Fabrizio Capuani

Modeling Networks of Coupled Enzymatic Reactions Using the Total Quasi-Steady State Approximation

In metabolic networks, metabolites are usually present in great excess over the enzymes that catalyze their interconversion, and describing the rates of these reactions by using the Michaelis–Menten rate law is perfectly valid. This rate law assumes that the concentration of enzyme–substrate complex (C) is much less than the free substrate concentration (S 0). However, in protein interaction networks, the enzymes and substrates are all proteins in comparable concentrations, and neglecting C with respect to S 0 is not valid. Borghans, DeBoer, and Segel developed an alternative description of enzyme kinetics that is valid when C is comparable to S 0. We extend this description, which Borghans et al. call the total quasi-steady state approximation, to networks of coupled enzymatic reactions. First, we analyze an isolated Goldbeter–Koshland switch when enzymes and substrates are present in comparable concentrations. Then, on the basis of a real example of the molecular network governing cell cycle progression, we couple two and three Goldbeter–Koshland switches together to study the effects of feedback in networks of protein kinases and phosphatases. Our analysis shows that the total quasi-steady state approximation provides an excellent kinetic formalism for protein interaction networks, because (1) it unveils the modular structure of the enzymatic reactions, (2) it suggests a simple algorithm to formulate correct kinetic equations, and (3) contrary to classical Michaelis–Menten kinetics, it succeeds in faithfully reproducing the dynamics of the network both qualitatively and quantitatively.

Threshold‐controlled ubiquitination of the EGFR directs receptor fate

How the cell converts graded signals into threshold‐activated responses is a question of great biological relevance. Here, we uncover a nonlinear modality of epidermal growth factor receptor (EGFR)‐activated signal transduction, by demonstrating that the ubiquitination of the EGFR at the PM is threshold controlled. The ubiquitination threshold is mechanistically determined by the cooperative recruitment of the E3 ligase Cbl, in complex with Grb2, to the EGFR. This, in turn, is dependent on the simultaneous presence of two phosphotyrosines, pY1045 and either one of pY1068 or pY1086, on the same EGFR moiety. The dose–response curve of EGFR ubiquitination correlate precisely with the non‐clathrin endocytosis (NCE) mode of EGFR internalization. Finally, EGFR‐NCE mechanistically depends on EGFR ubiquitination, as the two events can be simultaneously re‐engineered on a phosphorylation/ubiquitination‐incompetent EGFR backbone. Since NCE controls the degradation of the EGFR, our findings have implications for how the cell responds to increasing levels of EGFR signalling, by varying the balance of receptor signalling and degradation/attenuation.

Discrete solution of the electrokinetic equations

We present a robust scheme for solving the electrokinetic equations. This goal is achieved by combining the lattice-Boltzmann method with a discrete solution of the convection-diffusion equation for the different charged and neutral species that compose the fluid. The method is based on identifying the elementary fluxes between nodes, which ensures the absence of spurious fluxes in equilibrium. We show how the model is suitable to study electro-osmotic flows. As an illustration, we show that, by introducing appropriate dynamic rules in the presence of solid interfaces, we can compute the sedimentation velocity (and hence the sedimentation potential) of a charged sphere. Our approach does not assume linearization of the Poisson-Boltzmann equation and allows us for a wide variation of the Peclet number.

Low duplicability and network fragility of cancer genes

We identified genomic and network properties of approximately 600 genes mutated in different cancer types. These genes tend not to duplicate but, unlike most human singletons, they encode central hubs of highly interconnected modules within the protein-protein interaction network (PIN). We find that cancer genes are fragile components of the human gene repertoire, sensitive to dosage modification. Furthermore, other nodes of the human PIN with similar properties are rare and probably enriched in candidate cancer genes.

Counting and correcting thermodynamically infeasible flux cycles in genome-scale metabolic networks.

