, it is possible that a long chain of increasingly primitive cells gets activated in response to the loss of differentiated cells. We expect that an important type of selection pressure acting upon tissue design is the minimization of mutations that happen in the course of everyday tissue maintenance (homeostasis). For example, tumor suppressor gene inactivation (two consecutive mutations) is an early rate-limiting step in many cancers. Using mathematical and computational methods, we find that the length of division trees is anti-correlated with the likelihood of double mutations, and lengthening the trees may provide an evolutionary advantage to the organism by delaying the onset of cancer.

Telomeres open a window on stem cell division

Measuring the length distribution of telomeres can reveal information about biological processes that are otherwise difficult to analyze experimentally.

Quantifying replicative senescence as a tumor suppressor pathway and a target for cancer therapy

To study quantitatively replicative senescence as a tumor suppressor mechanism, we investigate the distribution of a growing clonal cell population restricted by Hayflick’s limit. We find that in the biologically relevant range of parameters, if the imbalance between cell division and death is moderate or low (high death-to-birth ratio), senescence offers significant protection against cancer by halting abnormal cell proliferation at early pre-diagnostic stages of tumor development. We also find that by the time tumors are typically detected, there is a high probability that telomerase is activated, even if the cell of origin was telomerase negative. Hence, the fact that most cancers are positive for telomerase is not necessarily an indication that cancer originated in a telomerase positive cell. Finally, we discuss how the population dynamics of cells can determine the outcomes of anti-telomerase cancer therapies, and provide guidelines on how the model could potentially be applied to develop clinically useful tools to predict the response to treatment by telomerase inhibitors in individual patients.

Preventing clonal evolutionary processes in cancer: Insights from mathematical models

Clonal evolutionary processes can drive pathogenesis in human diseases, with cancer being a prominent example. To prevent or treat cancer, mechanisms that can potentially interfere with clonal evolutionary processes need to be understood better. Mathematical modeling is an important research tool that plays an ever-increasing role in cancer research. This paper discusses how mathematical models can be useful to gain insights into mechanisms that can prevent disease initiation, help analyze treatment responses, and aid in the design of treatment strategies to combat the emergence of drug-resistant cells. The discussion will be done in the context of specific examples. Among defense mechanisms, we explore how replicative limits and cellular senescence induced by telomere shortening can influence the emergence and evolution of tumors. Among treatment approaches, we consider the targeted treatment of chronic lymphocytic leukemia (CLL) with tyrosine kinase inhibitors. We illustrate how basic evolutionary mathematical models have the potential to make patient-specific predictions about disease and treatment outcome, and argue that evolutionary models could become important clinical tools in the field of personalized medicine.