Thermodynamics #2: Metabolism's Master

Metabolism’s Master

This article is the second part of a two part series. Link to part #1: Metabolism’s Motivation.

Metabolic regulation and metabolic control

The human body is an open system. In order to perform maximum work, it maintains a steady state. In such a state, the flux of metabolites is constant. There are two aspects to maintaining the steady state: flux control and flux regulation. Say your goal was to eat a cake. For that, you would need to:

a) Cut up the cake into bite size pieces
b) lift each piece to your mouth

This basic algorithm to eat the cake (maintain steady state) is analogous to metabolic regulation. However, if your friends were to show up, you would have to eat the cake faster, before they can get a bite. This tweaking of the basic algorithm to adapt to changes in the environment (internal or external) is analogous to metabolic control.

Metabolic regulation is the process by which the steady-state flow of metabolites through a pathway is maintained, whereas metabolic control is the influence exerted on the enzymes of a pathway in response to an external signal in order to alter the flux of metabolites. - Donald Voet and Judith G Voet

To regulate and control metabolism means to regulate and control the flux through the numerous metabolic pathways. Thus, these two sets of terms can be used interchangeably. With the varied amount of stimuli we are exposed to, it is not hard to see the need for flux control mechanisms.

Flux

Flux is the rate of flow of metabolites. Mathematically, flux ($J$) through a reaction is the difference between the rate of forward reaction ($v_f$) and the rate of backward reaction ($v_b$).
$J = v_f - v_b \tag{1}$

For an irreversible reaction, the rate of forward reaction is equal to its flux. For a reaction at equilibrium, there is no flux.

To study the mechanisms of flux control and regulation, lets categorize the reactions in a metabolic pathway into two types:

• the rate determining, irreversible steps
• and the other steps that communicate flux set by the rate determining steps though out the pathway.

Reactions in a metabolic pathway:
a) the rate determining reactions
b) other "communicating" reactions

Rate determining reactions

The rate of rate determining reactions are solely dependent upon their respective enzyme concentrations. Thus, the changes in flux of these reactions are a reflection of changes in their enzyme concentrations. A pathway maintains a constant flux and can have multiple rate determining steps. Thus, the sum of changes in the enzyme concentrations of all the rate determining steps of a pathway is directly proportional to change in flux of the pathway. The flux control coefficient of an enzyme ($C^J$) measures its contribution to the change in flux of the pathway. Below, $[E]$ is the concentration of the enzyme, $i$ is each rate determining enzyme in the pathway and $n$ is the total number of rate determining enzymes in the pathway.
$C^J = \frac{\Delta J/J} {\Delta [E]/[E]} \tag{2}$

$\sum^ {n}_{i}C^J_i=1 \tag{3}$

If an enzyme has a high flux control coefficient, then a small change in its concentration will result in a magnified change in flux through the reaction it catalyzes. Such a reaction is more sensitive to changes in enzyme concentration than a reaction whose enzyme has a low flux control coefficient. Thus, the flux control coefficient is a measure of sensitivity of a reaction to the change in its enzyme concentration.

Communicating reactions

For a communicating step, the rate of forward reaction ($v_f$) needs to be equal to the change in flux ($\Delta J$) set by the rate determining step(s). Only then can the entire pathway maintain a constant flux.
$\Delta J = v_f \tag{4}$

On dividing by $J$ both sides and multiplying and dividing the left hand side by $v_f$ we get:
$\frac{\Delta J}{J} = \frac{\Delta v_f} {J} \frac{v_f}{v_f}\tag {5a}$

Substituting the value of $J$ form equation $(1)$ we get:
$\frac{\Delta J}{J} = \frac{\Delta v_f} {v_f-v_r} \frac{v_f}{v_f} \tag{5b}$

Under conditions of high $K_m$,
$\frac{\Delta v_f}{v_f} = \frac{\Delta [A]}{[A]}$
where $[A]$ is substrate concentration. For the derivation of the above equation refer to this article. On substitution in equation $(5b)$ we end up with:
$\frac{\Delta J}{J} = \frac{\Delta [A]}{[A]} \frac{v_f} {v_f-v_r}\tag{5c}$

The above equation relates the change in flux of the reaction to the change in substrate concentration required to bring about such a change. Note that the enzymes catalyzing communicating steps unlike those of the rate determining step have high $K_m$ values. As a consequence, their rates are primarily dependent on substrate concentration and not enzyme concentration.

The term $\frac{v_f} {v_f-v_r}$ is know as the elasticity coefficient. Consider an irreversible reaction. For this reaction, $v_r = 0$ and so the elasticity coefficient is equal to one. To change the flux of such a reaction, an equal change in the substrate concentration is necessary. Such a reaction does not change its flux easily and is not very elastic. However, if the reaction were at equilibrium, $v_f$ would equal $v_r$ and the elasticity coefficient would become infinite. Thus, to change the flux of such a reaction very little increase in substrate concentration is required. Communicating reactions are at equilibrium and thus are efficient communicators of flux changes.

