Abstract
Biological regulation is what allows an organism to handle the effects of a perturbation, modulating its own constitutive dynamics in response to particular changes in internal and external conditions. With the central focus of analysis on the case of minimal living systems, we argue that regulation consists in a specific form of second-order control, exerted over the core (constitutive) regime of production and maintenance of the components that actually put together the organism. The main argument is that regulation requires a distinctive architecture of functional relationships, and specifically the action of a dedicated subsystem whose activity is dynamically decoupled from that of the constitutive regime. We distinguish between two major ways in which control mechanisms contribute to the maintenance of a biological organisation in response to internal and external perturbations: dynamic stability and regulation. Based on this distinction an explicit definition and a set of organisational requirements for regulation are provided, and thoroughly illustrated through the examples of bacterial chemotaxis and the lac-operon. The analysis enables us to mark out the differences between regulation and closely related concepts such as feedback, robustness and homeostasis.
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Notes
In bacterial metabolism, these are shifts between different growth phases, which rely on distinct sources of sugar.
See for example Fell (1997: 2), according to whom regulation is defined in a way that almost coincides with homeostasis: regulation «is occurring when a system maintains some variable constant over time, in spite of fluctuations in external conditions (…) regulation is therefore linked to homeostasis».
This principle states that, if any change is imposed on a chemical system at equilibrium, then the system tends to adjust itself spontaneously, against the direction of change, to the same --or a slightly new-- equilibrium condition.
Constraints are here generally conceived as material structures that harness underlying thermodynamic processes. In more explicit and accurate terms, we can use the definition (adapted from Mossio et al. 2013) that, given a particular process P, a material structure C acts as a constraint if: (1) at a time scale characteristic of P, C is locally unaffected by P; (2) at this time scale C exerts a causal role on P, i.e. there is some observable difference between free P, and P under the influence of C.
As Stuart Kauffman (2000) has pointed out, «constraints beget work, which in turn begets constraints» . Kauffman elaborates on Atkins’ definition of work as a constrained release of energy (Atkins 1984) and argues that a mutual relationship between work and constraints must be established in a system in order to achieve self-maintenance, in the form of a “work- constraint (W–C) cycle” (Kauffman 2000). A self-maintaining system, by coupling endergonic and exergonic processes, is capable of using work to regenerate at least some of the constraints (such as enzymes and the membrane) that make that work possible.
Over the past decades this idea, usually known as “organisational closure” has been invoked by a number of authors in biology and systems science (Piaget 1967; Rosen 1958, 1972, 1991; Maturana and Varela 1973, 1980; Ganti 1975, 2003a, 2003b; Kauffman 2000; Ruiz-Mirazo and Moreno 2004; Letelier et al. 2006; Mossio and Moreno 2010). Even though their conceptions may differ with regard to important aspects, the common idea is that a circular organisation produces the same components and processes which realise it, and it is maintained invariant despite the continuous change at the structural level of molecular parts and subsystems (and the continuous interaction with the environment). For a detailed analysis of this question and a theoretical definition of closure in terms of constraints, see Montévil and Mossio (2015).
Stoichiometry concerns the quantitative relationship between substances in chemical processes. It is founded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products. «Chemical processes are stoichiometrically coupled if a component produced by one of the reactions is the starting component of another reaction. The balance equation of the overall process is obtained by the summation of the stoichiometric equations of elementary processes, and is called overall equation» (Ganti 2003b: 20).
The rate of activity of an individual constraint (like an enzyme, or a membrane) is, in general, indirectly controlled by the other constraints in the network because they have diverse cross effects on the very synthesis of each constraint, as well as on the processes that supply the substrates or consume the products of the activity of other constraints (Hofmeyr and Cornish-Bowden 1991, 2000; Heinrich and Schuster 1996; Fell 1997).
Ganti (2003a), together with di Paolo (2005), consider that the template subsystem of the chemoton might be playing an incipient regulatory role in the system, in so far as oligonucleotide replication processes are template-length-dependent and modelled to operate only above a certain ‘activation threshold’ -- a feature specific to that particular subsystem, which could de-synchronise it, partially at least, from the rest. However, in our view, this slight asymmetry can only introduce a relative delay in the coordination of the various autocatalytic cycles: the actual chemoton response to perturbations is always the result of the coupled activities of all three subsystems, so no distinction between regulator and regulated subsystems can be made in this scenario.