Thermodynamics constrains the flow of matter in a reaction network to occur through routes along which the Gibbs energy decreases, implying that viable steady-state flux patterns should be void of closed reaction cycles. Identifying and removing cycles in large reaction networks can unfortunately be a highly challenging task from a computational viewpoint. We propose here a method that accomplishes it by combining a relaxation algorithm and a Monte Carlo procedure to detect loops, with ad hoc rules (discussed in detail) to eliminate them. As test cases, we tackle (a) the problem of identifying infeasible cycles in the E. coli metabolic network and (b) the problem of correcting thermodynamic infeasibilities in the Flux-Balance-Analysis solutions for 15 human cell-type-specific metabolic networks. Results for (a) are compared with previous analyses of the same issue, while results for (b) are weighed against alternative methods to retrieve thermodynamically viable flux patterns based on minimizing specific global quantities. Our method, on the one hand, outperforms previous techniques and, on the other, corrects loopy solutions to Flux Balance Analysis. As a byproduct, it also turns out to be able to reveal possible inconsistencies in model reconstructions.

Quantitative analysis reveals how EGFR activation and downregulation are coupled in normal but not in cancer cells

Ubiquitination of the epidermal growth factor receptor (EGFR) that occurs when Cbl and Grb2 bind to three phosphotyrosine residues (pY1045, pY1068 and pY1086) on the receptor displays a sharp threshold effect as a function of EGF concentration. Here we use a simple modelling approach together with experiments to show that the establishment of the threshold requires both the multiplicity of binding sites and cooperative binding of Cbl and Grb2 to the EGFR. While the threshold is remarkably robust, a more sophisticated model predicted that it could be modulated as a function of EGFR levels on the cell surface. We confirmed experimentally that the system has evolved to perform optimally at physiological levels of EGFR. As a consequence, this system displays an intrinsic weakness that causes—at the supraphysiological levels of receptor and/or ligand associated with cancer—uncoupling of the mechanisms leading to signalling through phosphorylation and attenuation through ubiquitination.

Lattice-Boltzmann simulation of the sedimentation of charged disks

We report a series of lattice-Boltzmann simulations of the sedimentation velocity of charged disks. In these simulations, we explicitly account for the hydrodynamic and electrostatic forces on disks and on their electrical double layer. By comparing our results with those for spheres with equal surface and charge, we can clarify the effect of the particle shape on the sedimentation process. We find that disks and spheres exhibit a different dependence of the sedimentation velocity on the Debye screening length. An analysis of the behavior of highly charged disks (beyond the scope of the linearized Poisson-Boltzmann equation) shows that, in that regime, the charge dependence of the sedimentation velocity of disks and spheres is similar. This suggests that, at high charge, the effective hydrodynamic shape of the disks becomes more spherical.

Mesoscopic lattice modeling of electrokinetic phenomena

The development of models for electrolytes is challenging due to the long-range nature of electric interactions. We propose a novel implementation of a lattice Boltzmann model that solves a number of limitations and inconsistencies in previously proposed variants and discuss the range of parameters the model can cover. We show how the relevant electrohydrodynamic couplings are recovered analyzing a particular electrokinetic phenomena.

Growth against entropy in bacterial metabolism: the phenotypic trade-off behind empirical growth rate distributions in E. coli.

The solution space of genome-scale models of cellular metabolism provides a map between physically viable flux configurations and cellular metabolic phenotypes described, at the most basic level, by the corresponding growth rates. By sampling the solution space of E. colis metabolic network, we show that empirical growth rate distributions recently obtained in experiments at single-cell resolution can be explained in terms of a trade-off between the higher fitness of fast-growing phenotypes and the higher entropy of slow-growing ones. Based on this, we propose a minimal model for the evolution of a large bacterial population that captures this trade-off. The scaling relationships observed in experiments encode, in such frameworks, for the same distance from the maximum achievable growth rate, the same degree of growth rate maximization, and/or the same rate of phenotypic change. Being grounded on genome-scale metabolic network reconstructions, these results allow for multiple implications and extensions in spite of the underlying conceptual simplicity.

Lattice-Boltzmann Simulations of Ionic Current Modulation by DNA Translocation

We present a numerical study of the effect of DNA translocation on the ionic current through a nanopore. We use a coarse-grained model to solve the electrokinetic equations at the Poisson-Boltzmann level for the microions, coupled to a lattice-Boltzmann equation for the solvent hydrodynamics. In most cases, translocation leads to a reduction in the ionic current. However, at low salt concentrations (large screening lengths) we find ionic current enhancement due to translocation. In an unstructured pore, translocation of the helical charge distribution of the DNA has no effect on the ionic current. However, if a localized charge probe is placed on the wall of the nanopore, we observe ionic current modulations that, though weak, should be experimentally observable.