Metabolic Futile Cycles and Their Functions: A Systems Analysis of Energy and Control

It has long been hypothesized that futile cycles in cellular metabolism are involved in the regulation of biochemical pathways. Following the work of Newsholme and Crabtree, we develop a quantitative theory for this idea based on open-system thermodynamics and metabolic control analysis. It is shown that the {\it stoichiometric sensitivity} of an intermediary metabolite concentration with respect to changes in steady-state flux is governed by the effective equilibrium constant of the intermediate formation, and the equilibrium can be regulated by a futile cycle. The direction of the shift in the effective equilibrium constant depends on the direction of operation of the futile cycle. High stoichiometric sensitivity corresponds to ultrasensitivity of an intermediate concentration to net flow through a pathway; low stoichiometric sensitivity corresponds to super-robustness of concentration with respect to changes in flux. Both cases potentially play important roles in metabolic regulation. Futile cycles actively shift the effective equilibrium by expending energy; the magnitude of changes in effective equilibria and sensitivities is a function of the amount of energy used by a futile cycle. This proposed mechanism for control by futile cycles works remarkably similarly to kinetic proofreading in biosynthesis. The sensitivity of the system is also intimately related to the rate of concentration fluctuations of intermediate metabolites. The possibly different roles of the two major mechanisms for cellular biochemical regulation, namely reversible chemical modifications via futile cycles and shifting equilibrium by macromolecular binding, are discussed.Comment: 11 pages, 5 figure

Dynamical robustness of biological networks with hierarchical distribution of time scales

We propose the concepts of distributed robustness and r-robustness, well adapted to functional genetics. Then we discuss the robustness of the relaxation time using a chemical reaction description of genetic and signalling networks. First, we obtain the following result for linear networks: for large multiscale systems with hierarchical distribution of time scales the variance of the inverse relaxation time (as well as the variance of the stationary rate) is much lower than the variance of the separate constants. Moreover, it can tend to 0 faster than 1/n, where n is the number of reactions. We argue that similar phenomena are valid in the nonlinear case as well. As a numerical illustration we use a model of signalling network that can be applied to important transcription factors such as NFkB

Noise control and utility: From regulatory network to spatial patterning

Stochasticity (or noise) at cellular and molecular levels has been observed extensively as a universal feature for living systems. However, how living systems deal with noise while performing desirable biological functions remains a major mystery. Regulatory network configurations, such as their topology and timescale, are shown to be critical in attenuating noise, and noise is also found to facilitate cell fate decision. Here we review major recent findings on noise attenuation through regulatory control, the benefit of noise via noise-induced cellular plasticity during developmental patterning, and summarize key principles underlying noise control

A Chemistry-Inspired Framework for Achieving Consensus in Wireless Sensor Networks

The aim of this paper is to show how simple interaction mechanisms, inspired by chemical systems, can provide the basic tools to design and analyze a mathematical model for achieving consensus in wireless sensor networks, characterized by balanced directed graphs. The convergence and stability of the model are first proven by using new mathematical tools, which are borrowed directly from chemical theory, and then validated by means of simulation results, for different network topologies and number of sensors. The underlying chemical theory is also used to derive simple interaction rules that may account for practical issues, such as the estimation of the number of neighbors and the robustness against perturbations. Finally, the proposed chemical solution is validated under real-world conditions by means of a four-node hardware implementation where the exchange of information among nodes takes place in a distributed manner (with no need for any admission control and synchronism procedure), simply relying on the transmission of a pulse whose rate is proportional to the state of each sensor.Comment: 12 pages, 10 figures, submitted to IEEE Sensors Journa

Stochastic focusing coupled with negative feedback enables robust regulation in biochemical reaction networks

Nature presents multiple intriguing examples of processes which proceed at high precision and regularity. This remarkable stability is frequently counter to modelers' experience with the inherent stochasticity of chemical reactions in the regime of low copy numbers. Moreover, the effects of noise and nonlinearities can lead to "counter-intuitive" behavior, as demonstrated for a basic enzymatic reaction scheme that can display stochastic focusing (SF). Under the assumption of rapid signal fluctuations, SF has been shown to convert a graded response into a threshold mechanism, thus attenuating the detrimental effects of signal noise. However, when the rapid fluctuation assumption is violated, this gain in sensitivity is generally obtained at the cost of very large product variance, and this unpredictable behavior may be one possible explanation of why, more than a decade after its introduction, SF has still not been observed in real biochemical systems. In this work we explore the noise properties of a simple enzymatic reaction mechanism with a small and fluctuating number of active enzymes that behaves as a high-gain, noisy amplifier due to SF caused by slow enzyme fluctuations. We then show that the inclusion of a plausible negative feedback mechanism turns the system from a noisy signal detector to a strong homeostatic mechanism by exchanging high gain with strong attenuation in output noise and robustness to parameter variations. Moreover, we observe that the discrepancy between deterministic and stochastic descriptions of stochastically focused systems in the evolution of the means almost completely disappears, despite very low molecule counts and the additional nonlinearity due to feedback. The reaction mechanism considered here can provide a possible resolution to the apparent conflict between intrinsic noise and high precision in critical intracellular processes

Model Reduction Tools For Phenomenological Modeling of Input-Controlled Biological Circuits

We present a Python-based software package to automatically obtain phenomenological models of input-controlled synthetic biological circuits that guide the design using chemical reaction-level descriptive models. From the parts and mechanism description of a synthetic biological circuit, it is easy to obtain a chemical reaction model of the circuit under the assumptions of mass-action kinetics using various existing tools. However, using these models to guide design decisions during an experiment is difficult due to a large number of reaction rate parameters and species in the model. Hence, phenomenological models are often developed that describe the effective relationships among the circuit inputs, outputs, and only the key states and parameters. In this paper, we present an algorithm to obtain these phenomenological models in an automated manner using a Python package for circuits with inputs that control the desired outputs. This model reduction approach combines the common assumptions of time-scale separation, conservation laws, and species' abundance to obtain the reduced models that can be used for design of synthetic biological circuits. We consider an example of a simple gene expression circuit and another example of a layered genetic feedback control circuit to demonstrate the use of the model reduction procedure