The Regularizing Capacity of Metabolic Networks

Despite their topological complexity almost all functional properties of metabolic networks can be derived from steady-state dynamics. Indeed, many theoretical investigations (like flux-balance analysis) rely on extracting function from steady states. This leads to the interesting question, how metabolic networks avoid complex dynamics and maintain a steady-state behavior. Here, we expose metabolic network topologies to binary dynamics generated by simple local rules. We find that the networks' response is highly specific: Complex dynamics are systematically reduced on metabolic networks compared to randomized networks with identical degree sequences. Already small topological modifications substantially enhance the capacity of a network to host complex dynamic behavior and thus reduce its regularizing potential. This exceptionally pronounced regularization of dynamics encoded in the topology may explain, why steady-state behavior is ubiquitous in metabolism.Comment: 6 pages, 4 figure

Fkh1 and Fkh2 associate with Sir2 to control CLB2 transcription under normal and oxidative stress conditions

The Forkhead (Fkh) box family of transcription factors is evolutionary conserved from yeast to higher eukaryotes and its members are involved in many physiological processes including metabolism, DNA repair, cell cycle, stress resistance, apoptosis, and aging. In budding yeast, four Fkh transcription factors were identified, namely Fkh1, Fkh2, Fhl1, and Hcm1, which are implicated in chromatin silencing, cell cycle regulation, and stress response. These factors impinge transcriptional regulation during cell cycle progression, and histone deacetylases (HDACs) play an essential role in this process, e.g., the nuclear localization of Hcm1 depends on Sir2 activity, whereas Sin3/Rpd3 silence cell cycle specific gene transcription in G2/M phase. However, a direct involvement of Sir2 in Fkh1/Fkh2-dependent regulation of target genes is at present unknown. Here, we show that Fkh1 and Fkh2 associate with Sir2 in G1 and M phase, and that Fkh1/Fkh2-mediated activation of reporter genes is antagonized by Sir2. We further report that Sir2 overexpression strongly affects cell growth in an Fkh1/Fkh2-dependent manner. In addition, Sir2 regulates the expression of the mitotic cyclin Clb2 through Fkh1/Fkh2-mediated binding to the CLB2 promoter in G1 and M phase. We finally demonstrate that Sir2 is also enriched at the CLB2 promoter under stress conditions, and that the nuclear localization of Sir2 is dependent on Fkh1 and Fkh2. Taken together, our results show a functional interplay between Fkh1/Fkh2 and Sir2 suggesting a novel mechanism of cell cycle repression. Thus, in budding yeast, not only the regulation of G2/M gene expression but also the protective response against stress could be directly coordinated by Fkh1 and Fkh2. © 2013 Linke, Klipp, Lehrach, Barberis and Krobitsch

Rigorous elimination of fast stochastic variables from the linear noise approximation using projection operators

The linear noise approximation (LNA) offers a simple means by which one can study intrinsic noise in monostable biochemical networks. Using simple physical arguments, we have recently introduced the slow-scale LNA (ssLNA) which is a reduced version of the LNA under conditions of timescale separation. In this paper, we present the first rigorous derivation of the ssLNA using the projection operator technique and show that the ssLNA follows uniquely from the standard LNA under the same conditions of timescale separation as those required for the deterministic quasi-steady state approximation. We also show that the large molecule number limit of several common stochastic model reduction techniques under timescale separation conditions constitutes a special case of the ssLNA.Comment: 10 pages, 1 figure, submitted to Physical Review E; see also BMC Systems Biology 6, 39 (2012

Coupling biochemistry and mechanics in cell adhesion: a model for inhomogeneous stress fiber contraction

Biochemistry and mechanics are closely coupled in cell adhesion. At sites of cell-matrix adhesion, mechanical force triggers signaling through the Rho-pathway, which leads to structural reinforcement and increased contractility in the actin cytoskeleton. The resulting force acts back to the sites of adhesion, resulting in a positive feedback loop for mature adhesion. Here we model this biochemical-mechanical feedback loop for the special case when the actin cytoskeleton is organized in stress fibers, which are contractile bundles of actin filaments. Activation of myosin II molecular motors through the Rho-pathway is described by a system of reaction-diffusion equations, which are coupled into a viscoelastic model for a contractile actin bundle. We find strong spatial gradients in the activation of contractility and in the corresponding deformation pattern of the stress fiber, in good agreement with experimental findings.Comment: Revtex, 35 pages, 13 Postscript figures included, in press with New Journal of Physics, Special Issue on The Physics of the Cytoskeleto

