Session T11: Focus Session: Systems Biology

Quantifying the robustness of circadian oscillations at the single-cell level

Cyanobacteria are light-harvesting microorganisms that contribute to 30\% of the photosynthetic activity on Earth and contain one of the simplest circadian systems in the animal kingdom. In $Synechococcus\ elongatus$, a species of freshwater cyanobacterium, circadian oscillations are regulated by the KaiABC system, a trio of interacting proteins that act as a biomolecular pacemaker of the circadian system. While the core oscillator precisely anticipates Earth's 24h light/dark cycle, it is unclear how much individual cells benefit from the expression and maintenance of a circadian clock. By studying the growth dynamics of individual $S.\ elongatus$ cells under sudden light variations, we show that several aspects of cellular growth, such as a cell's division probability and its elongation rate, are tightly coupled to the circadian clock. We propose that the evolution and maintenance of a circadian clock increases the fitness of cells by allowing them to take advantage of cyclical light/dark environments by alternating between two phenotypes: expansionary, where cells grow and divide at a fast pace during the first part of the day, and conservative, where cells enter a more quiescent state to better prepare to the stresses associated with the night's prolonged darkness.   

Entrainment of a Synthetic Oscillator through Queueing Coupling

Many biological systems naturally exhibit (often noisy) oscillatory patterns that are capable of being entrained by external stimuli, though the mechanism of entrainment is typically obscured by the complexity of native networks. A synthetic biology approach, where genetic programs are wired ``by hand,'' has proven useful in this regard. In the present study, we use a synthetic oscillator in Escherichia coli to demonstrate a novel and potentially widespread mechanism for biological entrainment: competition of proteins for degradation by common pathway, i.e. a entrainment by a bottleneck. To faithfully represent the discrete and stochastic nature of this bottleneck, we leverage results from a recent biological queueing theory, where in particular, the queueing theoretic concept of workload is discovered to simplify the analysis.   

Large scale spontaneous synchronization of cell cycles in amoebae

Unicellular eukaryotic amoebae Dictyostelium discoideum are generally believed to grow in their vegetative state as single cells until starvation, when their collective aspect emerges and they differentiate to form a multicellular slime mold. While major efforts continue to be aimed at their starvation-induced social aspect, our understanding of population dynamics and cell cycle in the vegetative growth phase has remained incomplete. We show that substrate-growtn cell populations spontaneously synchronize their cell cycles within several hours. These collective population-wide cell cycle oscillations span millimeter length scales and can be completely suppressed by washing away putative cell-secreted signals, implying signaling by means of a diffusible growth factor or mitogen. These observations give strong evidence for collective proliferation behavior in the vegetative state and provide opportunities for synchronization theories beyond classic Kuramoto models.   

Real-time dynamics of RNA Polymerase II clustering in live human cells

Transcription is the first step in the central dogma of molecular biology, when genetic information encoded on DNA is made into messenger RNA. How this fundamental process occurs within living cells (in vivo) is poorly understood,\footnote{C. Rickman {\&} W. A. Bickmore Science \textbf{341} (2013). } despite extensive biochemical characterizations with isolated biomolecules (in vitro). For high-order organisms, like humans, transcription is reported to be spatially compartmentalized in nuclear foci consisting of clusters of RNA Polymerase II, the enzyme responsible for synthesizing all messenger RNAs. However, little is known of when these foci assemble or their relative stability. We developed an approach based on photo-activation localization microscopy (PALM) combined with a temporal correlation analysis, which we refer to as tcPALM. The tcPALM method enables the real-time characterization of biomolecular spatiotemporal organization, with single-molecule sensitivity, directly in living cells.\footnote{I.I. Cisse et. al. Science \textbf{341} (2013).} Using tcPALM, we observed that RNA Polymerase II clusters form transiently, with an average lifetime of 5.1 ($\pm$ 0.4) seconds. Stimuli affecting transcription regulation yielded orders of magnitude changes in the dynamics of the polymerase clusters, implying that clustering is regulated and plays a role in the cells ability to effect rapid response to external signals. Our results suggest that the transient crowding of enzymes may aid in rate-limiting steps of genome regulation.   

Constrictor: Flux Balance Analysis Constraint Modification Provides Insight for Design of Biochemical Networks

The use of in silico methods has become standard practice to correlate the structure of a biochemical network to the expression of a desired phenotype. Flux balance analysis (FBA) is one of the most prevalent techniques for modeling metabolism. FBA models have been successfully applied to obtain growth predictions, theoretical product yields from heterologous pathways, and genome engineering targets. We take inspiration from high-throughput recombineering techniques, which show that combinatorial exploration can reveal optimal mutants, and apply the advantages of computational techniques to analyze these combinations. We introduce Constrictor, an in silico tool for FBA that allows gene mutations to be analyzed in a combinatorial fashion, by applying simulated constraints accounting for regulation of gene expression. We apply this algorithm to study ethylene production in E. coli through the addition of the heterologous ethylene-forming enzyme from P. syringae. Targeting individual reactions as well as sets of reactions results in theoretical ethylene yields that are as much 65\% greater than yields calculated using typical FBA. Constrictor is an adaptable technique that can be used to generate and analyze disparate populations of in silico mutants \& select gene expression levels.   

