John Wentworth

John Wentworth, David Lorell

Suppose two Bayesian agents each learn a generative model of the same environment. We will assume the two have converged on the predictive distribution, i.e. distribution over some observables in the environment, but may have different generative models containing different latent variables. Under what conditions can one agent guarantee that their latents are a function of the other agents latents? We give simple conditions under which such translation is guaranteed to be possible: the natural latent conditions. We also show that, absent further constraints, these are the most general conditions under which translatability is guaranteed. Crucially for practical application, our theorems are robust to approximation error in the natural latent conditions.

Emma Wentworth, John Wentworth

Almost all current approaches for engineering modular logic components in synthetic biology use first-order regulators, including most CRISPR/CAS, TAL, zinc finger, and RNA interference systems. Many practitioners understand intuitively that second and higher order binding is necessary for scalability, and this is easy to show for single-input single-output systems. However, no study to date has analysed whether a more complex system, utilizing e.g. feedback or error correction, can produce scalable computation from first-order regulators. We prove here that first order repressor systems cannot support bistability. In the process, we introduce a function G to measure signal quality in molecular systems, and we show that G always decreases in dynamic feedback systems as well as static feed-forward logic cascades of first-order repressors. As a result, first order repressors cannot build memory or signal buffering elements. Finally, we suggest G as a potential new property for characterization of standard biological parts.