1. D.D. Jatkar, M.A. Al-Radhawi, C. A. Voigt, and E.D. Sontag. Modeling and minimization of dCas9-induced competition in CRISPRi-based genetic circuits. bioRxiv, 2025. [WWW] [doi:10.1101/2025.11.05.686856] Keyword(s): CRISPRi, retroactivity, feedback, logic-circuit, synthetic biology. Abstract:

   Implementing logic functions in living cells is a fundamental area of interest among synthetic biologists. The goal of designing biochemical circuits in synthetic biology is to make modular and tractable systems that perform well with predictable behaviors. Developing formalisms towards the design of such systems has proven to be difficult with the diverse retroactive effects that appear with respect to the context of the cell. Repressor-based circuits have various applications in biosynthesis, therapeutics, and bioremediation. Particularly using CRISPRi, competition for components of the system (unbound dCas9) can affect the achievable dynamic range of repression. Moreover, the toxicity of dCas9 via non-specific binding inhibits high levels of expression and limits the performance of genetic circuits. In this work, we study the computation of Boolean functions through CRISPRi based circuits built out of NOT and NOR gates. We provide algebraic expressions that allow us to evaluate the steady-state behaviors of any realized circuit. Our mathematical analysis reveals that the effective non-cooperativity of any given gate is a major bottleneck for increasing the dynamic range of the outputs. Further, we find that under the condition of competition between promoters for dCas9, certain circuit architectures perform better than others depending on factors such as circuit depth, fan-in, and fan-out. We pose optimization problems to evaluate the effects engineerable parameter values to find regimes in which a given circuit performs best. This framework provides a mathematical template and computational library for evaluating the performance of repressor-based circuits with a focus on effective cooperativity.




2. D.D. Jatkar, K. M. Aravind, E. D. Sontag, and D. Del Vecchio. Paradoxical gene regulation explained by competition for genomic sites. bioRxiv, 2025. [WWW] [doi:10.1101/2025.11.27.691022] Abstract:

   Understanding how opposing regulatory factors shape gene expression is essential for interpreting complex biological systems. A motivating observation, drawn from cancer epigenetics, is that removing an activating factor can sometimes lead to higher, not lower, expression of a gene that is also subject to repression. This counterintuitive behavior suggests that competition between activators and repressors for limited genomic binding sites may produce unexpected transcriptional outcomes. Prior theoretical work proposed this mechanism, but it has been difficult to test directly in natural systems, where layers of chromatin regulation obscure causal relationships. This paper introduces a fully synthetic, tunable genetic platform in a prokaryotic model system that isolates this competition mechanism in a clean and interpretable setting. The engineered construct contains a target gene with binding sites for both an activator and a repressor, together with a separate decoy region that carries overlapping binding sites for the same regulators. Activator and repressor functions are implemented using CRISPRa and CRISPRi, which permit independent control of regulator expression levels and binding affinities. Using this minimal system, the paper shows that increasing activator expression can reduce expression of the target gene when both regulators are present, consistent with the prediction that additional activator molecules displace the repressor from decoy sites and allow it to more effectively repress the target. By demonstrating how competition alone can invert expected regulatory responses, this synthetic framework provides a validated model for understanding similar paradoxical behaviors in natural regulatory networks and establishes a foundation for future studies in more complex mammalian contexts.




3. A.C.B de Oliveira, D.D. Jatkar, and E.D. Sontag. On the convergence of overparameterized problems: Inherent properties of the compositional structure of neural networks. 2025. Note: Submitted. Also arXiv:2511.09810 [cs.LG]. [WWW] Keyword(s): neural networks, optimization, gradient methods, overparameterization. Abstract:

   This paper investigates how the compositional structure of neural networks shapes their optimization landscape and training dynamics. We analyze the gradient flow associated with overparameterized optimization problems, which can be interpreted as training a neural network with linear activations. Remarkably, we show that the global convergence properties can be derived for any cost function that is proper and real analytic. We then specialize the analysis to scalar-valued cost functions, where the geometry of the landscape can be fully characterized. In this setting, we demonstrate that key structural features -- such as the location and stability of saddle points -- are universal across all admissible costs, depending solely on the overparameterized representation rather than on problem-specific details. Moreover, we show that convergence can be arbitrarily accelerated depending on the initialization, as measured by an imbalance metric introduced in this work. Finally, we discuss how these insights may generalize to neural networks with sigmoidal activations, showing through a simple example which geometric and dynamical properties persist beyond the linear case.

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