The Spatial Chemical Langevin and Reaction Diffusion Master Equations: Moments and Qualitative Solutions

Spatial stochastic effects are prevalent in many biological systems spanning a variety of scales, from intracellular (e.g. gene expression) to ecological (plankton aggregation). The most common ways of simulating such systems involve drawing sample paths from either the Reaction Diffusion Master Equation (RDME) or the Smoluchowski Equation, using methods such as Gillespie's Simulation Algorithm, Green's Function Reaction Dynamics and Single Particle Tracking. The simulation times of such techniques scale with the number of simulated particles, leading to much computational expense when considering large systems. The Spatial Chemical Langevin Equation (SCLE) can be simulated with fixed time intervals, independent of the number of particles, and can thus provide significant computational savings. However, very little work has been done to investigate the behavior of the SCLE. In this talk we summarize our findings on comparing the SCLE to the well-studied RDME. We use both analytical and numerical procedures to show when one should expect the moments of the SCLE to be close to the RDME, and also when they should differ.   

Universal fluctuations in noisy biological time-keeping

In this talk, I shall discuss the scalings of fluctuations in cellular time-keeping, by considering the specific example of fluctuations in cell cycle durations, and how they are informed by fluctuations in cell growth. I will make connections to our observations of stochastic growth and division in single C. crescentus cells, made under different experimental conditions.   

Spatial stochastic modeling of intracellular Ca$^{2+}$ dynamics using two-regime methods

The signaling pathways in many cell types depend on the controlled release of calcium ions from the endoplasmatic reticulum (ER) into the cytoplasm, via clusters of inisitol triphosphate (IP$_3$) receptor channels. At low concentrations, Ca$^{2+}$ ions facilitate channel activation, while acting as inhibitory agents at high concentrations. An activation event causes the opening of other channels in a cluster, resulting in a calcium puff. We simulate calcium ion dynamics using a recently-developed hybrid two-regime technique, wherein the positions of calcium ions in the vicinity of a channel cluster are tracked by employing an off-lattice Brownian dynamics algorithm. An efficient compartment-based algorithm is used in the remainder of the computational domain to correctly capture the diffusive spread of ions. We characterize calcium puffs via the distributions of inter-puff times and amplitudes and investigate the influence of diffusive noise on the puff characteristics by comparing our results with data obtained from an effective non-spatial model.   

Multistable Phase Patterns of Spatially Structured Chemical Oscillators

Recent experiments of two-dimensional microfluidic arrays of droplets containing Belousov-Zhabotinsky reactants show a rich variety of spatio-temporal patterns. Using optical techniques a variety of boundary conditions can be set within the system, including finite rings of droplets. These experiments have provided an interesting and easily reproducible system for probing the effects of nonlinearities and fluctuations in a spatially extended system. Motivated by this experimental set up, we study a simple model of chemical oscillators in the highly nonlinear excitable regime in order to gain insight into the mechanism giving rise to the observed multistable attractors. We map the attractor space of a simple two species activator-inhibitor model coupled via three different coupling mechanism: simple inhibitor diffusion, inhibitor diffusion through an inhomogenous medium where active droplets are separated by inactive holding cells, and coupling through diffusion of an inert signaling species, which arrises through a coarse graining of the inhomogenous medium. Once the attractor space of the mean-field level model has been mapped, we check the robustness of the attractors when subject to intrinsic noise.   

Event-triggered feedback in a noise-driven phase oscillator

Using a stochastic nonlinear phase oscillator model, we study the effect of event-triggered feedback on the statistics of interevent intervals (IEI). Whenever the oscillator enters a new cycle, i.e., an event occurs, feedback is applied to the system by increasing (positive) or decreasing (negative) the oscillators frequency. Such models can be used to study spike-triggered currents in neurons, or feedback mechanisms in laser physics. Beside the known excitable and oscillatory regime positive feedback can lead to bistable dynamics and a change of the excitability class. Furthermore, in the excitable regime the feedback has a strong influence on noise-induced phenomena like coherence resonance or anti-coherence resonance, i.e., the minimization or maximization of IEI variability for a certain amount of noise. Interestingly, positive feedback increases IEI variability for a weak noise, but reduces the variability in the strong noise regime, whereas negative feedback acts in the opposite way. Therefore, both types of feedback can enhance the coherence resonance effect by further reducing the IEI variability, but only positive feedback can lead to anti-coherence resonance, which does not occur in the absence of feedback.