Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Experiments show that proteins are translated in sharp bursts; similar bursty phenomena have been observed for protein import into compartments. Here we investigate the effect of burstiness in protein expression and import on the stochastic properties of downstream pathways. We consider two identical pathways with equal mean input rates, except in one pathway proteins are input one at a time and in the other proteins are input in bursts. Deterministically the dynamics of these two pathways are indistinguishable. However the stochastic behavior falls in three categories: (i) both pathways display or do not display noise-induced oscillations; (ii) the non-bursty input pathway displays noise-induced oscillations whereas the bursty one does not; (iii) the reverse of (ii). We derive necessary conditions for these three cases to classify systems involving autocatalysis, trimerization and genetic feedback loops. Our results suggest that single cell rhythms can be controlled by regulation of burstiness in protein production

Critical Self-Organized Self-Sustained Oscillations in Large Regulatory Networks: Towards Understanding the Gene Expression Initiation

In this paper, a new model of self-organized criticality is introduced. This model, called the gene expression paradigm, is motivated by the problem of gene expression initiation in the newly-born daughter cells after mitosis. The model is fundamentally different in dynamics and properties from the well known sand-pile paradigm. Simulation experiments demonstrate that a critical total number of proteins exists below which transcription is impossible. Above this critical threshold, the system enters the regime of self-sustained oscillations with standard deviations and periods proportional to the genes’ complexities with probability one. The borderline between these two regimes is very sharp. Importantly, such a self-organization emerges without any deterministic feedback loops or external supervision, and is a result of completely random redistribution of proteins between inactive genes. Given the size of the genome, the domain of self-organized oscillatory motion is also limited by the genes’ maximal complexities. Below the critical complexity, all the regimes of self-organized oscillations are self-similar and largely independent of the genes’ complexities. Above the level of critical complexity, the whole-genome transcription is impossible. Again, the borderline between the domains of oscillations and quiescence is very sharp. The gene expression paradigm is an example of cellular automata with the domain of application potentially far beyond its biological context. The model seems to be simple enough for staging an experiment for verification of its remarkable properties

Ordered patterning of the sensory system is susceptible to stochastic features of gene expression

Sensory neuron numbers and positions are precisely organized to accurately map environmental signals in the brain. This precision emerges from biochemical processes within and between cells that are inherently stochastic. We investigated impact of stochastic gene expression on pattern formation, focusing on senseless (sens), a key determinant of sensory fate in Drosophila. Perturbing microRNA regulation or genomic location of sens produced distinct noise signatures. Noise was greatly enhanced when both sens alleles were present in homologous loci such that each allele was regulated in trans by the other allele. This led to disordered patterning. In contrast, loss of microRNA repression of sens increased protein abundance but not sensory pattern disorder. This suggests that gene expression stochasticity is a critical feature that must be constrained during development to allow rapid yet accurate cell fate resolution

Reconciling Kinetic and Equilibrium Models of Bacterial Transcription

The study of transcription remains one of the centerpieces of modern biology with implications in settings from development to metabolism to evolution to disease. Precision measurements using a host of different techniques including fluorescence and sequencing readouts have raised the bar for what it means to quantitatively understand transcriptional regulation. In particular our understanding of the simplest genetic circuit is sufficiently refined both experimentally and theoretically that it has become possible to carefully discriminate between different conceptual pictures of how this regulatory system works. This regulatory motif, originally posited by Jacob and Monod in the 1960s, consists of a single transcriptional repressor binding to a promoter site and inhibiting transcription. In this paper, we show how seven distinct models of this so-called simple-repression motif, based both on equilibrium and kinetic thinking, can be used to derive the predicted levels of gene expression and shed light on the often surprising past success of the equilibrium models. These different models are then invoked to confront a variety of different data on mean, variance and full gene expression distributions, illustrating the extent to which such models can and cannot be distinguished, and suggesting a two-state model with a distribution of burst sizes as the most potent of the seven for describing the simple-repression motif

