Chapter 1: Background to Modelling the Circadian Clock
1.3 Accounting for Stochastic Variation
1.3.1 Biological systems are noisy
Much bio-molecular research may aim to neatly identify pathways, classify interaction partners, and measure concentrations, but even so, at a microscopic level many biological processes are fundamentally characterized by noisy and random events that, among other things, lead to fluctuating amounts of substance molecules. As genes are generally only present in very few copies, i.e. one or two, and transcription factor molecules in the order of tens or hundreds, deterministic modeling approaches, where a given initial state always leads to the same observed state at a specific time later, may not be unconditionally valid. Rather, such fluctuating dynamics may be more accurately represented by several types of mathematical random or stochastic processes, based either on individual reaction events such as in the Chemical Master Equation and direct simulation, with frequencies in a given time interval as utilized in τ-leaping, or randomly drifting substance concentration, for instance implemented in Chemical Langevin Equations.
Noise as a Selective Advantage
It has been frequently observed that even genetically identical or highly similar cells, which are furthermore at least apparently exposed to entirely the same environmental conditions and stimuli, can show marked divergence in gene expression, protein levels, and more general phenotype. Such variability is attributed to inherent stochasticity, or the presence of random behaviours, which can not only frustrate research studies not prepared for its impact, but which has also been linked to detrimental clinical outcomes. For instance, increased transcriptional noise in older cardiomyocytes has generated the suggestion that DNA damage in the aging heart may be at least in part attributed to this increased stochasticity (Bahar et al. 2006). Overall though, stochastic gene expression and the resulting phenotypic diversity across population of cells or organisms is mostly described as highly evolutionary advantageous, and for instance genes highly involved in stress response and energy production have been shown to display greater
translational fluctuations than other genes (Bar-Even et al. 2006). Indeed, in cells exposed to extreme stress, noisy gene expression provides a demonstrable fitness advantage (Blake et al. 2006). In particular, noisy expression has frequently linked to flipping cellular switches, such as the entry and exit from "persistence" in bacteria, which relies on the stochastic expression of the hipA gene and transforms a fraction of a given populations into a slow-growing state that can protect from antibiotic treatment or other environmental stress (Rotem et al. 2010). Related mechanisms also exist in complex multicellular organisms, and so it was shown that a population of haematopoietic progenitor cells exhibited frequently arising outliers as determined by SCA1 levels, with either very high or low SCA1 expression. Subsequent populations propagated from these outlier cells started off with similarly unusual SCA1 levels, but slowly self-corrected to the more broadly distributed SCA1 levels of the original cell population (Chang et al. 2008). There are also various examples, in which a switch appears originally fuelled by stochastic behaviour, but is subsequently stabilized in a more robust state. For example, somatic cells can be reprogrammed into induced pluripotent stem cells (iPS) by the TFs OCT4, SOX2, KLF4, and MYC (Wernig et al. 2007) in a stochastic manner, but subsequently display a stable pluripotent state and robust expression program (Boyer et al. 2005). Moreover, noisy gene expression can also be an ingrained part of guiding permanent cellular variation, such as the stochastic expression of olfactory receptors in mammals, whereby each sensory neuron expresses only one of hundreds of potential olfactory receptors encoded by the genome (Mombaerts 1999). The resulting distribution of different receptors across a population of cells is critical for establishing a response to odors with immense granularity. Finally, it should be noted that processes may also quickly switch from stochastic to more robust modes. For example, in Drosophila eye development only a single cell in each ommatidium develops into an R8 photoreceptor, whereupon other cells are immediately repressed from developing into R8 cells and instead guided to become other photoreceptors (Roignant & Treisman 2009).
