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Synthetic biology sets out to implement new functions in cells, and to develop a deeper understanding of biological design principles. In 2000, Elowitz and Leibler showed that by rational design of the reaction network, and using existing…
Circadian clocks play a pivotal role in orchestrating numerous physiological and developmental events. Waveform shapes of the oscillations of protein abundances can be informative about the underlying biochemical processes of circadian…
Many real-world systems can be modeled as networks of interacting oscillatory units. Collective dynamics that are of functional relevance for the oscillator network, such as switching between metastable states, arise through the interplay…
In the brain, coherent neuronal activities often appear simultaneously in multiple frequency bands, e.g., as combinations of alpha (8-12 Hz), beta (12.5-30 Hz), gamma (30-120 Hz) oscillations, among others. These rhythms are believed to…
Eukaryotic cells are mechanically supported by a polymer network called the cytoskeleton, which consumes chemical energy to dynamically remodel its structure. Recent experiments in vivo have revealed that this remodeling occasionally…
We examine microscopic mechanisms for coupling stochastic oscillators so that they display similar and correlated temporal variations. Unlike oscillatory motion in deterministic dynamical systems, complete synchronization of stochastic…
Stochasticity is both exploited and controlled by cells. Although the intrinsic stochasticity inherent in biochemistry is relatively well understood, cellular variation, or 'noise', is predominantly generated by interactions of the system…
Systems with the coexistence of different stable attractors are widely exploited in systems biology in order to suitably model the differentiating processes arising in living cells. In order to describe genetic regulatory networks several…
Brownian clocks are biomolecular networks that can count time. A paradigmatic example are proteins that go through a cycle thus regulating some oscillatory behaviour in a living system. Typically, such a cycle requires free energy often…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
Overdamped stochastic systems maintained far from equilibrium can display sustained oscillations with fluctuations that decrease with the system size. The correlation time of such noisy limit cycles expressed in units of the cycle period is…
We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral…
In many applied settings, the chemical Langevin equation and linear noise approximation are used in the simulation and data analysis of stochastic reaction networks. With the goal of exploring the sensitivities of reaction network paths to…
Biological oscillators coordinate individual cellular components so that they function coherently and collectively. They are typically composed of multiple feedback loops, and period mismatch is unavoidable in biological implementations. We…
Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Most theoretical approaches describe them as purely deterministic or stochastic dynamical…
A number of biological rhythms originate from networks comprised of multiple cellular oscillators. But analytical results are still lacking on the collective oscillation period of inter-coupled gene regulatory oscillators, which, as has…
Fluctuations in the abundance of molecules in the living cell may affect its growth and well being. For regulatory molecules (e.g., signaling proteins or transcription factors), fluctuations in their expression can affect the levels of…
Biochemical reactions with oscillatory behavior play an essential role in synthetic biology at the microscopic scale. Although a robust stability theory for deterministic chemical oscillators in the macroscopic limit exists, the dynamical…