The transition of Large Language Models (LLMs) from passive generators to autonomous agents has introduced significant challenges in reliability, security, and state management. Current agentic architectures are often constructed ad-hoc, prone to hallucination cascades, infinite loops, and prompt injection attacks. This paper argues that many of these failure modes can be analyzed using control motifs long studied in systems biology, provided the comparison is made at the level of typed interfaces and coordination structure rather than literal biological mechanism. We develop a typed interface correspondence between Gene Regulatory Networks and agentic software systems using polynomial functors and wiring diagrams. Five biological motifs are mapped to composable software design patterns: Coherent Feed-Forward Loops for noise suppression, Adaptive Immunity for layered security, Mitochondrial Signaling for resource governance, Endosymbiosis for neuro-symbolic integration, and Morphogen Diffusion for spatially varying coordination. An epistemic topology layer derives Kripke-style knowledge operators from the wiring diagram's observation structure and proves four predictive theorems for multi-agent scaling. The core contributions are: (1) the Agentic Operad, a typed syntax for agent composition with provable error suppression bounds for feed-forward topologies; (2) an epistemic topology with four theorems (error amplification, sequential penalty, parallel acceleration, and tool density scaling) whose qualitative predictions are consistent with published multi-agent benchmarks; and (3) a six-layer progression from structure through development, grounded in autonomous learning frameworks and convergence proxies from the empirical literature. A reference implementation with 1,813 tests and 116 examples illustrates practical feasibility.

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