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Register a new userClustering and optimal arrangement of enzymes in reaction-diffusion systems
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Enzymes within biochemical pathways are often colocalized, yet the consequences of specific spatial enzyme arrangements remain poorly understood. We study the impact of enzyme arrangement on reaction efficiency within a reaction-diffusion model. The optimal arrangement transitions from a cluster to a distributed profile as a single parameter, which controls the probability of reaction versus diffusive loss of pathway intermediates, is varied. We introduce the concept of enzyme exposure to explain how this transition arises from the stochastic nature of molecular reactions and diffusion.
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Transforming Growth Factor-beta (TGF-beta) signalling is an important regulator of cellular growth and differentiation. The principal intracellular mediators of TGF-beta signalling are the Smad proteins, which upon TGF-beta stimulation accumulate in the nucleus and regulate transcription of target genes. To investigate the mechanisms of Smad nuclear accumulation, we developed a simple mathematical model of canonical Smad signalling. The model was built using both published data and our experimentally determined cellular Smad concentrations (isoforms 2, 3, and 4). We found in mink lung epithelial cells that Smad2 (8.5-12 x 10^4 molecules/cell) was present in similar amounts to Smad4 (9.3-12 x 10^4 molecules/cell), while both were in excess of Smad3 (1.1-2.0 x 10^4 molecules/cell). Variation of the model parameters and statistical analysis showed that Smad nuclear accumulation is most sensitive to parameters affecting the rates of RSmad phosphorylation and dephosphorylation and Smad complex formation/dissociation in the nucleus. Deleting Smad4 from the model revealed that rate-limiting phospho-R-Smad dephosphorylation could be an important mechanism for Smad nuclear accumulation. Furthermore, we observed that binding factors constitutively localised to the nucleus do not efficiently mediate Smad nuclear accumulation if dephosphorylation is rapid. We therefore conclude that an imbalance in the rates of R-Smad phosphorylation and dephosphorylation is likely an important mechanism of Smad nuclear accumulation during TGF-beta signalling.
Signaling pathways serve to communicate information about extracellular conditions into the cell, to both the nucleus and cytoplasmic processes to control cell responses. Genetic mutations in signaling network components are frequently associated with cancer and can result in cells acquiring an ability to divide and grow uncontrollably. Because signaling pathways play such a significant role in cancer initiation and advancement, their constituent proteins are attractive therapeutic targets. In this review, we discuss how signaling pathway modeling can assist with identifying effective drugs for treating diseases, such as cancer. An achievement that would facilitate the use of such models is their ability to identify controlling biochemical parameters in signaling pathways, such as molecular abundances and chemical reaction rates, because this would help determine effective points of attack by therapeutics.
The primary activation of the epidermal growth factor receptor (EGFR) has become a prominent target for molecular therapies against several forms of cancer. But despite considerable progress during the last years, many of its aspects remain poorly understood. Experiments on lateral spreading of receptor activity into ligand-free regions challenge the current standard models of EGFR activation. Here, we propose and study a theoretical model, which explains spreading into ligand-free regions without introducing any new, unknown kinetic parameters. The model exhibits bistability of activity, induced by a generic reaction mechanism, which consists of activation via dimerization and deactivation via a Michaelis-Menten reaction. It possesses slow propagating front solutions and faster initial transients. We analyze relevant experiments and find that they are in quantitative accordance with the fast initial modes of spreading, but not with the slow propagating front. We point out that lateral spreading of activity is linked to pathological levels of persistent receptor activity as observed in cancer cells and exemplify uses of this link for the design and quick evaluation of molecular therapies targeting primary activation of EGFR.
The living cell is an open nonequilibrium biochemical system, where ATP hydrolysis serves as the energy source for a wide range of intracellular processes including the assurance for decision-making. In the fission yeast cell cycle, the transition from G2 phase to M phase is triggered by the activation of Cdc13/Cdc2 and Cdc25, and the deactivation of Wee1. Each of these three events involves a phosphorylation-dephosphorylation (PdP) cycle, and together they form a regulatory circuit with feedback loops. Almost all quantitative models for cellular networks in the past have invalid thermodynamics due to the assumption of irreversible enzyme kinetics. We constructed a thermodynamically realistic kinetic model of the G2/M circuit, and show that the phosphorylation energy ($Delta G$), which is determined by the cellular ATP/ADP ratio, critically controls the dynamics and the bistable nature of Cdc2 activation. Using fission yeast nucleoplasmic extract (YNPE), we are able to experimentally verify our model prediction that increased , being synergistic to the accumulation of Cdc13, drives the activation of Cdc2. Furthermore, Cdc2 activation exhibits bistability and hysteresis in response to changes in phosphorylation energy. These findings suggest that adequate maintenance of phosphorylation energy ensures the bistability and robustness of the activation of Cdc2 in the G2/M transition. Free energy might play a widespread role in biological decision-making processes, connecting thermodynamics with information processing in biology.
The evolution of the genome has led to very sophisticated and complex regulation. Because of the abundance of non-coding RNA (ncRNA) in the cell, different species will promiscuously associate with each other, suggesting collective dynamics similar to artificial neural networks. Here we present a simple mechanism allowing ncRNA to perform computations equivalent to neural network algorithms such as Boltzmann machines and the Hopfield model. The quantities analogous to the neural couplings are the equilibrium constants between different RNA species. The relatively rapid equilibration of RNA binding and unbinding is regulated by a slower process that degrades and creates new RNA. The model requires that the creation rate for each species be an increasing function of the ratio of total to unbound RNA. Similar mechanisms have already been found to exist experimentally for ncRNA regulation. With the overall concentration of RNA regulated, equilibrium constants can be chosen to store many different patterns, or many different input-output relations. The network is also quite insensitive to random mutations in equilibrium constants. Therefore one expects that this kind of mechanism will have a much higher mutation rate than ones typically regarded as being under evolutionary constraint.
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