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Register a new userGeneric temperature compensation of biological clocks by autonomous regulation of catalyst concentration
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Circadian clocks ubiquitous in life forms ranging bacteria to multi-cellular organisms, often exhibit intrinsic temperature compensation; the period of circadian oscillators is maintained constant over a range of physiological temperatures, despite the expected Arrhenius form for the reaction coefficient. Observations have shown that the amplitude of the oscillation depends on the temperature but the period does not---this suggests that although not every reaction step is temperature independent, the total system comprising several reactions still exhibits compensation. We present a general mechanism for such temperature compensation. Consider a system with multiple activation energy barriers for reactions, with a common enzyme shared across several reaction steps with a higher activation energy. These reaction steps rate-limit the cycle if the temperature is not high. If the total abundance of the enzyme is limited, the amount of free enzyme available to catalyze a specific reaction decreases as more substrates bind to common enzyme. We show that this change in free enzyme abundance compensate for the Arrhenius-type temperature dependence of the reaction coefficient. Taking the example of circadian clocks with cyanobacterial proteins KaiABC consisting of several phosphorylation sites, we show that this temperature compensation mechanisms is indeed valid. Specifically, if the activation energy for phosphorylation is larger than that for dephosphorylation, competition for KaiA shared among the phosphorylation reactions leads to temperature compensation. Moreover, taking a simpler model, we demonstrate the generality of the proposed compensation mechanism, suggesting relevance not only to circadian clocks but to other (bio)chemical oscillators as well.
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Circadian clocks exhibit the robustness of period and plasticity of phase against environmental changes such as temperature and nutrient conditions. Thus far, however, it is unclear how both are simultaneously achieved. By investigating distinct models of circadian clocks, we demonstrate reci- procity between robustness and plasticity: higher robustness in the period implies higher plasticity in the phase, where changes in period and in phase follow a linear relationship with a negative coef- ficient. The robustness of period is achieved by the adaptation on the limit cycle via a concentration change of a buffer molecule, whose temporal change leads to a phase shift following a shift of the limit-cycle orbit in phase space. Generality of reciprocity in clocks with the adaptation mechanism is confirmed with theoretical analysis of simple models, while biological significance is discussed.
Information transmission in biological signaling circuits has often been described using the metaphor of a noise filter. Cellular systems need accurate, real-time data about their environmental conditions, but the biochemical reaction networks that propagate, amplify, and process signals work with noisy representations of that data. Biology must implement strategies that not only filter the noise, but also predict the current state of the environment based on information delayed due to the finite speed of chemical signaling. The idea of a biochemical noise filter is actually more than just a metaphor: we describe recent work that has made an explicit mathematical connection between signaling fidelity in cellular circuits and the classic theories of optimal noise filtering and prediction that began with Wiener, Kolmogorov, Shannon, and Bode. This theoretical framework provides a versatile tool, allowing us to derive analytical bounds on the maximum mutual information between the environmental signal and the real-time estimate constructed by the system. It helps us understand how the structure of a biological network, and the response times of its components, influences the accuracy of that estimate. The theory also provides insights into how evolution may have tuned enzyme kinetic parameters and populations to optimize information transfer.
Motivated by recent experimental work, we define and study a deterministic model of the complex miRNA-based regulatory circuit that putatively controls the early stage of myogenesis in human. We aim in particular at a quantitative understanding of (i) the roles played by the separate and independent miRNA biosynthesis channels (one involving a miRNA-decoy system regulated by an exogenous controller, the other given by transcription from a distinct genomic locus) that appear to be crucial for the differentiation program, and of (ii) how competition to bind miRNAs can efficiently control molecular levels in such an interconnected architecture. We show that optimal static control via the miRNA-decoy system constrains kinetic parameters in narrow ranges where the channels are tightly cross-linked. On the other hand, the alternative locus for miRNA transcription can ensure that the fast concentration shifts required by the differentiation program are achieved, specifically via non-linear response of the target to even modest surges in the miRNA transcription rate. While static, competition-mediated regulation can be achieved by the miRNA-decoy system alone, both channels are essential for the circuits overall functionality, suggesting that that this type of joint control may represent a minimal optimal architecture in different contexts.
The majority of mammalian genomic transcripts do not directly code for proteins and it is currently believed that most of these are not under evolutionary constraint. However given the abundance non-coding RNA (ncRNA) and its strong affinity for inter-RNA binding, these molecules have the potential to regulate proteins in a highly distributed way, similar to artificial neural networks. We explore this analogy by devising a simple architecture for a biochemical network that can function as an associative memory. We show that the steady state solution for this chemical network has the same structure as an associative memory neural network model. By allowing the choice of equilibrium constants between different ncRNA species, the concentration of unbound ncRNA can be made to follow any pattern and many patterns can be stored simultaneously. The model is studied numerically and within certain parameter regimes it functions as predicted. Even if the starting concentration pattern is quite different, it is shown to converge to the original pattern most of the time. The network is also robust to mutations in equilibrium constants. This calls into question the criteria for deciding if a sequence is under evolutionary constraint.
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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