The adaptation of neural codes to the statistics of their environment is well captured by efficient coding approaches. Here we solve an inverse problem: characterizing the objective and constraint functions that efficient codes appear to be optimal for, on the basis of how they adapt to different stimulus distributions. We formulate a general efficient coding problem, with flexible objective and constraint functions and minimal parametric assumptions. Solving special cases of this model, we provide solutions to broad classes of Fisher information-based efficient coding problems, generalizing a wide range of previous results. We show that different objective function types impose qualitatively different adaptation behaviors, while constraints enforce characteristic deviations from classic efficient coding signatures. Despite interaction between these effects, clear signatures emerge for both unconstrained optimization problems and information-maximizing objective functions. Asking for a fixed-point of the neural code adaptation, we find an objective-independent characterization of constraints on the neural code. We use this result to propose an experimental paradigm that can characterize both the objective and constraint functions that an observed code appears to be optimized for.

The rapid evolution of RNA-encoded viruses such as HIV presents a major barrier to infectious disease control using conventional pharmaceuticals and vaccines. Previously, it was proposed that defective interfering particles could be developed to indefinitely control the HIV/AIDS pandemic; in individual patients, these engineered molecular parasites were further predicted to be refractory to HIV's mutational escape (i.e., be 'resistance-proof'). However, an outstanding question has been whether these engineered interfering particles-termed Therapeutic Interfering Particles (TIPs)-would remain resistance-proof at the population-scale, where TIP-resistant HIV mutants may transmit more efficiently by reaching higher viral loads in the TIP-treated subpopulation. Here, we develop a multi-scale model to test whether TIPs will maintain indefinite control of HIV at the population-scale, as HIV ('unilaterally') evolves toward TIP resistance by limiting the production of viral proteins available for TIPs to parasitize. Model results capture the existence of two intrinsic evolutionary tradeoffs that collectively prevent the spread of TIP-resistant HIV mutants in a population. First, despite their increased transmission rates in TIP-treated sub-populations, unilateral TIP-resistant mutants are shown to have reduced transmission rates in TIP-untreated sub-populations. Second, these TIP-resistant mutants are shown to have reduced growth rates (i.e., replicative fitness) in both TIP-treated and TIP-untreated individuals. As a result of these tradeoffs, the model finds that TIP-susceptible HIV strains continually outcompete TIP-resistant HIV mutants at both patient and population scales when TIPs are engineered to express >3-fold more genomic RNA than HIV expresses. Thus, the results provide design constraints for engineering population-scale therapies that may be refractory to the acquisition of antiviral resistance.