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Protein mean and variance levels in a simple stochastic gene expression circuit are controlled using proportional integral feedback. It is shown that the protein mean level can be globally and robustly tracked to any desired value using a…
Moment control of a simple quadratic reaction network describing a dimerization process is addressed. It is shown that the moment closure problem can be circumvented without invoking any moment closure technique. Local stabilization and…
Gene expression in a cell entails random reaction events occurring over disparate time scales. Thus, molecular noise that often results in phenotypic and population-dynamic consequences sets a fundamental limit to biochemical signaling.…
Synthetic biology is an interdisciplinary field aiming to design biochemical systems with desired behaviors. To this end, molecular controllers have been developed which, when embedded into a pre-existing ambient biochemical network,…
Auto-regulation, a process wherein a protein negatively regulates its own production, is a common motif in gene expression networks. Negative feedback in gene expression plays a critical role in buffering intracellular fluctuations in…
An important occurrence in many cellular contexts is the crossing of a prescribed threshold by a regulatory protein. The timing of such events is stochastic as a consequence of the innate randomness in gene expression. A question of…
This paper analyzes, in the context of a prokaryotic cell, the stochastic variability of the number of proteins when there is a control of gene expression by an autoregulation scheme. The goal of this work is to estimate the efficiency of…
Stochasticity in gene expression can result in fluctuations in gene product levels. Recent experiments indicated that feedback regulation plays an important role in controlling the noise in gene expression. A quantitative understanding of…
A wealth of new research has highlighted the critical roles of small RNAs (sRNAs) in diverse processes such as quorum sensing and cellular responses to stress. The pathways controlling these processes often have a central motif comprising…
A detailed stochastic model of single-gene auto-regulation is established and its solutions are explored when mRNA dynamics is fast compared with protein dynamics and in the opposite regime. The model includes all the sources of randomness…
We study a high-dimensional stochastic optimization problem which features both control and stopping. In particular, a central planner steers a large population of particles, and can also remove particles at any time by paying a penalty. In…
The intrinsic stochasticity of gene expression can lead to large variability of protein levels across a population of cells. Variability (or noise) in protein distributions can be modulated by cellular mechanisms of gene regulation; in…
Diffusion models have emerged as powerful tools for generative modeling, demonstrating exceptional capability in capturing target data distributions from large datasets. However, fine-tuning these massive models for specific downstream…
We study the optimal control of discrete time mean filed dynamical systems under partial observations. We express the global law of the filtered process as a controlled system with its own dynamics. Following a dynamic programming approach,…
Gene expression is a fundamental process in a living system. The small RNAs (sRNAs) is widely observed as a global regulator in gene expression. The inherent nonlinearity in this regulatory process together with the bursty production of…
We consider a data-driven formulation of the classical discrete-time stochastic control problem. Our approach exploits the natural structure of many such problems, in which significant portions of the system are uncontrolled. Employing the…
In this paper, we consider two stochastic models of gene expression in prokaryotic cells. In the first model, sixteen biochemical reactions involved in transcription, translation and transcriptional regulation in the presence of inducer…
The ribosomal density along the coding region of the mRNA molecule affect various fundamental intracellular phenomena including: protein production rates, organismal fitness, ribosomal drop off, and co-translational protein folding. Thus,…
The general context of this work is the feedback control of an infinite-dimensional system so that the closed-loop system satisfies a fading-memory property and achieves the setpoint tracking of a given reference signal. More specifically,…
In order to survive, reproduce and (in multicellular organisms) differentiate, cells must control the concentrations of the myriad different proteins that are encoded in the genome. The precision of this control is limited by the inevitable…