Santiago Schnell

The Circadian Clock in Oral Health and Diseases

Most physiological processes in mammals display circadian rhythms that are driven by the endogenous circadian clock. This clock is comprised of a central component located in the hypothalamic suprachiasmatic nucleus and subordinate clocks in peripheral tissues. Circadian rhythms sustain 24-hour oscillations of a large number of master genes controlling the correct timing and synchronization of diverse physiological and metabolic processes within our bodies. This complex regulatory network provides an important communication link between our brain and several peripheral organs and tissues. At the molecular level, circadian oscillations of gene expression are regulated by a family of transcription factors called “clock genes”. Dysregulation of clock gene expression results in diverse human pathological conditions, including autoimmune diseases and cancer. There is increasing evidence that the circadian clock affects tooth development, salivary gland and oral epithelium homeostasis, and saliva production. This review summarizes current knowledge of the roles of clock genes in the formation and maintenance of oral tissues, and discusses potential links between “oral clocks” and diseases such as head and neck cancer and Sjögren’s syndrome.

Review: Stochastic approaches for modelling in vivo reactions

In recent years, stochastic modelling has emerged as a physically more realistic alternative for modelling in vivo reactions. There are numerous stochastic approaches available in the literature; most of these assume that observed random fluctuations are a consequence of the small number of reacting molecules. We review some important developments of the stochastic approach and consider its suitability for modelling intracellular reactions. We then describe recent efforts to include the fluctuation effects caused by the structural organisation of the cytoplasm and the limited diffusion of molecules due to macromolecular crowding.

A multiscale mathematical model of cancer, and its use in analyzing irradiation therapies

BackgroundRadiotherapy outcomes are usually predicted using the Linear Quadratic model. However, this model does not integrate complex features of tumor growth, in particular cell cycle regulation.MethodsIn this paper, we propose a multiscale model of cancer growth based on the genetic and molecular features of the evolution of colorectal cancer. The model includes key genes, cellular kinetics, tissue dynamics, macroscopic tumor evolution and radiosensitivity dependence on the cell cycle phase. We investigate the role of gene-dependent cell cycle regulation in the response of tumors to therapeutic irradiation protocols.ResultsSimulation results emphasize the importance of tumor tissue features and the need to consider regulating factors such as hypoxia, as well as tumor geometry and tissue dynamics, in predicting and improving radiotherapeutic efficacy.ConclusionThis model provides insight into the coupling of complex biological processes, which leads to a better understanding of oncogenesis. This will hopefully lead to improved irradiation therapy.

Hedgehog-responsive mesenchymal clusters direct patterning and emergence of intestinal villi

In the adult intestine, an organized array of finger-like projections, called villi, provide an enormous epithelial surface area for absorptive function. Villi first emerge at embryonic day (E) 14.5 from a previously flat luminal surface. Here, we analyze the cell biology of villus formation and examine the role of paracrine epithelial Hedgehog (Hh) signals in this process. We find that, before villus emergence, tight clusters of Hh-responsive mesenchymal cells form just beneath the epithelium. Cluster formation is dynamic; clusters first form dorsally and anteriorly and spread circumferentially and posteriorly. Statistical analysis of cluster distribution reveals a patterned array; with time, new clusters form in spaces between existing clusters, promoting approximately four rounds of villus emergence by E18.5. Cells within mesenchymal clusters express Patched1 and Gli1, as well as Pdgfrα, a receptor previously shown to participate in villus development. BrdU-labeling experiments show that clusters form by migration and aggregation of Hh-responsive cells. Inhibition of Hh signaling prevents cluster formation and villus development, but does not prevent emergence of villi in areas where clusters have already formed. Conversely, increasing Hh signaling increases the size of villus clusters and results in exceptionally wide villi. We conclude that Hh signals dictate the initial aspects of the formation of each villus by controlling mesenchymal cluster aggregation and regulating cluster size.

Modelling reaction kinetics inside cells

In the past decade, advances in molecular biology such as the development of non-invasive single molecule imaging techniques have given us a window into the intricate biochemical activities that occur inside cells. In this chapter we review four distinct theoretical and simulation frameworks: (i) non-spatial and deterministic, (ii) spatial and deterministic, (iii) non-spatial and stochastic and (iv) spatial and stochastic. Each framework can be suited to modelling and interpreting intracellular reaction kinetics. By estimating the fundamental length scales, one can roughly determine which models are best suited for the particular reaction pathway under study. We discuss differences in prediction between the four modelling methodologies. In particular we show that taking into account noise and space does not simply add quantitative predictive accuracy but may also lead to qualitatively different physiological predictions, unaccounted for by classical deterministic models.

