2 research outputs found
A novel methodology to estimate metabolic flux distributions in constraint-based models
Quite generally, constraint-based metabolic flux analysis describes the space of viable flux configurations for a metabolic network as a high-dimensional polytope defined by the linear constraints that enforce the balancing of production and consumption fluxes for each chemical species in the system. In some cases, the complexity of the solution space can be reduced by performing an additional optimization, while in other cases, knowing the range of variability of fluxes over the polytope provides a sufficient characterization of the allowed configurations. There are cases, however, in which the thorough information encoded in the individual distributions of viable fluxes over the polytope is required. Obtaining such distributions is known to be a highly challenging computational task when the dimensionality of the polytope is sufficiently large, and the problem of developing cost-effective ad hoc algorithms has recently seen a major surge of interest. Here, we propose a method that allows us to perform the required computation heuristically in a time scaling linearly with the number of reactions in the network, overcoming some limitations of similar techniques employed in recent years. As a case study, we apply it to the analysis of the human red blood cell metabolic network, whose solution space can be sampled by different exact techniques, like Hit-and-Run Monte Carlo (scaling roughly like the third power of the system size). Remarkably accurate estimates for the true distributions of viable reaction fluxes are obtained, suggesting that, although further improvements are desirable, our method enhances our ability to analyze the space of allowed configurations for large biochemical reaction networks. © 2013 by the authors; licensee MDPI, Basel, Switzerland
Replica theory for learning curves for Gaussian processes on random graphs
Statistical physics approaches can be used to derive accurate predictions for
the performance of inference methods learning from potentially noisy data, as
quantified by the learning curve defined as the average error versus number of
training examples. We analyse a challenging problem in the area of
non-parametric inference where an effectively infinite number of parameters has
to be learned, specifically Gaussian process regression. When the inputs are
vertices on a random graph and the outputs noisy function values, we show that
replica techniques can be used to obtain exact performance predictions in the
limit of large graphs. The covariance of the Gaussian process prior is defined
by a random walk kernel, the discrete analogue of squared exponential kernels
on continuous spaces. Conventionally this kernel is normalised only globally,
so that the prior variance can differ between vertices; as a more principled
alternative we consider local normalisation, where the prior variance is
uniform