20 research outputs found
Subtropical Real Root Finding
We describe a new incomplete but terminating method for real root finding for
large multivariate polynomials. We take an abstract view of the polynomial as
the set of exponent vectors associated with sign information on the
coefficients. Then we employ linear programming to heuristically find roots.
There is a specialized variant for roots with exclusively positive coordinates,
which is of considerable interest for applications in chemistry and systems
biology. An implementation of our method combining the computer algebra system
Reduce with the linear programming solver Gurobi has been successfully applied
to input data originating from established mathematical models used in these
areas. We have solved several hundred problems with up to more than 800000
monomials in up to 10 variables with degrees up to 12. Our method has failed
due to its incompleteness in less than 8 percent of the cases
Spontaneous Reaction Silencing in Metabolic Optimization
Metabolic reactions of single-cell organisms are routinely observed to become
dispensable or even incapable of carrying activity under certain circumstances.
Yet, the mechanisms as well as the range of conditions and phenotypes
associated with this behavior remain very poorly understood. Here we predict
computationally and analytically that any organism evolving to maximize growth
rate, ATP production, or any other linear function of metabolic fluxes tends to
significantly reduce the number of active metabolic reactions compared to
typical non-optimal states. The reduced number appears to be constant across
the microbial species studied and just slightly larger than the minimum number
required for the organism to grow at all. We show that this massive spontaneous
reaction silencing is triggered by the irreversibility of a large fraction of
the metabolic reactions and propagates through the network as a cascade of
inactivity. Our results help explain existing experimental data on
intracellular flux measurements and the usage of latent pathways, shedding new
light on microbial evolution, robustness, and versatility for the execution of
specific biochemical tasks. In particular, the identification of optimal
reaction activity provides rigorous ground for an intriguing knockout-based
method recently proposed for the synthetic recovery of metabolic function.Comment: 34 pages, 6 figure