Modeling Processes with No Beginning, an Adaptive Middle, and No End

Awhile back, PZ Myers posted a feature about tumor suppressor genes [1] on his blog, Pharyngula. The feature was very complete, and will serve as a good teaching tool. At the beginning, he mentions that cybernetic and homeostatic explanations can sometimes be incomplete. This is because cybernetics and biological homeostasis are based on an key assumption: every process should have an input and output. Tumor suppressor genes make this framework difficult, because there is no distinct "output" for the process of suppression. However, there are still ways in which systems analyses can shed light on phenomena such as tumor suppression. Two newer concepts (allostatic regulation and futile cycles) can provide better mechanisms for these phenomena.

The first involves the cybernetic conceptualization of regulatory pathways vs. what actually happens during the regulation of tumor suppressor genes. Namely, a cybernetic model requires inputs and outputs. While this is traditionally true, there are a few things about this statement that need clarification. One concept deserving of further attention is homeostatic regulation. While the basic concept of homeostasis is relatively straightforward, the idea is far more complicated than simply the sum of its Greek root words [2]. While homeostasis has been defined more formally as stability in the face of perturbation due to negative feedback [3], this concept also requires a host of allostatic mechanisms that make for a more consistent and predictive theory of regulation. In short, what are the rules of absorption for the maintenance homeostatic conditions?

McEwen and Gianaros [4] use the example of various brain networks to illustrate how allostatic mechanisms mitigate various environmental stressors (e.g. perturbations). Brain networks provide us with an example that involves a complex and distributed system with many interrelated and independent components. In this example, neuroplasticity throughout life-history provide a plausible mechanism for allodynamic processes (Figure 1). These processes correspond with functional changes that promote physiological stability (e.g. homeostasis) in the organism.

Figure 1. An example of allostatic load with respect to patterned environmental stimuli (a, b) and a measured physiological response (c, d). COURTESY: Figure 2 in [4].

A differential capacity for neuroplasticity between individuals and brain functions (e.g. learning and memory, HPA axis) leads to two distinct outcomes. The first outcome is allostatic drive, which is adaptive and provides a positive feedback mechanism with respect to environmental stimuli. This mechanism helps to condition the physiology to a wider range of environmental signals. The second outcome is allostatic load, which is maladaptive. This maladaptation occurs in two stages. First, the organism experiences repeated hits of an environmental stimulus to which it cannot compensate. Due to this lack of compensation, the second stage involves a lack of long-term adaptation. This pattern of overstimulation without a proper adaptive response can result in a range of dysregulative conditions, from chronic fatigue to cancers [3]. Yet there can also be allostatic states that are adaptive for the system in question but bad for the organism, particularly over the long term [5].

An important aspect of allostasis is the regulatory nature of anticipatory mechanisms that might respond to environmental stimuli (Figure 2). This allows for an allostatic model to more accurately represent the living nature of physiological systems [5]. Whereas allostatic drive involves positive feedback, allostasis can also involve feedforward control, or a combination of feedforward and feedback information. In cases where the anticipatory mechanisms overcompensate for a set of environmental signals, the physiological system can suffer from overshoot [5]. These results from purely feedforward control without appropriate feedback, and can have significant consequences for nonlinear physiological dynamics.

Figure 2. The relationship between physiological response, adaptation, and allostatic regulation. COURTESY: Figure 1-10 from [5].

There are also links between the short-term regulation of physiology and evolutionary processes that are generally underappreciated. One of these involves the evolutionary constraints of physiological adaptation. For example, individual variation and species-specific mechanisms can determine both the normal and permissable range of function [6]. Yet there is a difference between physiological adaptation and evolutionary adaptation, which can expand this range of function. While allostatic mechanisms can mitigate the former, they cannot result in the latter. The interplay between evolvability, enabling mutations, and allostatic regulatory mechanisms is a topic for future research.

