The regulation of expression states of genes in cells is a stochastic process. The relatively small numbers of protein molecules of a given type present in the cell and the nonlinear nature of chemical reactions result in behaviours, which are hard to anticipate without an appropriate mathematical development. In this dissertation, I develop theoretical approaches based on methods of statistical physics and many-body theory, in which protein and operator state dynamics are treated stochastically and on an equal footing. This development allows me to study the general principles of how noise arising on different levels of the regulatory system affects the complex collective characteristics of systems observed experimentally. I discuss simple models and approximations, which allow for, at least some, analytical progress in these problems. These have allowed us to understand how the operator state fluctuations may influence the steady state properties and lifetimes of attractors of simple gene systems. I show, that for fast binding and unbinding from the DNA, the operator state may be taken to be in equilibrium for highly cooperative binding, when predicting steady state properties as is traditionally done. Nevertheless, if proteins are produced in bursts, the DNA binding state fluctuations must be taken into account explicitly. Furthermore, even when the steady state probability distributions are weakly influenced by the operator state fluctuations, the escape rate in biologically relevant regimes strongly depends on transcription factor-DNA binding rates

B cells develop high affinity receptors during the course of affinity maturation, a cyclic process of mutation and selection. At the end of affinity maturation, a number of cells sharing the same ancestor (i.e. in the same "clonal family") are released from the germinal center; their amino acid frequency profile reflects the allowed and disallowed substitutions at each position. These clonal-family-specific frequency profiles, called "substitution profiles", are useful for studying the course of affinity maturation as well as for antibody engineering purposes. However, most often only a single sequence is recovered from each clonal family in a sequencing experiment, making it impossible to construct a clonal-family-specific substitution profile. Given the public release of many high-quality large B cell receptor datasets, one may ask whether it is possible to use such data in a prediction model for clonal-family-specific substitution profiles. In this paper, we present the method "Substitution Profiles Using Related Families" (SPURF), a penalized tensor regression framework that integrates information from a rich assemblage of datasets to predict the clonal-family-specific substitution profile for any single input sequence. Using this framework, we show that substitution profiles from similar clonal families can be leveraged together with simulated substitution profiles and germline gene sequence information to improve prediction. We fit this model on a large public dataset and validate the robustness of our approach on two external datasets. Furthermore, we provide a command-line tool in an open-source software package (https://github.com/krdav/SPURF) implementing these ideas and providing easy prediction using our pre-fit models.

Cells adapt to their environment through the integration of complex signals. Multiple signals can induce synergistic or antagonistic interactions, currently considered as homogenous behaviours. Here, we use a systematic theoretical approach to enumerate the possible interaction profiles for outputs measured in the conditions 0 (control), signals X, Y, X+Y. Combinatorial analysis reveals 82 possible interaction profiles, which we biologically and mathematically grouped into five positive and five negative interaction modes. To experimentally validate their use in living cells, we apply an original computational workflow to transcriptomics data of innate immune cells integrating physiopathological signal combinations. Up to 9 of the 10 defined modes coexisted in context-dependent proportions. Each interaction mode was preferentially used in specific biological pathways, suggesting a functional role in the adaptation to multiple signals. Our work defines an exhaustive map of interaction modes for cells integrating pairs of physiopathological and pharmacological stimuli.

Signal transmission among cells enables long-range coordination in biological systems. However, the scarcity of quantitative measurements hinders the development of theories that relate signal propagation to cellular heterogeneity and spatial organization. We address this problem in a bacterial community that employs electrochemical cell-to-cell communication. We developed a model based on percolation theory, which describes how signals propagate through a heterogeneous medium. Our model predicts that signal transmission becomes possible when the community is organized near a critical phase transition between a disconnected and a fully connected conduit of signaling cells. By measuring population-level signal transmission with single-cell resolution in wild-type and genetically modified communities, we confirm that the spatial distribution of signaling cells is organized at the predicted phase transition. Our findings suggest that at this critical point, the population-level benefit of signal transmission outweighs the single-cell level cost. The bacterial community thus appears to be organized according to a theoretically predicted spatial heterogeneity that promotes efficient signal transmission.