Biomechanics of Cells and Tissues

Tissue engineering has the potential to overcome the limitations associated with current reconstructions strategies of the Anterior Cruciate Ligament (ACL). However, the design of a scaffold satisfying the key requirements associated with ACL tissue engineering is a challenging task. In order to avoid a costly trial-and-error approach, computer-based methods have been widely used in the case of various applications such as bone or cartilage. These methods can help to define the best scaffold and culture conditions for a given list of criteria, and may also enable to predict the ultimate evolution of the scaffold and to better understand some mechanobiological principles. Some of these methods are reviewed in the current chapter, and are applied for the first time in the case of ACL tissue engineering. The morphological and mechanical properties of a new scaffold based on copoly(lactic acid-co-(\(\upvarepsilon \)-caprolactone)) (PLCL) fibers arranged into a multilayer braided structure will be assessed using dedicated numerical tools. Preliminary biological assessments are also presented, and some conclusions concerning the suitability of the scaffold and the interest of CATE in this case will be drawn.

We propose stochastic process models as a means for studying and rendering unbounded biological structures, involving mechanisms that extend over geometric space. As an example, we discuss a case study of actin polymerization dynamics, which plays a key role in many cellular activities and enjoys a rich structure. We provide a comparative review of various approaches in the literature for modeling actin. We then illustrate on actin models how otherwise challenging structures can be modeled. In these models the complexity of the structures are incrementally increased with respect to the biological data. We present a geometric representation of these models that we use to generate movies reflecting their dynamics while preserving formal cleanliness as well as loyalty to the biological data.

We present a stochastic model of the lymphocytes recruitment in inflamed brain microvessels. The framework used is based on stochastic process algebras for mobile systems. The automatic tool used in the simulation is the biochemical stochastic \(\pi \)-calculus. Lymphocytes roll along the walls of vessels to survey the endothelial surface for chemotactic signals, which stimulate the lymphocytes to stop rolling and migrate through the endothelium and its supporting basement membrane. In particular the lymphocytes extravasation is a critical event in the pathogenesis of multiple sclerosis, an autoimmune serious disease of the central nervous system. Recent studies have revealed that the process leading to lymphocytes extravasation is a sequence of dynamical states (contact with endothelium, rolling and firm adhesion), mediated by partially overlapped interactions of different adhesion molecules and activation factors. The biochemical stochastic \(\pi \)-calculus is an efficient tool for describing the concurrency of the different interactions driving the phases of lymphocytes recruitment. It models a biochemical systems as a set of concurrent processes selected according to a suitable probability distribution in order to quantitatively describe the rates and the times at which the reactions occur. We used this tool to model and simulate the molecular mechanisms involved in encephalitogenic lymphocytes recruitment. In particular, we show that the model predicts the percentage of lymphocytes involved in the rolling process on the endothelium of vessels of different diameters. The results of the model reproduce, within the estimated experimental errors, the functional exponential behavior of the data obtained from laboratory measurements.

Metabolism comprises a set of chemical reactions that are performed in biological systems in order to sustain life. Metabolism is responsible for deriving energy and biomolecules from the cells’ surrounding. Tumour cells’ very high metabolic needs have to be fulfilled under suboptimal conditions. Thus, tumour cells and tissues have a remarkably different metabolism than the tissues that they derive from. Many key oncogenic signaling pathways converge to create this change in order to support growth and survival of cancer cells. Some of these metabolic alterations are initiated by oncogenes and are required for malignant transformation. Altered metabolism allows cancer cells to sustain higher proliferative rates with faster energy and molecular building block production while resisting cell death signals particularly those that are mediated by increased oxidative damage. The very specific metabolic phenotype of cancer provides an interesting avenue for diagnosis and treatment and several examples of such applications are already in place. Novel methods for metabolic profiling, comprised under the term metabolomics, provide tools for collection of data on cancer cell and tissue’s metabolic properties in steady state and as a function of time and/or treatment. The time, i.e. flux data can provide components for creation of more detailed kinetic models of metabolic processes in cancer leading to more information about possible markers as well as platforms for in silico treatment testing. Once a more detailed understanding of the characteristics of cancer metabolism including energy and biomolecules production is in place, further clinical developments will follow.

Boolean models have proven to be effective in capturing some features of the dynamical behavior of the gene regulatory network of isolated cells. Cells are however constantly exposed to several signals that affect the regulation of their genes and are therefore not isolated. Moreover, cells in multi-cellular organisms and, to some extent, also in colonies of unicellular ones modify their gene expression profiles in a coordinated fashion. Many of these processes are controlled by cell–cell communication mechanisms. It appears therefore important to understand how the interplay among gene regulatory networks, by means of the signaling network, may alter their dynamical properties. In order to explore the issue, a model based on interconnected identical Boolean networks has been proposed, which has allowed to investigate the influence that cell-signaling may have on the expression patterns of individual cells, with particular regard on their variety and homeostasis. The main results described in this chapter show that both the diversity of emergent behaviors and the diffusion of perturbations may not depend linearly on the fraction of genes involved in the signaling network. On the contrary, when cells exchange a moderate quantity of signals with neighbors, the variety of their activation patterns is maximized, together with the number of genes that can be damaged as a consequence of a minor alteration of the system.

We presents two models of glucose metabolism in astrocytes based on ordinary differential equations calibrated on \({}^{18}\)F-deoxyglucose PET images. The signals detected during physiological activation of the brain with \({}^{18}\)F-deoxyglucose PET reflect predominantly uptake of this tracer into astrocytes. This notion provides a cellular and molecular basis for the FDG PET technique. In recent years the functional brain imaging has experienced enormous advances. These advancements provided new observational data about the inter- and intra-cellular mechanisms of the brain glucose metabolism. Our models specify of the molecular interactions governing the energy metabolism. The first model describes the glutamate-stimulated glucose uptake and use into astrocytes. It consists of a set of ordinary differential equations, each of which specifying the time-behavior of the main molecular species involved in the astrocytic glucose use (i.e. glutamate, glucose, \(\mathrm{{Na}}^{+}\), \(\beta \)-threohydroxyaspartate) and the dynamical rates of glutamate, glucose and \(\mathrm{{ Na}}^{+}\) uptake. The second model includes also the effects of inter-cellular waves of \(\mathrm{{Na}}^{+}\) and \(\mathrm{{Ca}}^{2+}\) generated by astrocytes on the glucose metabolism. The kinetic rates constants of the models have been identified by fitting the sets of ordinary differential equations to dynamic Positron Emision Tomography scans of 31 patients.