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You don't need to know any biology in order to study biological molecules, but it does help to have some background.

Aims

This chapter will briefly review the bare bones of biological (macro)molecules. By the end, and together with your previous knowledge and some background reading, you should be able to:

  • Describe the basic chemical structures of polypeptides, polynucleotides, fats, lipids, and carbohydrates

  • Explain what is meant by the primary, secondary, tertiary and quaternary structure of proteins

  • Describe the behaviour of fats, lipids and detergents in water

  • Explain the anomalous properties of liquid water

  • Recall the fundamentals of acid–base equilibrium

This book is mainly about the experimental methods used to understand the physical properties and function of the molecules that make up living systems.

These molecules—proteins, polynucleotides, polysaccharides, lipids—are not necessarily any different from molecules we study in other branches of chemistry. But there are some additional factors, arising from their biological origin, which we need to be aware of.

  • Biological macromolecules are large molecules formed from many smaller units and are (usually) polymers of precise length and specific sequence.

  • They (usually) fold or associate into specific conformational assemblies stabilized by non-covalent interactions.

  • This (usually) happens in water.

  • The molecules are the (usually) successful outcomes of biological evolution.

It is this last point that makes things so exciting for the biophysical chemist. The molecules we see today are the results of countless random (more or less) experiments over millions of years during which living systems have evolved to take advantage of subtle principles of physical chemistry that we barely yet understand. By studying such systems we can learn much about physical chemistry in general, with potential for applications in other areas.

Proteins are polymers made up of specific sequences of l-amino acids linked together by covalent peptide (amide) bonds (Figure 1.1). Amino acids are chosen from a basic set of 20 building blocks differing in side chain (Figure 1.2), with occasional special purpose side chains made to order (e.g. hydroxyproline).

Figure 1.1

Polypeptide structure showing rotatable ϕ/ψ angles. The planar peptide (amide) bonds are shown in bold and are usually trans.

Figure 1.1

Polypeptide structure showing rotatable ϕ/ψ angles. The planar peptide (amide) bonds are shown in bold and are usually trans.

Close modal
Figure 1.2

The 20 naturally occurring amino acid side chains (residues) with their three-letter and single-letter abbreviations.

Figure 1.2

The 20 naturally occurring amino acid side chains (residues) with their three-letter and single-letter abbreviations.

Close modal

d-amino acids are encountered only in special instances such as bacterial cell walls and peptide antibiotics.

Typical proteins range in polypeptide chain length from around 50 to 5000 amino acids. The average relative molecular mass of an amino acid is around 110, so proteins can have RMMs from 500 to 500 000 (0.5–500 kDa) or more—especially in multi-subunit proteins consisting of specific aggregates (see Table 1.1).

The term ‘molecular weight’ is not strictly accurate (why?) but is commonly used, especially in the older (biochemical) literature. The more correct terms are ‘relative molecular mass (RMM)’ (no units) or ‘molar mass’ (kg mol−1 or g mol−1). One dalton (1 Da) is equal to 1 amu (atomic mass unit).

