On the linear algebra of biological homochirality.

We look for structural properties of chemical networks giving place to homochiral phenomena. We found a necessary condition for homochirality that we call Frank inequality, and which is a linear inequality related to the entries of the jacobian matrices that occur at racemic steady states. We also investigate the existence of stronger conditions that can be formulated in a similar algebraic way. Those investigations lead us to introduce a homochirality degree for the racemic states of chiral neworks, which is intended to measure the probability of observing homochiral dynamics after perturbing those states. It is important to stress that all the introduced concepts and degrees are effective. The later fact allows us to develop an algorithm that can be used to, given a chiral network as input, compute large samples of steady states of different degrees. [ABSTRACT FROM AUTHOR]