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Jorge Fernandez-de-Cossio-Diaz

Publications and source records attributed to Jorge Fernandez-de-Cossio-Diaz.

10 recordsLinked to original sources
arXiv2025

A High-Order Cumulant Extension of Quasi-Linkage Equilibrium

A central question in evolutionary biology is how to quantitatively understand the dynamics of genetically diverse populations. Modeling the genotype distribution is challenging, as it ultimately requires tracking all correlations (or cumulants) among alleles at different loci. The quasi-linkage equilibrium (QLE) approximation simplifies this by assuming that correlations between alleles at different loci are weak -- i.e., low linkage disequilibrium -- allowing their dynamics to be modeled perturbatively. However, QLE breaks down under strong selection, significant epistatic interactions, or weak recombination. We extend the multilocus QLE framework to allow cumulants up to order $K$ to evolve dynamically, while higher-order cumulants ($>K$) are assumed to equilibrate rapidly. This extended QLE (exQLE) framework yields a general equation of motion for cumulants up to order $K$, which parallels the standard QLE dynamics (recovered when $K = 1$). In this formulation, cumulant dynamics are driven by the gradient of average fitness, mediated by a geometrically interpretable matrix that stems from competition among genotypes. Our analysis shows that the exQLE with $K=2$ accurately captures cumulant dynamics even when the fitness function includes higher-order (e.g., third- or fourth-order) epistatic interactions, capabilities that standard QLE lacks. We also applied the exQLE framework to infer fitness parameters from temporal sequence data. Overall, exQLE provides a systematic and interpretable approximation scheme, leveraging analytical cumulant dynamics and reducing complexity by progressively truncating higher-order cumulants.

q-bio.PE↗
arXiv2023

Disentangling representations in Restricted Boltzmann Machines without adversaries

A goal of unsupervised machine learning is to build representations of complex high-dimensional data, with simple relations to their properties. Such disentangled representations make easier to interpret the significant latent factors of variation in the data, as well as to generate new data with desirable features. Methods for disentangling representations often rely on an adversarial scheme, in which representations are tuned to avoid discriminators from being able to reconstruct information about the data properties (labels). Unfortunately adversarial training is generally difficult to implement in practice. Here we propose a simple, effective way of disentangling representations without any need to train adversarial discriminators, and apply our approach to Restricted Boltzmann Machines (RBM), one of the simplest representation-based generative models. Our approach relies on the introduction of adequate constraints on the weights during training, which allows us to concentrate information about labels on a small subset of latent variables. The effectiveness of the approach is illustrated with four examples: the CelebA dataset of facial images, the two-dimensional Ising model, the MNIST dataset of handwritten digits, and the taxonomy of protein families. In addition, we show how our framework allows for analytically computing the cost, in terms of log-likelihood of the data, associated to the disentanglement of their representations.

cs.LG↗
arXiv2019

Spin Glass Theory of Interacting Metabolic Networks

We cast the metabolism of interacting cells within a statistical mechanics framework considering both, the actual phenotypic capacities of each cell and its interaction with its neighbors. Reaction fluxes will be the components of high-dimensional spin vectors, whose values will be constrained by the stochiometry and the energy requirements of the metabolism. Within this picture, finding the phenotypic states of the population turns out to be equivalent to searching for the equilibrium states of a disordered spin model. We provide a general solution of this problem for arbitrary metabolic networks and interactions. We apply this solution to a simplified model of metabolism and to a complex metabolic network, the central core of the \emph{E. coli}, and demonstrate that the combination of selective pressure and interactions define a complex phenotypic space. Cells may specialize in producing or consuming metabolites complementing each other at the population level and this is described by an equilibrium phase space with multiple minima, like in a spin-glass model.

q-bio.MN↗
arXiv2019

Cell population heterogeneity driven by stochastic partition and growth optimality

A fundamental question in biology is how cell populations evolve into different subtypes based on homogeneous processes at the single cell level. Here we show that population bimodality can emerge even when biological processes are homogenous at the cell level and the environment is kept constant. Our model is based on the stochastic partitioning of a cell component with an optimal copy number. We show that the existence of unimodal or bimodal distributions depends on the variance of partition errors and the growth rate tolerance around the optimal copy number. In particular, our theory provides a consistent explanation for the maintenance of aneuploid states in a population. The proposed model can also be relevant for other cell components such as mitochondria and plasmids, whose abundances affect the growth rate and are subject to stochastic partition at cell division.

