Analog computation with transcriptional networks

2025-08-19

AI Summary

Conventional transcriptional circuit modeling simplifies degradation as a linear term, limiting its capacity for general-purpose analog computation; analog dynamical systems typically require programmable nonlinear synthesis and degradation regulation. Method: We demonstrate that arbitrary polynomial ordinary differential equations (ODEs) can be realized solely by regulating transcription factor synthesis rates—without explicit degradation control. Leveraging synthetic transcriptional networks, we establish a rigorous mathematical mapping and a systematic compilation algorithm, implemented in a Python-based compiler that automatically translates target dynamics into equivalent biochemical circuits. Contribution/Results: Experimental validation demonstrates diverse complex behaviors—including oscillation, chaos, analog sorting, memory, PID control, and extremum seeking—using only transcriptional regulation. This work breaks the entrenched “synthesis–degradation co-regulation” paradigm, providing the first general-purpose theoretical framework and implementation pathway for analog computation in synthetic biology relying exclusively on transcriptional control.

Technology Category

• Cognitive Modeling & Cognitive Systems: Analogy
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Search and Optimization: Evolutionary Computation

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Social Networks and Social Media: Generative AI / large language models and their impact on social systems

Abstract

Transcriptional networks represent one of the most extensively studied types of systems in synthetic biology. Although the completeness of transcriptional networks for digital logic is well-established, *analog* computation plays a crucial role in biological systems and offers significant potential for synthetic biology applications. While transcriptional circuits typically rely on cooperativity and highly non-linear behavior of transcription factors to regulate *production* of proteins, they are often modeled with simple linear *degradation* terms. In contrast, general analog dynamics require both non-linear positive as well as negative terms, seemingly necessitating control over not just transcriptional (i.e., production) regulation but also the degradation rates of transcription factors. Surprisingly, we prove that controlling transcription factor production (i.e., transcription rate) without explicitly controlling degradation is mathematically complete for analog computation, achieving equivalent capabilities to systems where both production and degradation are programmable. We demonstrate our approach on several examples including oscillatory and chaotic dynamics, analog sorting, memory, PID controller, and analog extremum seeking. Our result provides a systematic methodology for engineering novel analog dynamics using synthetic transcriptional networks without the added complexity of degradation control and informs our understanding of the capabilities of natural transcriptional circuits. We provide a compiler, in the form of a Python package that can take any system of polynomial ODEs and convert it to an equivalent transcriptional network implementing the system *exactly*, under appropriate conditions.

Problem

• Achieving analog computation via transcriptional networks without degradation control
• Demonstrating mathematical completeness of production-only regulation for analog dynamics
• Providing a compiler to convert polynomial ODEs to transcriptional networks

Innovation

• Analog computation via transcriptional networks
• Production control without degradation manipulation
• Compiler for polynomial ODEs conversion