Single Cell Molecular Heterogeneity In Musculoskeletal Differentiation

Mesenchymal stem cells (MSCs) display substantial cell-to-cell variation that manifests across many aspects of cell phenotype and complicates the use of MSCs in regenerative applications. However, most conventional assays measure MSC properties in bulk and, as a consequence, mask this cell-to-cell variation. To better understand MSC heterogeneity and its underlying mechanisms, we quantitatively assessed MSC phenotype within the context of chondrogenesis, amongst clonal populations and single cells. Clonal MSCs differed in their contractility, ability to transmit extracellular strain the nucleus, capacity to form cartilage-like matrix, and transcriptomic signature. RNA FISH measurements of single cell gene expression found that both primary chondrocytes and chondrogenically-induced MSCs showed substantial mRNA expression heterogeneity. Surprisingly, variation in differentiation marker transcript levels only weakly associated with cartilage-like matrix production at the single cell level. This finding suggested that, although canonical markers have very clear functional roles in differentiation and matrix formation, their instantaneous mRNA abundance is only tenuously linked to the chondrogenic phenotype and matrix accumulation at the single cell level. One possible explanation for the apparent disconnect between gene and protein expression is that mRNA and protein exhibit different temporal dynamics. Using stochastic models of single cell behavior, we explored the impact of transcriptional stochasticity and temporal matrix dynamics on the perceived relationship between single cell mRNA and protein abundance. Simulations suggested that considering recent temporal fractions of protein (vs. total protein) increased the correlation between mRNA and protein abundance, and illustrated that mRNA stability was a crucial determinant of the timescale over which any such correlation persisted. Experimentally, non-canonical amino acid tagging was used to visualize and quantify temporal fractions of nascent extracellular matrix with high fidelity. The organization and temporal dynamics of the proteinaceous matrix depended on the biophysical features of the microenvironment, including the biomaterial scaffold and the niche constructed by cells themselves. Both chondrocytes and MSCs demonstrated marked cell-to-cell heterogeneity in nascent matrix production, consistent with model predictions. Ongoing work aims to combine these experimental measurements of nascent protein expression with instantaneous measures of mRNA abundance to better understand the mRNA-protein relationship, and to harness this understanding to improve regenerative therapies

Approximation methods and inference for stochastic biochemical kinetics

Recent experiments have shown the fundamental role that random fluctuations play in many chemical systems in living cells, such as gene regulatory networks. Mathematical models are thus indispensable to describe such systems and to extract relevant biological information from experimental data. Recent decades have seen a considerable amount of modelling effort devoted to this task. However, current methodologies still present outstanding mathematical and computational hurdles. In particular, models which retain the discrete nature of particle numbers incur necessarily severe computational overheads, greatly complicating the tasks of characterising statistically the noise in cells and inferring parameters from data. In this thesis we study analytical approximations and inference methods for stochastic reaction dynamics. The chemical master equation is the accepted description of stochastic chemical reaction networks whenever spatial effects can be ignored. Unfortunately, for most systems no analytic solutions are known and stochastic simulations are computationally expensive, making analytic approximations appealing alternatives. In the case where spatial effects cannot be ignored, such systems are typically modelled by means of stochastic reaction-diffusion processes. As in the non-spatial case an analytic treatment is rarely possible and simulations quickly become infeasible. In particular, the calibration of models to data constitutes a fundamental unsolved problem. In the first part of this thesis we study two approximation methods of the chemical master equation; the chemical Langevin equation and moment closure approximations. The chemical Langevin equation approximates the discrete-valued process described by the chemical master equation by a continuous diffusion process. Despite being frequently used in the literature, it remains unclear how the boundary conditions behave under this transition from discrete to continuous variables. We show that this boundary problem results in the chemical Langevin equation being mathematically ill-defined if defined in real space due to the occurrence of square roots of negative expressions. We show that this problem can be avoided by extending the state space from real to complex variables. We prove that this approach gives rise to real-valued moments and thus admits a probabilistic interpretation. Numerical examples demonstrate better accuracy of the developed complex chemical Langevin equation than various real-valued implementations proposed in the literature. Moment closure approximations aim at directly approximating the moments of a process, rather then its distribution. The chemical master equation gives rise to an infinite system of ordinary differential equations for the moments of a process. Moment closure approximations close this infinite hierarchy of equations by expressing moments above a certain order in terms of lower order moments. This is an ad hoc approximation without any systematic justification, and the question arises if the resulting equations always lead to physically meaningful results. We find that this is indeed not always the case. Rather, moment closure approximations may give rise to diverging time trajectories or otherwise unphysical behaviour, such as negative mean values or unphysical oscillations. They thus fail to admit a probabilistic interpretation in these cases, and care is needed when using them to not draw wrong conclusions. In the second part of this work we consider systems where spatial effects have to be taken into account. In general, such stochastic reaction-diffusion processes are only defined in an algorithmic sense without any analytic description, and it is hence not even conceptually clear how to define likelihoods for experimental data for such processes. Calibration of such models to experimental data thus constitutes a highly non-trivial task. We derive here a novel inference method by establishing a basic relationship between stochastic reaction-diffusion processes and spatio-temporal Cox processes, two classes of models that were considered to be distinct to each other to this date. This novel connection naturally allows to compute approximate likelihoods and thus to perform inference tasks for stochastic reaction-diffusion processes. The accuracy and efficiency of this approach is demonstrated by means of several examples. Overall, this thesis advances the state of the art of modelling methods for stochastic reaction systems. It advances the understanding of several existing methods by elucidating fundamental limitations of these methods, and several novel approximation and inference methods are developed