Table 1.1

Some common proteins

NameNo. of amino acidsRMMFunction
Insulin 51 (2 chains, 21+30) 5784 Hormone controlling blood sugar levels. A-chain and B-chain covalently linked by disulfide bonds. Globular. 
Lysozyme (hen egg white) 129 14 313 An enzyme that catalyses hydrolysis of bacterial cell wall polysaccharides. Found in egg white, tears and other biological secretions. Globular. 
Myoglobin 153 17 053 Oxygen transporter in muscle. Contains haem group. Globular. 
Haemoglobin 574 (2×141 + 2×146) 61 986 (2×15 126 + 2×15 867) Oxygen transporter in blood stream. Consists of four subunits (2 α and 2 β chains), with haem. Globular. 
Rhodopsin 348 38 892 Photoreceptor membrane protein in the retina of the eye. Contains 11-cis retinal as chromophore. 
Collagen 3200 (approx. 3×1060) 345 000 Connective tissue protein of skin, bone, tendon, etc. Three-stranded triple helix. Most abundant protein in animals. Fibrillar. 
RuBISCO (ribulose bisphosphate carboxylase/ oxygenase) 4784 (8×475+8×123) 538 104 (8×52 656+8×14 607) Carbon fixation enzyme of green plants and algae; 16 subunits (eight large, eight small). Most abundant protein on Earth. 
NameNo. of amino acidsRMMFunction
Insulin 51 (2 chains, 21+30) 5784 Hormone controlling blood sugar levels. A-chain and B-chain covalently linked by disulfide bonds. Globular. 
Lysozyme (hen egg white) 129 14 313 An enzyme that catalyses hydrolysis of bacterial cell wall polysaccharides. Found in egg white, tears and other biological secretions. Globular. 
Myoglobin 153 17 053 Oxygen transporter in muscle. Contains haem group. Globular. 
Haemoglobin 574 (2×141 + 2×146) 61 986 (2×15 126 + 2×15 867) Oxygen transporter in blood stream. Consists of four subunits (2 α and 2 β chains), with haem. Globular. 
Rhodopsin 348 38 892 Photoreceptor membrane protein in the retina of the eye. Contains 11-cis retinal as chromophore. 
Collagen 3200 (approx. 3×1060) 345 000 Connective tissue protein of skin, bone, tendon, etc. Three-stranded triple helix. Most abundant protein in animals. Fibrillar. 
RuBISCO (ribulose bisphosphate carboxylase/ oxygenase) 4784 (8×475+8×123) 538 104 (8×52 656+8×14 607) Carbon fixation enzyme of green plants and algae; 16 subunits (eight large, eight small). Most abundant protein on Earth. 
Worked Problem 1.1
  • Q: How many molecules are there in a 1 mg sample of a protein of 25 000 RMM?

  • A: 25 000 RMM ≡ 25 000 g mol−1

    graphic

Worked Problem 1.2
  • Q: In a 1 mg cm−3 solution of proteins with RMM 25 000, roughly how far apart are the molecules on average?

  • A: Volume per molecule=1 (cm3)/2.4×1016=4.2×10−17 cm3.

So each molecule might occupy a cube of side 3.5×10−6 cm (cube root of the volume), or 35 nm.

Worked Problem 1.3
  • Q: How does the answer to Worked Problem 1.2 compare to the size of one 25 000 RMM molecule?

  • A: Mass of 1 molecule=25 000/6×1023=4.2×10−20 g.

This corresponds to a molecular volume of around 4.2×10−20 cm3, assuming a density similar to water. This corresponds to a cube of side approximately 3.5 nm.

So in a 1 mg cm−3 solution, these molecules are separated on average by about 10 molecular diameters.

Proteins function as enzymes (biological catalysts), antibodies, messengers, carriers, receptors, structural units, etc. Their chemical structure and molecular conformation are commonly described in terms of:

Primary structure: the sequence of amino acids in the polypeptide chain (see Figure 1.3). This is unique to each protein, and is determined (primarily) by the genetic information encoded in the DNA of the relevant gene.

Figure 1.3

Primary structure of a 130-residue protein (human lysozyme) shown using single-letter amino acid codes.

Figure 1.3

Primary structure of a 130-residue protein (human lysozyme) shown using single-letter amino acid codes.

Close modal

Secondary structure: regular, repeating structures such as α-helix, β-sheets, etc. (see Figure 1.4).

Figure 1.4

Secondary structure.

Figure 1.4

Secondary structure.

Close modal

Tertiary structure: the three-dimensional arrangement of secondary structure elements that defines the overall conformation of the (globular) protein (see Figure 1.5).

Figure 1.5

Tertiary structure.

Figure 1.5

Tertiary structure.

