Energy, enzymes and metabolism

Staying alive costs energy. A cell must build proteins and membranes, pump ions against their gradients, move cargo along its cytoskeleton and divide, and every one of those jobs needs a supply of usable energy. Metabolism is the sum of all the chemical reactions in a cell, and it is organized into pathways: sequences of steps, each speeded up by a specific enzyme. This lesson covers the rules of energy that every pathway must obey, the molecule that cells use as energy currency, and the enzymes that make reactions happen fast enough to support life. Lessons 9 and 10 apply these ideas to respiration and photosynthesis; BIOC-330 and BIOC-331 go deeper into metabolism.

Energy and the laws of thermodynamics

Energy is the capacity to do work. Cells deal with kinetic energy (the energy of motion, including heat and the movement of molecules) and potential energy (stored energy, such as the chemical energy in the bonds of glucose or the energy stored in an ion gradient across a membrane).

Two laws of thermodynamics govern every energy transformation. The first law says energy cannot be created or destroyed, only converted from one form to another. A cell does not make energy; it converts the chemical energy of food, or in plants the energy of light, into forms it can use. The second law says every energy conversion increases the disorder (entropy) of the universe, and some energy is always lost as heat. No conversion is 100 percent efficient. Cells maintain their own high degree of order only by taking in energy and releasing heat and disorder to their surroundings, which is why you are warm.

Free energy: which reactions can happen?

To predict whether a reaction can occur on its own, biologists use the change in Gibbs free energy, ΔG, the energy available to do work. A reaction with a negative ΔG releases free energy and is called exergonic; it can proceed spontaneously, although spontaneous does not mean fast. A reaction with a positive ΔG requires an input of free energy and is called endergonic; it will not proceed on its own. Building a protein from amino acids is endergonic; breaking glucose down to carbon dioxide and water is strongly exergonic.

ΔG depends on conditions, especially the concentrations of reactants and products. Biochemists use a standard value, ΔG°′, measured at 1 M concentrations and pH 7, and correct it for real cell conditions:

Here \(R\) is the gas constant (8.314 J per mol per kelvin), \(T\) the temperature in kelvin, and \(Q\) the ratio of product concentrations to reactant concentrations. If products are scarce, \(Q\) is small, \(\ln Q\) is negative, and ΔG becomes more negative than ΔG°′. Cells exploit this: by constantly using up the product of one reaction in the next step of a pathway, they keep \(Q\) low and push reactions forward.

import math
# Actual free energy of ATP hydrolysis at cell concentrations
R, T = 8.314, 310.0           # J/(mol K), K
dG0 = -30.5                   # kJ/mol
def dG(atp_mM, adp_mM, pi_mM):
    Q = (adp_mM / 1000) * (pi_mM / 1000) / (atp_mM / 1000)
    return dG0 + R * T * math.log(Q) / 1000

print("Typical cell (5, 0.5, 5 mM):  ", round(dG(5, 0.5, 5), 1), "kJ/mol")
print("Exhausted muscle (2, 2, 20 mM):", round(dG(2, 2, 20), 1), "kJ/mol")
print("Standard conditions (1 M each):", round(dG(1000, 1000, 1000), 1), "kJ/mol")

Typical cell (5, 0.5, 5 mM):   -50.1 kJ/mol
Exhausted muscle (2, 2, 20 mM): -40.6 kJ/mol
Standard conditions (1 M each): -30.5 kJ/mol

ATP: the energy currency

Adenosine triphosphate (ATP) is a nucleotide (lesson 3) with a chain of three phosphate groups. The phosphates are negatively charged and repel each other, and the products of hydrolysis are more stable, so removing the end phosphate releases a lot of free energy. Cells use that release to drive endergonic processes through energy coupling: the exergonic hydrolysis of ATP is linked to an endergonic reaction so that the combined ΔG is negative.

Coupling usually works by transferring the phosphate group to another molecule, a process called phosphorylation. The phosphorylated molecule is more reactive or changes shape. The sodium–potassium pump (lesson 7) is phosphorylated by ATP, changes shape and moves ions. Motor proteins change shape each time they split an ATP, producing movement. In biosynthesis, ATP activates building blocks so they can be joined.

ATP is a currency, not a store. A cell holds only enough ATP for a few seconds to a minute of activity and regenerates it constantly. An active human turns over roughly their own body weight in ATP each day, recycling each ADP molecule hundreds of times a day. Long-term energy is stored as glycogen, starch or fat.

# How much ATP does a person turn over in a day? (rough estimate)
energy_kj_per_day = 8400        # about 2,000 kcal
fraction_captured = 0.45        # fraction of food energy captured as ATP (rough)
kj_per_mol_atp = 50             # actual free energy per ATP in cells
molar_mass_atp = 507            # g/mol
mol_atp = energy_kj_per_day * fraction_captured / kj_per_mol_atp
print(f"Moles of ATP made per day: {mol_atp:.0f}")
print(f"Mass of ATP turned over: {mol_atp * molar_mass_atp / 1000:.0f} kg")
print("Body content of ATP is only about 0.25 kg, so each molecule is recycled",
      round(mol_atp * molar_mass_atp / 250), "times a day")

Moles of ATP made per day: 76
Mass of ATP turned over: 38 kg
Body content of ATP is only about 0.25 kg, so each molecule is recycled 153 times a day

Enzymes: biological catalysts

Many exergonic reactions are extremely slow at body temperature. A sugar cube can sit in air for years without reacting with oxygen, although burning it releases a lot of energy. The barrier is the activation energy, the energy needed to start a reaction by straining or breaking existing bonds. Catalysts lower the activation energy, speeding reactions without being used up. Enzymes are biological catalysts, almost all of them proteins; a few RNA molecules, called ribozymes, also act as catalysts, including the joining of amino acids in the ribosome.