Communicating reactions are highly elastic because they are at equilibrium. Rate determining steps are far from equilibrium (irreversible) so they are not very elastic.

Understanding pathways: supply and demand

Consider a metabolite $M$. All the pathways in the body that produce $M$ are known as supply pathways and all the pathways that utilize $M$ as a substrate are known as demand pathways. This makes $M$ an intermediate metabolite.

While studying metabolic control and regulation, it is important to study this supply-demand system as a whole.

Degradation pathways are inextricably linked to the biosynthetic pathways that utilize their products. -Voet and Voet

As the concentration of $M$ increases, it acts as a feedback inhibitor of the supply block and decreases its flux. At the same time and increased concentration of $M$ increases the flux through the demand block (until saturation).

When supply and demand pathways have equal flux, the system reaches a steady state. The concentration of the intermediate in such a situation is known as its steady state concentration.

Who is actually in control: the supply block or the demand block?

Consider that the elasticity coefficient of the supply block is higher than that of the demand block.

Situation #1: The supply block has greater flux
The greater flux of the supply block, causes a build up of the intermediate metabolite. Due to its higher elasticity, the supply block is inhibited faster than the flux of the demand block can be increased. Thus, ultimately the both blocks reach the flux of the demand block.

Situation #2: The demand block has greater flux
Greater utilization of the intermediate metabolite causes a reduction in its concentration. Due to its high elasticity coefficient, the substrate block reacts quickly to the lack of its inhibitor. Its flux increases until it matches that of the demand block.

In conclusion, the demand block controlled the rate of flux through the supply block in both the cases by causing its flux to either increase or decrease. The supply block regulated itself to match the rate set by the demand block.

The block with the lesser elasticity coefficient controls the flux through the supply-demand system. The other block regulates the flux thorough the said system.

Metabolic regulation

Algorithm of metabolic regulation:

1. The reactions of the supply block form the intermediate metabolite.
2. The reactions of the demand block utilize the intermediate metabolite.
3. Increased concentration of the intermediate metabolite:
   • increases the flux through the demand block.
   • decreases the flux though the supply block (feedback inhibition).
4. Decreased concentration of the intermediate metabolite:
   • increases the flux through the supply block.
   • decreases the flux though the demand block
5. Depending on the situation (c) or (d) respective changes are continued until flux of both pathways is equalized and steady state is reached.

Metabolic control

The block with lower elasticity coefficient dictates how metabolism is regulated. It is the control pathway. The body employs several mechanisms to set the flux of the control pathway. All of these mechanism target the enzymes of irreversible rate determining steps of the control pathway. Allosteric control mechanisms and covalent modification of enzymes are often used to activate or deactivate enzymes.

Non-shivering thermogenesis and substrate cycling

The flux control for the regulatory block lies outside the pathway. Glycolysis is an example of regulatory pathway. It is the energy supply block while the cell’s requirement for energy is the demand block. In this case, the demand block controls the flux and glycolysis has a regulatory function. We know that glycolysis has irreversible reactions (those of enzymes phosphofructokinase, hexokinase, etc) and that these reactions have poor elasticity coefficients. So how is glycolysis an effective communicator of flux change? The presence of alternative enzymes performing reverse reactions make effective communication possible.

When an enzyme is catalyzing the reverse reaction, the rate of reverse reaction ($v_r$) for the irreversible reaction is no longer zero. Thus, there is an overall increase in the elasticity coefficient ($\frac{v_f} {v_f-v_r}$).

The simultaneous functioning of two antagonistic enzymes in a pathway while forming no new metabolite but releasing stored chemical energy in the form of heat is known as a substrate cycle.

Since no new metabolite is formed and ATP is utilized, these pathways were thought to be futile. However, now their important role in metabolic regulation has been understood.

Due to their seemingly reversible nature, substrate cycles are as good communicators and regulators of metabolism. However, since their constituent reactions are independent, irreversible reactions, they can also act as sensitive flux control points. Thus, substrate cycles have found a way to be both effective flux controllers and effective flux regulators.

Obesity and feeling cold

During substrate cycling, the hydrolysis of $ATP$ liberates heat. This liberation of heat (thermogenesis) without muscle shivering is referred to as non-shivering thermogenesis. Shivering thermogenesis refers to the heat liberated during the shivering of muscles in the body. The rate of non-shivering thermogenesis is regulated by thyroid hormones. Obese people have a lower metabolic rate and reduced non-shivering thermogenesis causing them to feel cold more often when compared to a healthy individual.

Sources

• Harper’s Illustrated Biochemistry 31st Edition
• Biochemistry by Donald Voet and Judith G. Voet