\begin{abstract}
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, expressed in the language of polynomial functors and
wiring diagrams, between Gene Regulatory Networks (GRNs) and agentic software systems. At the
atomic level, genes and agent capabilities are modeled as polynomial interfaces; at the composite
level, cells and agents are modeled as structured compositions of those interfaces plus shared
organelles; tissues correspond to multi-agent subsystems. On top of this abstraction, we derive a typed
syntax for agent composition by mapping biological
mechanisms---including Quorum Sensing for consensus, Chaperone Proteins for structural validation,
Innate and Adaptive Immunity for layered security, Mitochondrial Signaling for bioenergetic resource
governance, and Endosymbiosis for neuro-symbolic integration---to software design patterns. This framework
provides a mathematical basis for ``Epigenetic'' state management (RAG), a \textit{Provenance Functor} for
trust-gated resistance to content-level trust forgery, \textit{Epiplexity} for detecting epistemic stagnation, a \textit{Metabolic
Coalgebra} that provides a qualified termination criterion under explicit resource-monotonicity
assumptions, wire-level \textit{Optics} (Prisms and Traversals) for conditional routing, graph-based
\textit{Morphogen Diffusion} for spatially varying coordination, and composable \textit{Coalgebraic State
Machines} with observational equivalence criteria. A reference implementation, interactive
demonstrations, and a synthetic evaluation harness illustrate the framework's practical feasibility.
\end{abstract}