Close modal

Quaternary structure: in multi-subunit proteins, the three-dimensional arrangement of the subunits (see Figure 1.6).

Figure 1.6

Quaternary structure.

Figure 1.6

Quaternary structure.

Close modal

Haemoglobin, for example, is made up of four globular subunits—two of one kind (α) and two of another (β)—which combine to form a tetramer quaternary structure. Interaction between these subunits is responsible for the delicate control of oxygen uptake and release by the haem groups in this protein.

Because of rotational flexibility in the polypeptide backbone, primarily around the N–Cα (ϕ) and Cα–C (ψ) angles, there is a very large number of possible conformations that any one polypeptide molecule might adopt. Unlike most synthetic polymers, however, proteins have the ability to fold up (under the right conditions) into specific conformations and it is these conformations (structures) that give rise to their individual properties.

Box 1.1 The ‘Protein Folding Problem’

Most proteins do not have a problem folding—they just do it. However, we have a problem understanding how they do it and predicting what the conformation of a particular amino acid sequence will be.

The complexity of the problem was highlighted some years ago by Cyrus Levinthal,1  a computer scientist who was one of the first to tackle the problem.

Each ϕ or ψ angle in a peptide might have roughly three possible values, giving 3×3=9 possible conformers for each peptide (not counting side chain conformers). For even a small polypeptide of 100 amino acids, this corresponds to at least 9100 ≈ 3×1095 possible different conformations of the polypeptide chain—only one of which (or a relatively small set) will be the ‘correct’ one.

You may be surprised to find that your calculator has trouble doing calculations such as 9100. Why? How can you get around it?

Assuming (optimistically) that peptide conformations can switch on the femtosecond timescale (10−15 sec), it would take a time of order 3 × 1080 seconds or about 1073 years to search through all these possibilities to find the right one. This is a time much longer than the known age of the Universe. Yet proteins actually fold quite rapidly, in microseconds to minutes, depending on the protein and conditions. This is the so-called ‘Levinthal Paradox’.

It is not really a paradox, of course. What it means is that polypeptides do not need to explore all possible conformations before they find the right one. Just as in any other rate process, there are kinetic pathways or reaction mechanisms that direct the system to the required state, in the same way that the water molecules in a mountain stream do not need to try all possible paths before finding they should flow downhill.

However, what Levinthal was pointing out was that if we don't know these pathways for protein folding, a computational search for the correct fold—no matter how powerful our computers—is doomed to failure.

Repetition of the same ϕψ angles from one amino acid to the next gives rise to a regular secondary structure element, of which α-helix and β-sheets are the most common examples. In these structures the ϕψ angles repeat in such a way that hydrogen bonds may form between different peptide groups to stabilize the structure.

Many structural elements such as loops, turns or other motifs that determine the tertiary structure of the protein do not have a regular repeating ϕψ signature, but are nonetheless unique.

The term ‘random coil’ is sometimes used incorrectly to designate non-regular structural elements within a protein structure. There is of course nothing random about this: the ϕ–ψ angles are well defined.

One important feature is that, in samples of a particular protein (if pure and properly folded), all the molecules will have the same conformation, give or take a little bit of variation due to thermal fluctuation. This contrasts with the situation normally found in polymer chemistry, where the macromolecules rarely have a well-defined structure and samples are made up of a heterogeneous mix of conformations, quite often in dynamic interconversion.

Folded proteins are relatively unstable and can unfold (‘denature’) easily—especially with change in temperature or pH, or on addition of chemical denaturants such as urea, guanidine hydrochloride or alcohols. Denatured proteins have lost their tertiary and quaternary structure, but may retain some secondary structure features. They rarely approach the true random coil state.

A true ‘random coil’ is a hypothetical state in which the conformation (ϕ–ψ angles) of any one peptide group is totally uncorrelated with any other in the chain, and especially its neighbours.