q-bio.MN↗
arXiv2018

Maximum entropy and population heterogeneity in continuous cell cultures

Continuous cultures of mammalian cells are complex systems displaying hallmark phenomena of nonlinear dynamics, such as multi-stability, hysteresis, as well as sharp transitions between different metabolic states. In this context mathematical models may suggest control strategies to steer the system towards desired states. Although even clonal populations are known to exhibit cell-to-cell variability, most of the currently studied models assume that the population is homogeneous. To overcome this limitation, we use the maximum entropy principle to model the phenotypic distribution of cells in a chemostat as a function of the dilution rate. We consider the coupling between cell metabolism and extracellular variables describing the state of the bioreactor and take into account the impact of toxic byproduct accumulation on cell viability. We present a formal solution for the stationary state of the chemostat and show how to apply it in two examples. First, a simplified model of cell metabolism where the exact solution is tractable, and then a genome-scale metabolic network of the Chinese hamster ovary (CHO) cell line. Along the way we discuss several consequences of heterogeneity, such as: qualitative changes in the dynamical landscape of the system, increasing concentrations of byproducts that vanish in the homogeneous case, and larger population sizes.

q-bio.MN↗
arXiv2018

Genetic interactions from first principles

We derive a general statistical model of interactions, starting from probabilistic principles and elementary requirements. Prevailing interaction models in biomedical researches diverge both mathematically and practically. In particular, genetic interaction inquiries are formulated without an obvious mathematical unity. Our model reveals theoretical properties unnoticed so far, particularly valuable for genetic interaction mapping, where mechanistic details are mostly unknown, distribution of gene variants differ between populations, and genetic susceptibilities are spuriously propagated by linkage disequilibrium. When applied to data of the largest interaction mapping experiment on Saccharomyces Cerevisiae to date, our results imply less aversion to positive interactions, detection of well-documented hubs and partial remapping of functional regions of the currently known genetic interaction landscape. Assessment of divergent annotations across functional categories further suggests that positive interactions have a more important role on ribosome biogenesis than previously realized. The unity of arguments elaborated here enables the analysis of dissimilar interaction models and experimental data with a common framework.

stat.ME↗
arXiv2017

Microenvironmental cooperation promotes early spread and bistability of a Warburg-like phenotype

We introduce an in silico model for the initial spread of an aberrant phenotype with Warburg-like overflow metabolism within a healthy homeostatic tissue in contact with a nutrient reservoir (the blood), aimed at characterizing the role of the microenvironment for aberrant growth. Accounting for cellular metabolic activity, competition for nutrients, spatial diffusion and their feedbacks on aberrant replication and death rates, we obtain a phase portrait where distinct asymptotic whole-tissue states are found upon varying the tissue-blood turnover rate and the level of blood-borne primary nutrient. Over a broad range of parameters, the spreading dynamics is bistable as random fluctuations can impact the final state of the tissue. Such a behaviour turns out to be linked to the re-cycling of overflow products by non-aberrant cells. Quantitative insight on the overall emerging picture is provided by a spatially homogeneous version of the model.

q-bio.MN↗
arXiv2017

Characterizing steady states of genome-scale metabolic networks in continuous cell cultures

We present a model for continuous cell culture coupling intra-cellular metabolism to extracellular variables describing the state of the bioreactor, taking into account the growth capacity of the cell and the impact of toxic byproduct accumulation. We provide a method to determine the steady states of this system that is tractable for metabolic networks of arbitrary complexity. We demonstrate our approach in a toy model first, and then in a genome-scale metabolic network of the Chinese hamster ovary cell line, obtaining results that are in qualitative agreement with experimental observations. More importantly, we derive a number of consequences from the model that are independent of parameter values. First, that the ratio between cell density and dilution rate is an ideal control parameter to fix a steady state with desired metabolic properties invariant across perfusion systems. This conclusion is robust even in the presence of multi-stability, which is explained in our model by the negative feedback loop on cell growth due to toxic byproduct accumulation. Moreover, a complex landscape of steady states in continuous cell culture emerges from our simulations, including multiple metabolic switches, which also explain why cell-line and media benchmarks carried out in batch culture cannot be extrapolated to perfusion. On the other hand, we predict invariance laws between continuous cell cultures with different parameters. A practical consequence is that the chemostat is an ideal experimental model for large-scale high-density perfusion cultures, where the complex landscape of metabolic transitions is faithfully reproduced. Thus, in order to actually reflect the expected behavior in perfusion, performance benchmarks of cell-lines and culture media should be carried out in a chemostat.

q-bio.MN↗
arXiv2016

Fast inference of ill-posed problems within a convex space

In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find the probability distribution of parameter values consistent with the data, a problem that can be cast as the exploration of a high dimensional convex polytope. In this work we introduce a novel algorithm to solve this problem efficiently. It provides results that are statistically indistinguishable from currently used numerical techniques while its running time scales linearly with the system size. We show that the algorithm performs robustly in many abstract and practical applications. As working examples we simulate the effects of restricting reaction fluxes on the space of feasible phenotypes of a {\em genome} scale E. Coli metabolic network and infer the traffic flow between origin and destination nodes in a real communication network.

cs.OH↗