In cybernetic terms (Wiener 1948) the loop is established by connecting the effector (output) with a sensor (input), in a way that their relation is controlled by a corrector capable of acting on the effector on the basis of a perturbatory deviation detected by the sensor, so as to activate a compensatory action. In turn, the compensatory action modifies the environment that caused the perturbation. In so doing, the system creates a loop between the state of the effector and the sensor through the environment. The effect is to damp environmental perturbations and to keep a variable within a specific range of values.
It is important to point out that feedback loop and the circular organisation (“organisational closure”) introduced in “Control in biological systems” section are two distinct notions, even though they both appeal to circular causal relations. The fundamental difference in this respect is that feedback realises a circularity of processes, and it depends, in its basic instances, on the action of only one constraint (whose existence does not require that circularity). Organisational closure, instead, consists in a circular generative relation among constraints, and implies the mutual dependence of several constraints that control the underlying processes, which produce and maintain one another.
Allosterism (Monod et al. 1963, 1965; Koshland et al. 1966) concerns the change in the structure and functioning of a protein due to the interaction with an effector molecule in a site different from the active one (primary functional activity). The nature and variety of allosteric mechanisms has been widely discussed in the literature (see Morange 2012; Cornish-Bowden 2014 for a review of the debate) and, still, new theoretical models have been recently formulated (Del Sol et al. 2009; Motlagh et al. 2014). The important aspect of allosteric proteins is that, having two distinct sites, they can respond to effectors and change their activity accordingly.
The inhibitor N does not act as an additional, second-order controller on the constitutive enzyme E, but realises a chemical interaction: the change is just that a new complex E + N acts as the (damped/inhibited) constraint now.
It is important to point out that ruling out allosteric feedback inhibition as a regulatory mechanism does not mean that allosteric interactions are never involved in regulation. It just means that they do not contribute as regulation when they are part of basic negative feedback mechanisms. See the example of the lac-operon for a case in which allosteric interactions are recruited into regulatory mechanisms.
See: Hofmeyr and Cornish-Bowden (1991, 2000), and Fell (1997). In addition, the deactivating effects of allosteric inhibitors affect only the activity of E (and just to a certain degree): they do not necessarily switch the constitutive regime to a new one, unless many enzymes are controlled at the same time. In fact, the power of this mechanism is usually very limited, because the control over the pathway is often shared by all the enzymes which participate in it (see Kacser and Burns 1973).
The need to introduce the idea of dynamical decoupling follows from the fact that regulation implies a strong asymmetry and a basic hierarchical relationship between different modules or subsystems of a system. In artificial systems regulation is implicitly understood as a change in the parameters of the system operated by human designers, whose construction protocols and technologically biased goals introduce completely different temporal/spatial scales of behaviour. In natural systems, however, one cannot identify a process of regulation unless the system generates within itself a clear-cut dynamic differentiation, which of course must satisfy the global functional and stoichiometric requirements involved.
The idea at the basis of this property, which can be traced back to Jacob and Monod’s models of regulation (Jacob and Monod 1961; Monod et al. 1963, 1965; See also Fox Keller 2002), is that the regulatory mechanism is somehow detached from the constitutive one. Consequently, the effect of the perturbation on the constitutive system is indirect, due to the specific properties of the regulatory subsystem, that has no constitutive activity of its own (see, for example, Monod 1970).
An example of this property is given in (Grisemer and Szathmáry 2009: 505): «The composition property should reflect the concentrations of monomers produced and circulating in the internal milieu of the chemoton. That is, composition is a stoichiometric function of the metabolism that produces the monomers and the polymerization reactions that incorporate them. The order property of monomers, or sequence, however, is a stoichiometrically free property: It does not depend on the stoichiometry of the chemoton, except insofar as possible sequences are constrained to given compositions (and assuming there are no steric constraints among adjacent monomers).» These authors propose a way in which a form of decoupling (although they do not use the term) could have appeared during the transition from self-maintaining systems (driven by non sequentially dependent molecules—like the specific chemoton of Fig. 4), to more complex chemoton-like systems (including a template composed of different monomers, which would have enabled sequence-based interactions not directly determined by the chemical stoichiometry of the components). A development of this idea has been proposed through a theoretical model by Zachar et al. (2011).