Unfolded protein is also quite sticky stuff and has a tendency to aggregate with other denatured proteins or to stick to surfaces.

Traditional animal glues are made from denatured skin and bone. The main connective tissue protein, collagen, takes its name from the Greek word for glue.

This intrinsic stickiness of unfolded polypeptides appears to be one of the causes of prion diseases and other amyloid-related conditions such as mad cow disease, CJD and Alzheimer's. In such conditions, unfolded or misfolded proteins aggregate into lumps or ‘plaques’ that interfere with normal cell function.

The genetic information which encodes protein sequences is found in DNA (deoxyribonucleic acid), and the transcription and translation process involves RNA (ribonucleic acid). Both are polynucleotides consisting of long sequences of nucleic acids made up of a phosphoribose backbone with a choice of four different purine or pyrimidine side-chains or ‘bases’ attached (see Figures 1.7 and 1.8).

Figure 1.7

DNA structure illustrating the deoxyribose–phosphate backbone to which may be attached purine (A, G) or pyrimidine (C, T) bases.

Figure 1.7

DNA structure illustrating the deoxyribose–phosphate backbone to which may be attached purine (A, G) or pyrimidine (C, T) bases.

Close modal
Figure 1.8

RNA structure illustrating the sugar (ribose) -phosphate backbone, to which may be attached purine (A, G) or pyrimidine (C, U) bases.

Figure 1.8

RNA structure illustrating the sugar (ribose) -phosphate backbone, to which may be attached purine (A, G) or pyrimidine (C, U) bases.

Close modal

The specific, complementary base pairing in the double helical structures of DNA and RNA (Figure 1.9) is what gives rise to the ability to translate and proliferate this genetic information. (See Further Reading: Biology for Chemists for molecular biology details.)

Figure 1.9

Complementary base pairing (Watson–Crick) in DNA (RNA is similar, with uracil replacing thymine).

Figure 1.9

Complementary base pairing (Watson–Crick) in DNA (RNA is similar, with uracil replacing thymine).

Close modal

When complementary strands of DNA and/or RNA come together, they form the characteristic right-handed double helix structures that lie at the heart of molecular biology. In the most common form (‘B-DNA’), the base pairs stack in a twisted ladder-like conformation, with the purine–pyrimidine rings lying flat and perpendicular to the helix axis and spaced 0.34 nm apart. The negatively charged sugar–phosphate backbone lies to the outside of this cylindrical structure, which is roughly 2 nm in diameter.

Worked Problem 1.4
  • Q: The DNA in each of your cells (i.e. the human genome) contains about three billion (3×109) base pairs. How far would this stretch if laid out in a straight line?

  • A: Assume 0.34 nm spacing: 3×109×3.4×10−10=1.02 m.

One of the major challenges of current research is to understand how such long DNA polymers are packaged within the cell nucleus while still allowing access for genetic control and transcription. See Further Reading for more detail.

Many other polynucleotide conformations are possible, including the left-handed helical ‘Z-DNA’ and more complicated structures thought to be involved in chain replication, together with supercoiling and more globular structures in single-stranded transfer RNA.

Complex polysaccharides such as starch, glycogen, cellulose, etc. play an important part in biochemistry both as energy stores and structural components. Many proteins are glycosylated (‘glycoproteins’), with oligosaccharide chains (often branched) attached to specific amino acid residues, usually at the protein surface. The carbohydrate portion of glycoproteins is often involved in antigenicity, cell receptor and other molecular recognition processes.

Reminder: glycosylation is the covalent attachment of carbohydrate (sugar) groups; an oligosaccharide is a short chain polymer of sugars.

Human blood groups are determined by the different oligosaccharides attached to glycoproteins and glycolipids on red blood cells.

Polysaccharides (and the smaller oligosaccharides) are polymers formed by linkage of individual sugar monomers, and may be linear (e.g. cellulose) or branched (e.g. glycogen).