Types of Noise
Noise can be classified into intrinsic and extrinsic noise. Intrinsic noise cannot be controlled for and stems from the inherently probabilistic nature of such cellular mechanisms as promoter/DNA binding events, mRNA transcription and degradation, translation, as well as protein-protein interactions. Notably, it can be observed even for identical genes in the same intracellular environment, and these chance events are able to have such a prominent effect due to the small number of molecules within a single cell. Extrinsic noise, on the other hand, can theoretically be controlled for and is related to different cellular environments, e.g. cell-to-cell differences in cell size and number of ribosomes, or to inputs from elsewhere in the network, such as in the concentrations of the specific trans-acting gene regulators (Swain et al. 2002).
While noise is undoubtedly an inherent feature of practically all biological system, it can be reduced or otherwise regulated in a gene specific mode. In fact, individual genes have been found to range considerably in their propensity for plasticity, and inspecting elements of their genetic architecture, the promoters of high-plasticity genes display high nucleosome occupancy upstream of transcriptional start sites and low occupancy more distally, whereas low-plasticity genes exhibit with greater frequency nucleosome free regions around their promoters (Tirosh & Barkai 2008). Nucleosomes are known to adversely affect the binding of TFs to target DNA segments, and so interactions or competitions between nucleosomes and TFs may contribute to stochasticity (Choi & Kim 2009). Further to this proposed link between gene architecture and expression noise, gene promoters featuring a TATA box were also shown to display more noise in their expression pattern (Tirosh & Barkai 2008). On the side of TFs, it is evident that their expression levels can also have an impact on noise in their target gene expression levels. After all, the interactions of TFs and genes are inherently probabilistic and depend not only on TF diffusion rates, affinity for different DNA sequences, the DNA's orientation, etc., but critically also the TFs concentration. TFs with low expression levels may thus exhibit a lower probability of binding a particular DNA sequence, especially if it competes for
the same downstream target with a more abundant TF, and the response to the lowly expressed TF may thus show greater variability. Genes with low expression levels have also been shown to fluctuate more in their expression (Bar-Even et al. 2006), and noise can further be transmitted through a network from a TF to a downstream target (Pedraza & van Oudenaarden 2005), including other activator or repressor TFs, which may further propagate this noisiness. On a tightly related note, mutations in the binding sites of TFs may also change the strength and residence time of its interaction with regulatory DNA sites, thus altering the level of stochasticity in the expression of these genes. It could be speculated that a change to a lower binding affinity would increase noise in this way, while an approximation of the theoretically optimal TF motif would strengthen protein– DNA interactions and result in more robust downstream target expression.
Stochastic Timing of Expression
It should also be noted that stochastic or robust expression patterns are not limited to the variation in acute mRNA levels, but may also manifest in the timing of expression. For instance, it has been shown that in the embryogenesis of Drosophila many promoters are preloaded with RNA polymerase II, a mechanism that can accelerate the induction of gene expression (Hendrix et al. 2008), and furthermore that this preloading can reduce variability in not only transcriptional induction, but also overall phenotype; conversely, genes lacking stalled RNA polymerase II displayed not only significant stochasticity in their activation times across different cells, but also much greater variability in the expression profiles in the Drosophila presumptive mesoderm (Boettiger & Levine 2009). Furthermore, there is evidence that transcription occurs in bursts, with short periods of rapid production of multiple transcripts, interspersed with relatively long periods of no production, and this pattern, in turn, would have considerable implications for our understanding of general system dynamics and the origin of noise. However, it may be useful to remember at this point that stochastic behaviour is neither strictly negative nor positive, but rather that it depends on the precise nature of target genes whether changes in noise level may be
beneficial or not; e.g. stress genes could possibly benefit from increased plasticity, whereas the disruption of robust essential processes might be more problematic. As such, it is not surprising that some systems have evolved to suppress noisy gene expression or to exploit it, e.g. the bi-stable systems in which cells can select from two phenotypes even in uniform genetic and surrounding conditions to facilitate adaptation to fluctuating environments. Even at the GRN level, different notes have been found to display different levels of noise. For example, highly connected nodes in protein-protein interaction networks, which are more likely to be essential and involved in multiple regulatory processes, also exhibit significantly lower levels of noise in the expression pattern when compared to nodes with fewer edges (Lehner 2008).