Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

Fundamental properties of Ca²⁺ signals

Background Ca²⁺ is a ubiquitous and versatile second messenger that transmits information through changes of the cytosolic Ca²⁺ concentration. Recent investigations changed basic ideas on the dynamic character of Ca²⁺ signals and challenge traditional ideas on information transmission. Scope of review We present recent findings on key characteristics of the cytosolic Ca²⁺ dynamics and theoretical concepts that explain the wide range of experimentally observed Ca²⁺ signals. Further, we relate properties of the dynamical regulation of the cytosolic Ca²⁺ concentration to ideas about information transmission by stochastic signals. Major conclusions We demonstrate the importance of the hierarchal arrangement of Ca²⁺ release sites on the emergence of cellular Ca²⁺ spikes. Stochastic Ca²⁺ signals are functionally robust and adaptive to changing environmental conditions. Fluctuations of interspike intervals (ISIs) and the moment relation derived from ISI distributions contain information on the channel cluster open probability and on pathway properties. General significance Robust and reliable signal transduction pathways that entail Ca²⁺ dynamics are essential for eukaryotic organisms. Moreover, we expect that the design of a stochastic mechanism which provides robustness and adaptivity will be found also in other biological systems. Ca2 + dynamics demonstrate that the fluctuations of cellular signals contain information on molecular behavior. This article is part of a Special Issue entitled Biochemical, biophysical and genetic approaches to intracellular calcium signaling. Highlights ► We review recent findings on key characteristics of cytosolic Ca²⁺ dynamics. ► We demonstrate the importance of the hierarchal arrangement of Ca²⁺ release sites. ► New theoretical concepts exploit emergent behavior of cellular Ca²⁺ spikes. ► We relate the dynamical regulation of [Ca²⁺] to information transmission. ► Stochastic Ca²⁺ signals are functionally robust and adaptive to changing conditions

Inverse Problems in data-driven multi-scale Systems Medicine: application to cancer physiology

Systems Medicine is an interdisciplinary framework involving reciprocal feedback between clinical investigation and mathematical modeling/analysis. Its aim is to improve the understanding of complex diseases by integrating knowledge and data across multiple levels of biological organization. This Thesis focuses on three inverse problems, arising from three kinds of data and related to cancer physiology, at different scales: tissues, cells, molecules. The general assumption of this piece of research is that cancer is associated toa path ological glucose consumption and, in fact, its functional behavior can be assessed by nuclear medicine experiments using [18F]-fluorodeoxyglucose (FDG) as a radioactive tracer mimicking the glucose properties. At tissue-scale, this Thesis considers the Positron Emission Tomography (PET) imaging technique, and deals with two distinct issues within compartmental analysis. First, this Thesis presents a compartmental approach, referred to as reference tissue model, for the estimation of FDG kinetics inside cancer tissues when the arterial blood input of the system is unknown. Then, this Thesis proposes an efficient and reliable method for recovering the compartmental kinetic parameters for each PET image pixel in the context of parametric imaging, exploiting information on the tissue physiology. Standard models in compartmental analysis assume that phosphorylation and dephosphorylation of FDG occur in the same intracellular cytosolic volume. Advances in cell biochemistry have shown that the appropriate location of dephosphorylation is the endoplasmic reticulum (ER). Therefore, at cell-scale, this Thesis formalizes a biochemically-driven compartmental model accounting for the specific role played by the ER, and applies it to the analysis of in vitro experiments on FDG uptake by cancer cell cultures obtained with a LigandTracer (LT) device. Finally, at molecule-scale, this Thesis provides a preliminary mathematical investigation of a chemical reaction network (CRN), represented by a huge Molecular Interaction Map (MIM), describing the biochemical interactions occurring between signaling proteins in specific pathways within a cancer cell. The main issue addressed in this case is the network parameterization problem, i.e. how to determine the reaction rate coefficients from protein concentration data