Sic1 plays a role in timing and oscillatory behaviour of B-type cyclins

Budding yeast cell cycle oscillates between states of low and high cyclin-dependent kinase activity, driven by association of Cdk1 with B-type (Clb) cyclins. Various Cdk1-Clb complexes are activated and inactivated in a fixed, temporally regulated sequence, inducing the behaviour known as "waves of cyclins". The transition from low to high Clb activity is triggered by degradation of Sic1, the inhibitor of Cdk1-Clb complexes, at the entry to S phase. The G(1) phase is characterized by low Clb activity and high Sic1 levels. High Clb activity and Sic1 proteolysis are found from the beginning of the S phase until the end of mitosis. The mechanism regulating the appearance on schedule of Cdk1-Clb complexes is currently unknown. Here, we analyse oscillations of Clbs, focusing on the role of their inhibitor Sic1. We compare mathematical networks differing in interactions that Sic1 may establish with Cdk1-Clb complexes. Our analysis suggests that the wave-like cyclins pattern derives from the binding of Sic1 to all Clb pairs rather than from Clb degradation. These predictions are experimentally validated, showing that Sic1 indeed interacts and coexists in time with Clbs. Intriguingly, a sic1Delta strain looses cell cycle-regulated periodicity of Clbs, which is observed in the wild type, whether a SIC1-0P strain delays the formation of Clb waves. Our results highlight an additional role for Sic1 in regulating Cdk1-Clb complexes, coordinating their appearance

Alterations of mTOR signaling impact metabolic stress resistance in colorectal carcinomas with BRAF and KRAS mutations

Metabolic reprogramming is as a hallmark of cancer, and several studies have reported that BRAF and KRAS tumors may be accompanied by a deregulation of cellular metabolism. We investigated how BRAF(V600E) and KRAS(G12V) affect cell metabolism, stress resistance and signaling in colorectal carcinoma cells driven by these mutations. KRAS(G12V) expressing cells are characterized by the induction of glycolysis, accumulation of lactic acid and sensitivity to glycolytic inhibition. Notably mathematical modelling confirmed the critical role of MCT1 designating the survival of KRAS(G12V) cells. Carcinoma cells harboring BRAF(V600E) remain resistant towards alterations of glucose supply or application of signaling or metabolic inhibitors. Altogether these data demonstrate that an oncogene-specific decoupling of mTOR from AMPK or AKT signaling accounts for alterations of resistance mechanisms and metabolic phenotypes. Indeed the inhibition of mTOR in BRAF(V600E) cells counteracts the metabolic predisposition and demonstrates mTOR as a potential target in BRAF(V600E)-driven colorectal carcinomas

Bringing metabolic networks to life: convenience rate law and thermodynamic constraints

BACKGROUND: Translating a known metabolic network into a dynamic model requires rate laws for all chemical reactions. The mathematical expressions depend on the underlying enzymatic mechanism; they can become quite involved and may contain a large number of parameters. Rate laws and enzyme parameters are still unknown for most enzymes. RESULTS: We introduce a simple and general rate law called "convenience kinetics". It can be derived from a simple random-order enzyme mechanism. Thermodynamic laws can impose dependencies on the kinetic parameters. Hence, to facilitate model fitting and parameter optimisation for large networks, we introduce thermodynamically independent system parameters: their values can be varied independently, without violating thermodynamical constraints. We achieve this by expressing the equilibrium constants either by Gibbs free energies of formation or by a set of independent equilibrium constants. The remaining system parameters are mean turnover rates, generalised Michaelis-Menten constants, and constants for inhibition and activation. All parameters correspond to molecular energies, for instance, binding energies between reactants and enzyme. CONCLUSION: Convenience kinetics can be used to translate a biochemical network – manually or automatically - into a dynamical model with plausible biological properties. It implements enzyme saturation and regulation by activators and inhibitors, covers all possible reaction stoichiometries, and can be specified by a small number of parameters. Its mathematical form makes it especially suitable for parameter estimation and optimisation. Parameter estimates can be easily computed from a least-squares fit to Michaelis-Menten values, turnover rates, equilibrium constants, and other quantities that are routinely measured in enzyme assays and stored in kinetic databases

Ion Transport across Biological Membranes by Carborane-Capped Gold Nanoparticles

Carborane-capped gold nanoparticles (Au/carborane NPs, 2-3 nm) can act as artificial ion transporters across biological membranes. The particles themselves are large hydrophobic anions that have the ability to disperse in aqueous media and to partition over both sides of a phospholipid bilayer membrane. Their presence therefore causes a membrane potential that is determined by the relative concentrations of particles on each side of the membrane according to the Nernst equation. The particles tend to adsorb to both sides of the membrane and can flip across if changes in membrane potential require their repartitioning. Such changes can be made either with a potentiostat in an electrochemical cell or by competition with another partitioning ion, for example, potassium in the presence of its specific transporter valinomycin. Carborane-capped gold nanoparticles have a ligand shell full of voids, which stem from the packing of near spherical ligands on a near spherical metal core. These voids are normally filled with sodium or potassium ions, and the charge is overcompensated by excess electrons in the metal core. The anionic particles are therefore able to take up and release a certain payload of cations and to adjust their net charge accordingly. It is demonstrated by potential-dependent fluorescence spectroscopy that polarized phospholipid membranes of vesicles can be depolarized by ion transport mediated by the particles. It is also shown that the particles act as alkali-ion-specific transporters across free-standing membranes under potentiostatic control. Magnesium ions are not transported