Matrix glycation modulated cell behavior to induce inflammation equivalent to that produced by incubation with P. gingivalis LPS. Periodontal inflammation also led to matrix glycation, thus demonstrating a definite interaction between diabetes and periodontitis.

Understanding how the spatial arrangement of a population shapes its evolutionary dynamics has been of long-standing interest in population genetics. Most previous studies assume a small number of demes connected by migration corridors, symmetrical structures that most often act as well-mixed populations. Other studies use networks to model the more complex topologies of natural populations and to study the structures that suppress or amplify selection. However, they usually assume very small, regular networks, with strong constraints on the strength of selection considered. Here we build network generation algorithms, evolutionary simulations and derive general analytic approximations for probabilities of fixation in populations with complex spatial structure. By tuning network parameters and properties independent of each other, we systematically span across network families and show that both a network's degree distribution, as well as its node mixing pattern shape the evolutionary dynamics of new mutations. We analytically write the relevant selective parameter, predictive of evolutionary dynamics, as a combination of network statistics. As one application, we use recent imaging datasets and build the cellular spatial networks of the stem cell niches of the bone marrow. Across a wide variety of parameters and regardless of the birth-death process used, we find these networks to be strong suppressors of selection, delaying mutation accumulation in this tissue. We also find that decreases in stem cell population size decrease the suppression strength of the tissue spatial structure, hinting at a potential diminishing spatial suppression in the bone marrow tissue as individuals age.

To design population topologies that can accelerate rates of solution discovery in directed evolution problems or in evolutionary optimization applications, we must first systematically understand how population structure shapes evolutionary outcome. Using the mathematical formalism of evolutionary graph theory, recent studies have shown how to topologically build networks of population interaction that increase probabilities of fixation of beneficial mutations, at the expense, however, of longer fixation times, which can slow down rates of evolution under elevated mutation rate. Here we find that moving beyond dyadic interactions is fundamental to explain the trade-offs between probability and time to fixation. We show that higher-order motifs, and in particular three-node structures, allow tuning of times to fixation, without changes in probabilities of fixation. This gives a near-continuous control over achieving solutions that allow for a wide range of times to fixation. We apply our algorithms and analytic results to two evolutionary optimization problems and show that the rate at which evolving agents learn to navigate their environment can be tuned near continuously by adjusting the higher-order topology of the agent population. We show that the effects of population structure on the rate of evolution critically depend on the optimization landscape and find that decelerators, with longer times to fixation of new mutants, are able to reach the optimal solutions faster than accelerators in complex solution spaces. Our results highlight that no one population topology fits all optimization applications, and we provide analytic and computational tools that allow for the design of networks suitable for each specific task.