Enzymes do not change ΔG. They cannot make an endergonic reaction happen on its own or shift where the equilibrium lies; they only make the reaction reach equilibrium faster. But the speed-up is enormous: many enzymes accelerate reactions by factors of a million to more than a trillion. Without them, the chemistry of life would be far too slow to sustain it.

Each enzyme acts on a specific substrate, which binds in a pocket called the active site. The active site's shape and chemistry complement the substrate. The older lock-and-key picture has been replaced by the induced-fit model: the enzyme changes shape slightly as the substrate binds, gripping it more tightly and straining the bonds that need to break. Enzymes lower activation energy by orienting substrates correctly, straining bonds, providing a favorable chemical environment (for example, acidic or basic side chains) and sometimes briefly forming covalent bonds with the substrate.

Many enzymes need helpers. Cofactors are inorganic ions such as zinc, iron, magnesium or copper. Coenzymes are small organic molecules, often made from vitamins, such as NAD+ (from niacin) and FAD (from riboflavin), which carry electrons in respiration. That is why vitamin deficiencies cause disease: without the coenzyme, the enzyme cannot work.

Factors that affect enzyme activity

Because enzymes are proteins with precise shapes, their activity depends on conditions:

Human enzymes typically work best near 37 °C. Enzymes from organisms living in hot springs, such as Taq DNA polymerase from the bacterium Thermus aquaticus, work best above 70 °C and survive near boiling; Taq is used in the polymerase chain reaction (PCR), which repeatedly heats DNA to 95 °C.

Measuring enzyme speed: Michaelis–Menten kinetics

If you measure the initial rate of an enzyme reaction (v) at different substrate concentrations ([S]), the results usually follow a curve that rises steeply and then levels off at a maximum rate, Vmax, when the enzyme is saturated. Leonor Michaelis and Maud Menten described this in 1913 with a simple equation:

\(K_m\), the Michaelis constant, is the substrate concentration at which the rate is half of \(V_{\max}\). A low \(K_m\) means the enzyme reaches half its maximum speed at a low substrate concentration, which roughly indicates high affinity for the substrate. \(V_{\max}\) depends on how much enzyme is present; dividing it by the enzyme concentration gives the turnover number, \(k_{cat}\), the number of substrate molecules each active site converts per second. Values range from below 1 per second to about a million per second for carbonic anhydrase, which converts carbon dioxide and water to bicarbonate in red blood cells.

import numpy as np
from scipy.optimize import curve_fit

def mm(S, Vmax, Km):
    return Vmax * S / (Km + S)

rng = np.random.default_rng(107)
S = np.array([0.5, 1, 2, 4, 8, 16, 32])           # substrate, mM
true_v = mm(S, 100, 3.0)                          # true Vmax 100 umol/min, Km 3 mM
v = true_v * (1 + rng.normal(0, 0.04, S.size))     # 4% measurement noise

(Vmax, Km), cov = curve_fit(mm, S, v, p0=[80, 2])
print("Measured rates:", np.round(v, 1))
print(f"Fitted Vmax = {Vmax:.1f} umol/min, Km = {Km:.2f} mM")
print(f"Rate at [S] = Km: {mm(Km, Vmax, Km):.1f} (half of Vmax)")

Measured rates: [14.5 23.1 39.9 61.2 68.4 86.2 89.3]
Fitted Vmax = 98.6 umol/min, Km = 2.91 mM
Rate at [S] = Km: 49.3 (half of Vmax)

Before computers, biochemists turned the curve into a straight line by plotting 1/v against 1/[S] (the Lineweaver–Burk or double-reciprocal plot), whose intercepts give 1/Vmax and −1/Km. It is still useful for visualizing inhibitors, but it distorts measurement errors badly, magnifying the noisiest points at low substrate concentration. Fitting the curve directly by non-linear regression, as in the program above, gives more reliable estimates.

Regulating metabolism

Cells cannot run every pathway at full speed all the time; they must respond to need. Several mechanisms adjust enzyme activity. Competitive inhibitors resemble the substrate and compete for the active site; they raise the apparent Km but not Vmax, because enough substrate can outcompete them. Many drugs work this way: statins lower cholesterol by competitively inhibiting HMG-CoA reductase, an enzyme in cholesterol synthesis. Non-competitive inhibitors bind elsewhere and reduce Vmax. Some poisons are irreversible inhibitors: nerve agents and some insecticides permanently block acetylcholinesterase, an enzyme at nerve–muscle junctions.

Allosteric regulation is especially important. Many enzymes have regulatory sites separate from the active site; molecules binding there switch the enzyme between more and less active shapes. In feedback inhibition, the end product of a pathway allosterically inhibits an enzyme near the start, so the pathway slows down when its product builds up and speeds up when the product is scarce, just as a thermostat controls a furnace. Cells also switch enzymes on and off by adding or removing phosphate groups (lesson 11), control how much of each enzyme is made, and confine pathways to particular compartments.

Metabolism as a whole is divided into catabolism, pathways that break molecules down and release energy (such as respiration), and anabolism, pathways that build molecules and consume energy (such as protein synthesis and photosynthesis). ATP and electron carriers such as NADH and NADPH link the two, carrying energy and electrons from catabolic to anabolic reactions.