Clock and Induction Model for Somitogenesis

After many years of research, somitogenesis is still one of the major unresolved problems in developmental biology. Recent experimental findings show a novel type of pattern formation in which a signal sweeps along the presomitic mesoderm and narrows simultaneously as a new somite is formed. The signal then residues in the posterior half of the new somite, and another wave begins to sweep up from the caudal end. This behaviour is not easily explained by the existing theoretical models. We present a new model for somitogenesis that can account for this behaviour and is consistent with previous experimental observations. Dev Den;217:415–420.

Reactant Stationary Approximation in Enzyme Kinetics

In the application of the quasi-steady-state approximation, it is generally assumed that there is an initial transient during which the substrate concentration remains approximately constant while the complex concentration builds up. In this paper, we address the assumption that the substrate concentration does not change significantly during this initial transient and name it the reactant stationary approximation. For the single enzyme, single substrate reaction, the reactant stationary approximation is generally considered a sufficient condition to apply the quasi-steady-state approximation. Studying the dynamic behavior of this reaction with endogenous substrate, we show that the quasi-steady-state approximation and reactant stationary approximation are two separate approximations. We discuss the consequence of this result for the determination of reaction parameters in enzyme catalyzed reactions.

Logic-based models in systems biology: a predictive and parameter-free network analysis method

Highly complex molecular networks, which play fundamental roles in almost all cellular processes, are known to be dysregulated in a number of diseases, most notably in cancer. As a consequence, there is a critical need to develop practical methodologies for constructing and analysing molecular networks at a systems level. Mathematical models built with continuous differential equations are an ideal methodology because they can provide a detailed picture of a networks dynamics. To be predictive, however, differential equation models require that numerous parameters be known a priori and this information is almost never available. An alternative dynamical approach is the use of discrete logic-based models that can provide a good approximation of the qualitative behaviour of a biochemical system without the burden of a large parameter space. Despite their advantages, there remains significant resistance to the use of logic-based models in biology. Here, we address some common concerns and provide a brief tutorial on the use of logic-based models, which we motivate with biological examples.

Validity of the Michaelis-Menten equation--steady-state or reactant stationary assumption: that is the question.

The Michaelis–Menten equation is generally used to estimate the kinetic parameters, V and KM, when the steady‐state assumption is valid. Following a brief overview of the derivation of the Michaelis–Menten equation for the single‐enzyme, single‐substrate reaction, a critical review of the criteria for validity of the steady‐state assumption is presented. The application of the steady‐state assumption makes the implicit assumption that there is an initial transient during which the substrate concentration remains approximately constant, equal to the initial substrate concentration, while the enzyme–substrate complex concentration builds up. This implicit assumption is known as the reactant stationary assumption. This review presents evidence showing that the reactant stationary assumption is distinct from and independent of the steady‐state assumption. Contrary to the widely believed notion that the Michaelis–Menten equation can always be applied under the steady‐state assumption, the reactant stationary assumption is truly the necessary condition for validity of the Michaelis–Menten equation to estimate kinetic parameters. Therefore, the application of the Michaelis–Menten equation only leads to accurate estimation of kinetic parameters when it is used under experimental conditions meeting the reactant stationary assumption. The criterion for validity of the reactant stationary assumption does not require the restrictive condition of choosing a substrate concentration that is much higher than the enzyme concentration in initial rate experiments.

Mathematical Models for Somite Formation

Somitogenesis is the process of division of the anterior-posterior vertebrate embryonic axis into similar morphological units known as somites. These segments generate the prepattern which guides formation of the vertebrae, ribs and other associated features of the body trunk. In this work, we review and discuss a series of mathematical models which account for different stages of somite formation. We begin by presenting current experimental information and mechanisms explaining somite formation, highlighting features which will be included in the models. For each model we outline the mathematical basis, show results of numerical simulations, discuss their successes and shortcomings and avenues for future exploration. We conclude with a brief discussion of the state of modeling in the field and current challenges which need to be overcome in order to further our understanding in this area.