The problem with using a traditional cybernetics model to represent complex biological phenomena is not that they require formal endpoints (although that is a problem). The problem involves determining coherent inputs and outputs, or things that have an affect on or result from a complex process. Consider ocean geochemical cycling. Oceans are a complex system with both fluid and energy flows (currents, gyres) and physical structure (trophic, bathyscape). Some of these flows play a functional role in the system, while others do not. Likewise, processes associated with these flows are both completely internal to the ocean system and provide a tangible output.

There is a version of a cybernetics-like model that may deal fairly well with tumor suppressor gene regulation. I previously reviewed a type of metabolic pathway called the futile cycle [7] here on Synthetic Daisies. The sole purpose of a futile cycle (Figure 3) is to convert one product to another, and then re-convert to its original form, expending energy in the process but producing no distinct output [8]. In some ways, this resembles the repressilator motif in gene regulation [9]. However, the futile cycle might also be applied to gene expression and genetic regulation in its own right, particularly with respect to stochastic gene expression.

Figure 3. Schematic of a typical futile cycle (example is from a metabolic pathway). What is the input, what is the output, and is it anything more than a metaphenomenon? COURTESY: Figure 1 in [8].

There is also an evolutionary component to such models. Even though the futile cycle produces no output, this does not mean that there cannot be one (or more) functions related to the mechanism. Based on the metabolic function of the futile cycle, there are two potential mechanisms that could be selected for at the level of gene expression:

1) As a regulator. Much like how a throttle regulates the volume of fuel provided into an engine, products are deconverted when too much product exists and reconverted when needed.

2) As an exaptation. Suppose that the original function was for deconversion, but an extra function was built on top of this original function. The mechanism then evolves to counteract overactivity, and supplements production in cells that are evolving towards other functions.

But futile cycles and homeostatic regulation are also intimately linked. Besides serving as a model of metabolic pathway function, it can also be used as a general model of metabolic regulation at the organismal level [10]. It is also noteworthy that futile cycles can be linked together and produce multiple stable states [11], much like allostatic regulation. And much like allostatic regulatory mechanisms, the interplay between evolvability and enabling mutations needs further study. But they both have immense potential to describe the unique nature of actively-adapting (and evolving) physiological systems.

NOTES:

[1] Myers, P.Z.   What are tumor suppressor genes? Pharyngula blog, September 25 (2013).

[2] "homeo" = similar or same, "stasis" = stability in time. But physiology is a complex system that is a dynamic equilibrium, you say? This is exactly why the traditional conception of homeostasis is incomplete.

[3] Sterling, P. and Eyer, J.   Allostasis: a new paradigm to explain arousal pathology. In "Handbook of Life Stress, Cognition, and Health", S. Fisher and J. Reason eds., Wiley and Sons, New York (1988).

[4] McEwen, B.S. and Gianaros, P.J.  Stress- and Allostasis-Induced Brain Plasticity. Annual Reviews of Medicine, 62, 5.1-5.15 (2011).

[5] Schulkin, J.  Rethinking Homeostasis: allostatic regulation in physiology. MIT Press, Cambridge, MA (2003).

[6] Turner, J.S.   The Extended Organism: the physiology of animal-built structures. Harvard University Press, Cambridge, MA (2000).

[7] Alicea, B.   Resistance is a (futile) cycle! Synthetic Daisies blog, September 19 (2011).

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

[9] For more information on the repressilator and its dynamics, please see the following references:  

a) Pokhilko, A., Pinas Fernandez, A., Edwards, K.D., Southern, M.M., Halliday, K.J., and Millar, A.J.   The clock gene circuit in Arabidopsis includes a repressilator with additional feedback loops. Molecular Systems Biology, 8, 574 (2012).

b) Buse, O., Perez, R., and Kuznetsov, A.   Dynamical properties of the repressilator model. Physical Review E, 81(6-2), 066206. 

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

[11] 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).