The chemistry of life I: water, bonds and pH

Cells are chemical systems. Everything a cell does, from copying DNA to contracting a muscle, is a set of chemical reactions between molecules. Before we can understand membranes, enzymes or energy, we need a small toolkit of chemistry: which elements life uses, how atoms bond, why water is so unusual, and what pH measures. This lesson builds that toolkit; lesson 3 uses it to explain the large molecules of life.

The elements of life

About 25 chemical elements are essential to life, but four of them, carbon, hydrogen, oxygen and nitrogen, make up about 96 percent of the mass of a typical organism. Phosphorus and sulfur add most of the rest. A memory aid is CHNOPS. Smaller amounts of calcium, potassium, sodium, chlorine and magnesium play vital roles, and trace elements such as iron, zinc, copper and iodine are needed in tiny quantities, often as parts of enzymes.

Oxygen tops the list mainly because about 60 percent of a human body is water. Carbon is special because each carbon atom can form four stable covalent bonds, so carbon atoms can link into chains, branches and rings of almost unlimited variety. Molecules built around carbon are called organic molecules, a name left over from the time when people thought only living things could make them.

How atoms bond

An atom has a nucleus of protons and neutrons surrounded by electrons. Chemical behavior depends on the outer electrons. Atoms are most stable when their outer shell is full, and they reach that state by sharing or transferring electrons. The result is a chemical bond. Cells use several kinds of bonds and attractions, which differ hugely in strength, and the difference matters: strong bonds hold molecules together, while weak ones let molecules recognize, fold and release each other.

Whether electrons are shared equally depends on electronegativity, an atom's pull on electrons. Oxygen and nitrogen are strongly electronegative; carbon and hydrogen are similar to each other. In a C–H bond the electrons are shared about equally, so the bond is non-polar. In an O–H bond the oxygen pulls the electrons closer, giving it a partial negative charge and leaving the hydrogen partially positive. The bond is polar. These partial charges are behind most of what makes water, and life, work.

Water: the solvent of life

A water molecule is bent, with the oxygen at the apex and the two hydrogens at an angle of about 104.5 degrees. Because the oxygen is partially negative and the hydrogens partially positive, each molecule is a small dipole. The positive hydrogen of one molecule is attracted to the negative oxygen of a neighbor, forming a hydrogen bond. In liquid water each molecule makes up to four hydrogen bonds at any instant; they break and re-form trillions of times per second.

Hydrogen bonding gives water a set of properties that cells depend on:

Substances that dissolve in water, such as salt and sugar, are hydrophilic (water-loving). Substances that do not, such as oils and fats, are hydrophobic (water-fearing). Some molecules are both: one end is polar and the other non-polar. These amphipathic molecules, including the phospholipids of membranes (lesson 6) and soaps, arrange themselves with their polar parts facing water and their non-polar parts hidden.

Concentrations: moles and molarity

Cell biologists constantly prepare and dilute solutions, so it is worth getting the units right at the start. A mole is a fixed number of particles, Avogadro's number, \(6.022 \times 10^{23}\). The mass of one mole of a substance in grams equals its molecular mass in daltons: one mole of glucose (C6H12O6) weighs about 180 g. Molarity (M) is moles of solute per liter of solution. A 1 M glucose solution has 180 g of glucose per liter; 1 mM (millimolar) is a thousandth of that.

To dilute a stock solution, use the fact that the amount of solute does not change: \(C_1 V_1 = C_2 V_2\), where \(C_1\) and \(V_1\) are the concentration and volume of the stock, and \(C_2\) and \(V_2\) those of the diluted solution.

# Grams needed for a solution, and a dilution using C1 V1 = C2 V2
def grams_needed(molar_mass_g_per_mol, molarity_M, volume_L):
    return molar_mass_g_per_mol * molarity_M * volume_L

print("Glucose, 5 mM, 0.5 L:", round(grams_needed(180.16, 0.005, 0.5), 3), "g")
print("NaCl, 150 mM, 1 L:  ", round(grams_needed(58.44, 0.150, 1.0), 2), "g")

def stock_volume(c_stock, c_final, v_final):
    return c_final * v_final / c_stock

v1 = stock_volume(1000, 150, 250)    # mM, mM, mL
print("Stock needed:", v1, "mL; water:", 250 - v1, "mL")

Glucose, 5 mM, 0.5 L: 0.45 g
NaCl, 150 mM, 1 L:   8.77 g
Stock needed: 37.5 mL; water: 212.5 mL

Acids, bases and pH

Water molecules occasionally split into a hydrogen ion (H+, in reality attached to another water molecule as H3O+) and a hydroxide ion (OH−). In pure water at 25 °C the concentration of each is \(10^{-7}\) M. Acids are substances that release hydrogen ions and raise their concentration; bases remove hydrogen ions or release hydroxide.