The fact that R, strictly speaking, is not part of the constitutive regime, and that C and R are dynamically decoupled, by no means implies that they are independent. Although R possesses a high degree of freedom with respect to C, the two subsystems are functionally correlated (Sommerhoff 1950): the regulatory subsystem R is produced and maintained by the activity of the constitutive organisation C, whose dynamics is, in turn, modulated by R. Correlation in this context simply means that C and R are indirectly related through the system that they integrate.
This is not the only possible chemoton. As stated in Ganti (2003b), and Griesemer and Szathmáry (2009), different chemotons may include not only stoichiometrically rigid “AND” couplings, but also partially decoupled “OR” relationships between subsystems. As pointed out by an anonymous reviewer, in principle a system with a decoupled regulatory subsystem could nevertheless be a chemoton in so far as it still has the three constitutive cycles in strict stoichiometric coupling.
This does not exclude the possibility that at some intermediate stages of the evolution of regulation some components of R might have been readily available in the environment, so, strictly speaking, they would not have needed to be internally synthesized (but just uptaken). Yet, they would have had to be integrated in a mechanism that, globally speaking, was generated and articulated from within.
The causal action of the perturbation on the regulatory mechanism/subsystem is dependent on a) the specific features of the perturbation, and b) the specific organisation of the regulatory subsystem. For a dedicated subsystem whose function is to respond to perturbations through a shift in the constitutive regime, the sensitivity to the perturbation and the capability to work or not on the basis of different inputs is crucial. And the input can be neither the concentration of the regulator, nor that of the metabolites directly. Otherwise, the subsystem would work at the same level of the constitutive regime (stoichiometrically determined), and regulation would collapse into dynamic stability.
One of the most evident differences between metabolic and developmental regulation is that in the latter the regulatory change of regime tends to be irreversible, whereas in the former it is not. Metabolic regulation is usually reversible because the initial regime might be necessary again, for example in diauxic shifts between metabolic regimes based on different sugars. When the shift is reversible, it is obvious that the functional plasticity and robustness of the system increases, because it can specifically select, back and forth, between --at least-- two viable constitutive regimes, depending on the changes in the conditions. When they are irreversible (e.g., think of cell differentiation processes in multicellular development, see for example Arnellos et al. 2014) this does not necessarily follow. In so far as previous constitutive regimes are once and for all obliterated from the system (i.e., not available any more), the space for regulatory action seems to shrink. However, relatively often, these irreversible transitions operate as bifurcation points that lead to a richer dynamic scenario, where further regulatory relationships can be established.
The concentration of the components of R is usually very low and almost invariant, so that it does not affect the rates of the reactions in C.
Transcription, RNA transport, translation, post-translation, etc.
As we mentioned above (see “Dynamic stability and feedbacks” section) allosterism alone does not imply regulation, although it does not exclude it, either. A second-order functional architecture is, in fact, required in order to recruit allosteric activation for regulatory mechanisms. And this is missing in allosteric feedback inhibition (as shown in “Dynamic stability and feedbacks” section, above) but not, as we will see here, in the lac-operon.
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Acknowledgments
The authors wish to thank Athel Cornish-Bowden and two anonymous reviewers for their careful reading and useful remarks on a previous version of this paper. The authors acknowledge grants from the Basque Government (IT 590-13 to AM, LB and KRM, and postdoctoral fellowship to LB), from the Spanish Ministry of Economía y Competitividad (FFI2011-25665 to AM, LB and KRM), from the Spanish Ministry of Industria y Innovación (BFU2012-39816-C02-02 to AM) and from the Fondo Nacional de Desarrollo Científico y Tecnológico, Chile (Fondecyt Regular-1150052 to LB). In addition, they acknowledge support from European COST Actions CM1304 (to KRM) and TD1308 (to KRM and LB).
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Bich, L., Mossio, M., Ruiz-Mirazo, K. et al. Biological regulation: controlling the system from within. Biol Philos 31, 237–265 (2016). https://doi.org/10.1007/s10539-015-9497-8
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DOI: https://doi.org/10.1007/s10539-015-9497-8