Heterogeneity and noise in living systems: statistical physics perspectives

Even the most distracted observer could hardly miss noticing the extensive heterogeneity of traits and behaviors displayed by living systems. So great a variability is commonly ascribed to differences at the level of the genome, which originated from the evolution process to adapt the organisms to the different environments they live in. However, phenotypic heterogeneity is found even in genetically identical organisms, from monoclonal cellular populations to human twins. The multitude of microscopic causes that sum up to give such variability is commonly referred to as biological noise, coming both in the form of environmental fluctuations affecting the development of individual organisms (extrinsic noise) and as the unavoidable results of stochasticity at the level of molecular reaction (intrinsic noise). The latter persisting even when genetically identical organisms are kept under nearly identical conditions. For quite a long time, such fluctuations were considered a nuisance that makes experiments just difficult to interpret, needing to enlarge the number of observations to have reliable outcomes, and from the point of view of cells, a disturbance cells need to deal with. In the last two decades, however, experimental progresses allowed to investigate the system at single-cell scale. The emerging view is that noise under some circumstances can have a beneficial role, like promoting survival to adverse environments or enhancing differentiation. Ultimately, evolution tunes the systems so they can take advantage of natural stochastic fluctuations. We will follow noise and fluctuation from the cellular level to the higher level of organization of the cellular population where heterogeneity in the molecular reactions translate in the variability of phenotypes. Biology is very broad though, and noise affects all biological processes. Time restraint and my limited knowledge of biological systems did not allow for an exhaustive discussion of all the aspects in which noise and the subsequent heterogeneity play a role. Instead, we will focus on the regulation of noise. More in details, the first part of the thesis introduces to the impact of noise on gene expression and the regulation mechanisms cells use to control it. The action of large regulatory networks is to coordinate a huge of number molecular interactions to obtain robust system-level outcomes. This capability can emerge even when individual interactions are weak and/or strongly heterogeneous. This is the case of post-transcriptional regulation driven by microRNAs (miRNAs). microRNAs are small non-coding RNA molecules able to regulate gene expression at the post-transcriptional level by repressing target RNA molecules. It has been found that such regulation may lead the system to bimodal distributions in the expression of the target mRNA, usually fingerprint of the presence of two distinct phenotypes. Moreover, the nature of the interaction between miRNAs and their targets gives rise to a complex network of miRNAs interacting with several mRNA targets. Such targets may then cross-regulate each other in an indirect miRNA-mediated manner. This effect, called `competing endogenous RNA (ceRNA) effect', despite being typically weak, has been found to possess remarkable properties in the presence of extrinsic noise, where fluctuations affect all the components of the system. We will discuss crosstalk and illustrate how crosstalk patterns are enhanced by both transcriptional and kinetic heterogeneities and achieve high intensities even for RNAs that are not co-regulated. Moreover, we will see that crosstalk patterns are significantly non-local, i.e. correlate weakly with miRNA-RNA interaction parameters. Since these features appear to be encoded in the network's topology this suggests that such crosstalk is tunable by natural selection. Moving at the cellular level, we focus on the outcomes of gene expression, i.e. the observable phenotypes. Depending on the degree of regulation the cell manages to exert with respect to noise, the distribution of those phenotypes will display a certain extent of heterogeneity. Such cell-to-cell variability is found to have many implications especially for the growth of the whole population. In the second part of the thesis, we discuss some properties of those heterogeneous distributions. First, we focus on the dependence on the initial conditions for the different phases of growth, i.e. the adaptive phase and exponential growth phase. Since cellular populations grow in an exponential fashion, the size and composition of the inoculum shall matter. We discuss this following a novel extensive experimental investigation recently done on cancer cell lines in a controlled environment. Finally, we focus on the effects that a heterogeneous phenotype has on the growth in hostile environments, i.e. environments fluctuating between states in which the growth is favored and others where growth is inhibited. In such a case, if cells can only replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations), an exploration-exploitation trade-off is established, whose specifics depend on the statistics of the environment. The phenotypic distribution corresponding to maximum population fitness requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in periodic two-state environments. Most notably, the key parameter overseeing the trade-off is linked to the amount of regulation cells can exert.