Because hydrogen ion concentrations span many powers of ten, biologists use a logarithmic scale: \(\text{pH} = -\log_{10}[\text{H}^+]\). Pure water has pH 7. Each unit lower means ten times more hydrogen ions: a solution at pH 4 is a thousand times more acidic than one at pH 7.

Most of the inside of a cell is kept near pH 7.2, and human blood between 7.35 and 7.45. Some compartments are deliberately different: lysosomes, the cell's digestive organelles, are kept near pH 4.5 to 5 so that their enzymes work, and the stomach is near pH 2. Small changes matter, because the charges on proteins depend on pH, and a protein's shape depends on its charges. Blood pH below about 7.35 is called acidosis and is a medical emergency when severe.

import math
# Hydrogen ion concentration and pH
for label, h in [("pure water", 1e-7), ("cytoplasm", 6.3e-8), ("lysosome", 3.2e-5), ("stomach", 1e-2)]:
    print(f"{label:<11} [H+] = {h:.1e} M  ->  pH {-math.log10(h):.1f}")

ratio = 10 ** (7.2 - 4.7)
print(f"A lysosome at pH 4.7 has {ratio:.0f} times the [H+] of cytoplasm at pH 7.2")

pure water  [H+] = 1.0e-07 M  ->  pH 7.0
cytoplasm   [H+] = 6.3e-08 M  ->  pH 7.2
lysosome    [H+] = 3.2e-05 M  ->  pH 4.5
stomach     [H+] = 1.0e-02 M  ->  pH 2.0
A lysosome at pH 4.7 has 316 times the [H+] of cytoplasm at pH 7.2

Buffers keep pH steady

Cells and body fluids resist pH changes using buffers: mixtures of a weak acid and its conjugate base that can absorb added H+ or OH−. When acid is added, the base form picks up the extra hydrogen ions; when base is added, the acid form releases hydrogen ions to neutralize it. The main buffer in blood is the carbonic acid and bicarbonate pair; inside cells, phosphate ions and the side chains of proteins do much of the work.

The Henderson–Hasselbalch equation relates pH to the ratio of base to acid: \(\text{pH} = \text{p}K_a + \log_{10}\frac{[\text{A}^-]}{[\text{HA}]}\). The \(\text{p}K_a\) is the pH at which the acid is half dissociated. A buffer works best within about one pH unit of its \(\text{p}K_a\), where both forms are present in useful amounts.

import math
# Henderson-Hasselbalch: pH of a phosphate buffer (pKa about 6.86 at 25 C)
pKa = 6.86
for base, acid in [(1, 9), (1, 1), (2, 1), (9, 1)]:
    pH = pKa + math.log10(base / acid)
    print(f"[HPO4 2-]:[H2PO4 -] = {base}:{acid}  ->  pH {pH:.2f}")

# Ratio needed for pH 7.2
target = 7.2
print("Ratio needed for pH 7.2:", round(10 ** (target - pKa), 2), "to 1")

[HPO4 2-]:[H2PO4 -] = 1:9  ->  pH 5.91
[HPO4 2-]:[H2PO4 -] = 1:1  ->  pH 6.86
[HPO4 2-]:[H2PO4 -] = 2:1  ->  pH 7.16
[HPO4 2-]:[H2PO4 -] = 9:1  ->  pH 7.81
Ratio needed for pH 7.2: 2.19 to 1

Laboratory buffers such as phosphate-buffered saline (PBS) and HEPES are chosen for the same reason: they hold pH near 7.2 to 7.4 so that cells and proteins behave as they would in the body. Lesson 4 and the capstone in lesson 12 use them.

Functional groups: chemistry's building blocks

Organic molecules are carbon skeletons decorated with small clusters of atoms called functional groups. Each group behaves in a characteristic way, so knowing a handful of them lets you predict how a molecule will behave: whether it dissolves in water, carries a charge at cell pH, or reacts with other molecules.

Note that an amino acid has both a carboxyl group and an amino group. At pH 7 the carboxyl loses a hydrogen ion and the amino group gains one, so a single amino acid carries both a negative and a positive charge. That dual behavior, and the side chains attached to it, is the starting point for protein structure in lesson 3.