Emergent colinearity in a model of modular polyketide synthases Ben Callahan, Mukund Thattai, Boris Shraiman September 25, 2008 Abstract Polyketides are widespread, biologically active heteropolymers assem- bled by complexes of modular polyketide synthase(PKS) proteins. We implement a model of this system and explore its evolutionary behavior while subject to recombination in a changing environment. Under ap- propriate population parameters the combinatorial exploration of novelty allows a finite population to maintain high fitness indefinitely. Accompa- nying this maintenance of fitness is the phenomenon of emergent colin- earity, a correlation between genetic order and the functional order of the product polyketide. Colinearity is a known characteristic of modular PKS systems. In our model it arises despite the absence of phenotypic effect. We understand this by observing that colinearity enhances the likelihood of recombination forming novel high-fitness phenotypes. We are able to quantify this effect, successive selective sweeps drive our evolving popula- tions towards a fixed point in our colinearity parameter y. The existence and location of this fixed point is found to depend only on the density of states ρ(y) and the likelihood of recombination creating high-fitness phenotypes, q(y). 1 Introduction Polyketides are a class of structurally and functionally diverse heteropolymers found in bacteria, protozoa, plants and animals. In single-celled organisms these secondary metabolites mediate a variety of interactions between cells and their environment [23]: as channels of cell-to-cell communication between conspecifics [1], as anti-microbial agents against competitors, and as immuno-suppressors or virulence factors [7] between pathogens and their hosts. The enormous diversity of natural polyketide products might result from a ‘chemical arms race’ during inter-species and host-pathogen conflict; alternatively, the ability to generate chemical diversity might be an end in itself, increasing the likelihood of discovery of biologically potent molecules [4]. In bacteria, the chemical diversity of polyketides is achieved through a unique combinatorial biosynthesis mechanism. A large class of polyketides are gener- ated by ordered complexes of modular polyketide synthase (PKS) proteins via 1