1 Closed and open systems

All chemical (and hence enzymatic) reactions are reversible, but some are more reversible than others. With metabolic pathways, particularly in vivo, the rate of the forward component of a reaction can be much greater than that of the reverse component – to the extent that the reaction is regarded as irreversible. Consider the following hypothetical enzyme-catalysed reaction:

The reactants are x and y, and v1 and v2 represent the rates of the forward and reverse components. If such a reaction is isolated from its surroundings, so that there is no production or removal of x or y from the system, the concentrations of these substances will approach values that equate v1 and v2. Such a state, in which the rates of the forward and reverse reactions are equal, is referred to as equilibrium. For an isolated (i.e. closed) system, equilibrium is the only state in which the concentrations of x and y do not vary with time. However, at equilibrium there is no net interconversion of the reactants (since v1 = v2) and, as classical thermodynamics shows, such a system can do no useful work, A closed system does not therefore provide a valid model of the metabolism in living cells, which inter-convert substances at constant (through variable) rates and are capable of doing work on their surroundings. Nonetheless, some individual cell reactions may be at equilibrium under certain conditions, and some reactions in metabolic pathways may be very close to equilibrium.

Metabolic systems are examples of open thermodynamic reactions, characterised by continuous interchange of matter and energy with their surroundings. Such an open system can be illustrated as follows:

This system contains the same hypothetical reaction as the closed system described above. But, in this case, the preliminary reaction A continuously supplies x from the surroundings, while the subsequent reaction B continuously removes y from the system; reactions behaving in this way have been designated non-equilibrium. An important property of an open system is that the concentrations of x and y can be independent of time, even if the reaction x y is displaced from equilibrium (e.g. when v1 is greater than v2). In the above example, such a situation would arise if the rate of reaction A were constant and the rate of reaction B was a function of the concentration of y. The rate of conversion of one substance into the other would then be constant, and the system in steady-state, the rate of overall throughput being referred to as the flux.

Although the steady-state serves as a model for the operation of metabolic pathways, open systems can take other forms. Those in which the concentrations of substrate (or metabolic intermediates) are continuous functions of time include both transient (exponential) states, when the flux through a steady-state system changes, and oscillatory states.

2 Generation of flux in steady-state systems

The main characteristics of a system in steady-state are the time-independence of the concentrations of the intermediates and the presence of a constant flux; indeed, constancy of flux is the main factor determining steady-state. A steady-state system therefore consists of two types of reaction:

For example, in a steady-state system such as the following:

a constant flux is generated at reaction A. The rate of reaction B is determined by the concentration (which is constant) of its substrate x. The flux through reaction B is therefore equal to the rate of reaction A. For steady-state to be maintained, reaction A could not be isolated and substrate-dependent, because the concentration of the substrate, and hence the flux, would decline as the reaction progressed. In short, reaction A must be substrate-saturated if it is to generate a flux for the other reactions in the pathway to transmit. While such flux-generating reactions need to be substrate-saturated for a system to reach steady-state, other reactions which follow later in the pathway are substrate-dependent.

The term substrate needs to be used with care, as illustrated by the following hypothetical example:

A cofactor (a) is involved in the flux-generating reaction (A), and this cofactor is regenerated at some subsequent reaction in the pathway. In this example reaction A must be saturated with the pathway-substrate, which provides the flow of matter through such an open system, but it need not necessarily be saturated with co-factor a. Since the latter is continuously regenerated, it can be considered to belong to a ‘conserved system of metabolites’, whereas the pathway-substrate has to be made constantly available from an outside source – in the same or another tissue.

The reactions that make up a metabolic system need not necessarily be confined to just one cell or tissue; a pathway can span several tissues linked by the circulation. For example, the flux-generating reaction...