A mathematical model for a T cell fate decision algorithm during immune response

Bone remodeling: A tissue-level process emerging from cell-level molecular algorithms

The human skeleton undergoes constant remodeling throughout the lifetime. Processes occurring on microscopic and molecular scales degrade bone and replace it with new, fully functional tissue. Multiple bone remodeling events occur simultaneously, continuously and independently throughout the body, so that the entire skeleton is completely renewed about every ten years.Bone remodeling is performed by groups of cells called Bone Multicellular Units (BMU). BMUs consist of different cell types, some specialized in the resorption of old bone, others encharged with producing new bone to replace the former. These processes are tightly regulated so that the amount of new bone produced is in perfect equilibrium with that of old bone removed, thus maintaining bone microscopic structure.To date, many regulatory molecules involved in bone remodeling have been identified, but the precise mechanism of BMU operation remains to be fully elucidated. Given the complexity of the signaling pathways already known, one may question whether such complexity is an inherent requirement of the process or whether some subset of the multiple constituents could fulfill the essential role, leaving functional redundancy to serve an alternative safety role. We propose in this work a minimal model of BMU function that involves a limited number of signals able to account for fully functional BMU operation. Our main assumptions were i) at any given time, any cell within a BMU can select only one among a limited choice of decisions, i.e. divide, die, migrate or differentiate, ii) this decision is irreversibly determined by depletion of an appropriate internal inhibitor and iii) the dynamics of any such inhibitor are coupled to that of specific external mediators, such as hormones, cytokines, growth factors. It was thus shown that efficient BMU operation manifests as an emergent process, which results from the individual and collective decisions taken by cells within the BMU unit in the absence of any external planning.

The growth threshold conjecture: a theoretical framework for understanding T-cell tolerance

Adaptive immune responses depend on the capacity of T cells to target specific antigens. As similar antigens can be expressed by pathogens and host cells, the question naturally arises of how can T cells discriminate friends from foes. In this work, we suggest that T cells tolerate cells whose proliferation rates remain below a permitted threshold. Our proposal relies on well-established facts about T-cell dynamics during acute infections: T-cell populations are elastic (they expand and contract) and they display inertia (contraction is delayed relative to antigen removal). By modelling inertia and elasticity, we show that tolerance to slow-growing populations can emerge as a population-scale feature of T cells. This result suggests a theoretical framework to understand immune tolerance that goes beyond the self versus non-self dichotomy. It also accounts for currently unexplained observations, such as the paradoxical tolerance to slow-growing pathogens or the presence of self-reactive T cells in the organism.

On the interplay between mathematics and biology: hallmarks toward a new systems biology

This paper proposes a critical analysis of the existing literature on mathematical tools developed toward systems biology approaches and, out of this overview, develops a new approach whose main features can be briefly summarized as follows: derivation of mathematical structures suitable to capture the complexity of biological, hence living, systems, modeling, by appropriate mathematical tools, Darwinian type dynamics, namely mutations followed by selection and evolution. Moreover, multiscale methods to move from genes to cells, and from cells to tissue are analyzed in view of a new systems biology approach.