Chi Xue

Predator-prey dynamics of transposable elements

Transposable elements (TEs), or transposons, are a class of mobile genetic elements that can either move or duplicate themselves in the genome, sometimes interfering with gene expression as a result. Some TEs can code all necessary enzymes for their transposition and are thus autonomous, while non-autonomous TEs are parasitic and must depend on the machinery of autonomous ones.

Transposable elements occupy roughly 45% of the human genome. Among them, are the autonomous/non-autonomous pair of L1 and Alu elements. Both L1 and Alu belong to the retrotransposon catogory. They use the corresponding mRNA molecule as a template and retrotranscribe the mRNA into DNA to complete a transposition. This copy-and-paste route results in the growth of the element copy number. L1 elements are autonomous and code all the necessary enzymes. Alu elements do not code any proteins and depend on the retrotranscriptase of the L1 elements to profiliate.

We develop and solve a stochastic model to describe the interaction between the Alu/L1 non- autonomous/autonomous pair. We predict noise-induced persistent quasi-cycles in their copy numbers, analogous to predator-prey dynamics in an ecosystem. These quasi-cycles can potentially be observed in the genomic age distribution or be realized in engineered fast dividing organisms (e.g. E. coli).

Maintenance of diversity by Kill the Winner

The Kill the Winner (KtW) hypothesis is an attempt to explain the problem of diversity in biology, sometimes known as the Paradox of the Plankton: why do many species, feeding on the same resource, coexist instead of one species out-competing all the others?

The KtW hypothesis argues that a combination of host-specific and general predators control the populations of prey, preventing a winner from emerging, thus maintaining the coexistence of all species in the system.

We develop a stochastic model applying the Kill the Winner idea and show that the putative coexistence state of the deterministic Kill the Winner model is destroyed by demographic stochasticity, and that the system undergoes a cascade of extinction events. This stochastic effect is significant when population sizes are locally finite, for example, in a marine system, or near extinction.

We formulate an individual-level stochastic model in which coevolution of predator and prey promotes the high diversity of the stochastic system by generating a persistent population flux of species. Thus, the coexistence of species is a non-equilibrium steady state, rather than a static fixed point of a simple dynamical system such as generalized Lotka-Volterra equations.