September 19, 2011

Resistance is (a) futile (cycle)!

I just recently completed a review presentation about different systems architectures (e.g. feedback, feedforward control) found in biological systems. One example I am using is the futile cycle, which can be found in a number of biochemical systems.

To set the stage for this discussion, I am going to use a rather silly example from science fiction and relate it to real biological systems. Ever wonder why the machines might have used humans as batteries in the movie "The Matrix"? Or how birds can generate body heat on demand? In both cases, there are no great advances in bionics at work, just a set of forward and backward kinetic reactions called a futile cycle that produce nothing but heat energy as a by-product.

Some might argue that this is functionally pointless. For example, more energy would be expended feeding and maintaining each human than would be harvested as energy. However, in true Mythbusters fashion, a closer examination of futile cycle function might demonstrate why this fictitious example may not be so far-fetched, and why futile cycles might explain a lot about emergent complexity in biological systems.

Futile cycles consist of three processes: a forward reaction, a conversion the resulting product back into the original enzyme, and production of nothing but heat energy as an output. You can see an example of a futile cycle in the figure below. Hence, futility. Yet futile cycles may provide more than meets the eye, particularly when you consider the emergence, evolution, and context of the systems they are embodied within. I will now provide five examples of how futile cycles operate in and provide an opportunity for emergent complexity in biological systems.

Schematic of a typical futile cycle (example is from a metabolic pathway). COURTESY: Figure 1 in [1].

1) Futile cycles may be responsible for a facultative adaptation known as "thermoregulation on demand". In birds, a futile cycle reaction occurs in brown adipose tissue that allows for an "on-demand" heat source [2]. The creation of a thermoregulatory switch from what might otherwise be considered a wasteful interaction is a good example of a dissipative structure [3]. Dissipative structure are under-appreciated natural phenomena which may be addressed in a future post. The end result is that complex structure can emerge from and be supported by large fluctuations of energy (such as river systems or the bloodstream).

Qian and Beard [4] also suggest that futile cycles allow for high grade chemical energy to be converted into low grade heat energy. While this may appear to be a purely consumptive reaction, it actually enables different types of work to be done. One way to better understand this involves the change in information content resulting from a transformative process. In Samoilov, Plyasunov, and Arkin [1], it is suggested that colored noise (or other random fluctuations) can drive and even amplify the complex dynamics of a futile cycle. The relationship between noise, information content, and energy transformation is an interesting idea which I may explore in future posts.

2) Path-dependence are particularly important in maintaining the function of futile cycles, and is an important aspect of biological function in a number of systems. The path-dependence of components resembles the knocking-down of dominoes (see first figure below). A good example of this at the anatomical scale is the neural pathway in humans that governs striatal/basal ganglia function. In this case, regulation is contingent upon a carefully maintained sequence of disinhibitions (e.g. selective overriding of the default inhibitory state), which are ultimately key in enabling higher-level cognitive behaviors (for basic relationship, see second figure below). Futile cycles, particularly those that are coupled, are thought to enable complex processes at higher scales of organization in a similar fashion.

TOP: Sequence of dependent events (e.g. stacked dominoes). BOTTOM: neural circuit subject to sequential regulation. COURTESY: Figure from [5].

If this sequence of events is disturbed, futile cycles (and likewise neurobehavioral regulation) may no longer be able to function. However, in many cases, futile cycles may not be specific enough to exhibit this property. If all you need is a set of enzymes to provide a beneficial reaction, then there might be a large class of enzymatic pathways from which to choose.

3) How might a futile cycle arise in evolution? Perhaps in the course of producing two products needed by the cell in at alternating points in time. Viewed from an ecological perspective, the enzymes involved in the futile cycle become interdependent. For example, a futile cycle in one system (species A) might become the substrate for another system (Species B). One niche evolves on top of an established population, which can be seen in many bacterial and viral populations.

The resulting relationship can either be parasitic (where species B benefits over species A), mutualistic (both species A and B benefit" from the relationship). This ecological relationship enabled by one or a series of futile cycles is based on the creation and maintenance of a dissipative structure, while the species (B) that always benefits also exhibits characteristics of niche construction. Niche construction [6] is particularly interesting in that it plays an integral role in regulating the dynamics of coevolutionary relationships.

4) Futile cycles, or rather their recursive nature, may serve as generalized homeostatic mechanisms. One example is the seesaw model (see figure below), in which the degradation of one product initiates the production of the second product and vice versa. When viewed over time, this results in a mutual pulsing [see 7 for an example form cell cycle]. In the case of MPF and cell cycle, where MPF is produced and depleted cyclically, the basic cycle motif is dependent upon the initiation of a process (e.g. phase in cell cycle).

Eukaryotic cell cycle functioning as a futile cycle. 

5) Interconnected futile cycles -- in a larger-scale context, futile cycle may be interconnected. In these cases, the effects can be either processive or distributive. In isolation, futile cycles are processive, meaning that one input gives rise to a single set of reactions with one output. Upon linking together multiple futile cycles, however, a single input can give rise to a set of reactions with multiple potential outputs. Recall that this is related to the issue of path-dependence and functional stability. Wang and Sontag [8] have considered the behavior of interconnected futile cycles, and have proposed that when interconnected, such systems exhibit unique steady states. This can be particularly useful in enabling processes such as phosphorylation, dephosphorylation, and MAPK cascades, all of which are key in regulating biochemical signaling.

From early concepts of the second of law of thermodynamics to treatments of entropy in modern cosmological theory, the depletion of free energy in a complex system has been thought of as "heat death". And yet the connection between futile cycles and thermodynamic processes could be more accurately described as "heat life". While I would not make the claim that futile cycles break the second law of thermodynamics, they do provide a mechanism and substrate for building up complexity in the face of entropy.

Citations and Further Information:

[1] Samoilov, M., Plyasunov, S., and Arkin, A.P. (2005). Stochastic amplification and signaling in enzymatic futile cycles through noise-induced bistability with oscillations. PNAS USA, 102(7), 2310-2315.

[2] Loli, D. and Bicudo, J.E.   Control and Regulatory Mechanisms Associated with Thermogenesis in Flying Insects and Birds. Bioscience Reports, 25(3/4), 2005.

[3] Kondepudi, D. and Prigogine, I. (1998). Modern Thermodynamics: From Heat Engines to Dissipative Structures. Wiley, New York.

[4] Qian, H. and Beard, D.A. (2006). Metabolic futile cycles and their functions: a systems analysis of energy and control. IEEE Proceedings in Systems Biology, 153(4), 192-200.

[5] Stocco, A., Lebiere, C., and Anderson, J.R. (2010). Conditional routing of information to the cortex: A model of the basal ganglia’s role in cognitive coordination. Psychological Review, 117(2), 541-574.

* see also -- Chevalier, G. and Deniau, J.M. (1990). Disinhibition as a basic process in the expression of striatal functions. Trends in Neuroscience, 13, 277-280.

[6] Odling-Smee, F.J. and Laland, K.N. (2003). Niche Construction: The Neglected Process in Evolution. Princeton University Press, Princeton, NJ.

[7] Murray, A.W. and Kirschner, M.W (1989). Dominoes and Clocks: The Union of Two Views of the Cell Cycle. Science, 246(4930), 614-621.

[8] Wang, L. and Sontag, E.D.   On the number of steady states in a multiple futile cycle. Journal of Mathematical Biology, 57, 29-52 (2008).

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