Although some regular secondary structure is sometimes seen (e.g. in cellulose fibres), the complexity of chemical composition and polymer chain branching leads to much more disordered structures (or, at least, structures that are usually too complex to determine). This is why our understanding of polysaccharide structures and their interactions is still very poor.

Fats and lipids are common terms for those bits of biological organisms that are insoluble in water but can be extracted with organic solvents such as trichloromethane (chloroform), ethers, etc. They generally consist of a polar head group attached to non-polar tails of unbranched hydrocarbons. This amphiphilic nature (hydrophilic head, hydrophobic tail) gives this class of molecule important properties that are exploited both by biology itself, and by biophysical chemists in studying such systems.2 

Broadly speaking, the number of hydrocarbon tails governs the behaviour in water.

Detergents generally contain a polar head group attached to a single non-polar tail (or equivalent). This allows them to form micelles in water, i.e. roughly globular assemblies of a number of molecules clustered together, with their head groups exposed to water, while their non-polar tails are buried inside the cluster and away from direct contact with the surrounding water (see Figure 1.10).

Figure 1.10

A micelle.

Detergents can solubilize or disperse other non-polar molecules in water. In the laboratory they can be used to solubilize membrane proteins. Bile salts are detergent-like molecules synthesized in the gall bladder and secreted in the small intestine to assist the dispersion and digestion of fats.

Lipids have two tails. This makes it difficult to pack the hydrocarbon chains effectively into a globular micelle structure, but they can form lipid bilayers instead (see Figure 1.11). Here the molecules form into two-dimensional arrays or sheets, in which two layers of lipids bury their tails inside, leaving the hydrophilic heads exposed either side to the water. These lipid bilayers provide the basic structures of cell membranes.

Figure 1.11

Lipid bilayer.

Figure 1.11

Lipid bilayer.

Close modal

The fluid mosaic model pictures biological membranes as dynamic, two-dimensional seas of lipid bilayer, within which float the multitude of proteins and other molecules. These membrane-associated macromolecules may be partially submerged in the lipid bilayer or may traverse the entire membrane. Other peripheral membrane proteins may be more loosely associated at the surface of the bilayer.

Neutral fats or triglycerides commonly have three tails (Figure 1.12). This makes it difficult to form a compromise between the hydrophilic head and the bulky hydrophobic tails, so these substances tend to be very insoluble and just form an amorphous mass in water. This is what we commonly see as ‘fat’.

Alkaline hydrolysis of the ester groups in triglycerides (e.g. conversion of glyceryl tristearate to sodium stearate) has been used since ancient times to convert fat into soap.

Triglycerides (‘fats’) act as concentrated, long-term metabolic energy stores (as opposed to glycogen, which can be metabolized more rapidly, but has a lower metabolic energy density).

The metabolic oxidation energy or ‘calorific value’ of carbohydrates (glycogen) is around 17 kJ g−1 compared to about 39 kJ g−1 for fats (triglycerides). Moreover polysaccharides absorb a lot of water (typically around 2 g water per gram of carbohydrate), so it takes almost 7 g of hydrated glycogen to provide the same energy as 1 g of fat. (This is why people on long-distance walks to the North or South Poles eat a high fat diet.)

Life evolved in an aqueous environment, and water is the major component in most biological organisms and tissues. Despite its familiarity, water is an unusual liquid in many ways, with several apparently anomalous properties.

Compared to molecules of a similar size, water has a much higher melting point and boiling point, and the liquid has an unusually high heat capacity, surface tension and dielectric constant.

Solid water (ice) at 0 °C has a lower density than the liquid, so ice floats on water. This volume contraction on melting continues as the temperature is increased to about 4 °C, where liquid water has its highest density under normal conditions (Figure 1.13).

Figure 1.13

The density of ice and liquid water as a function of temperature (at atmospheric pressure). Solid ice has a much lower density (0.915 g cm−3) than water (left panel). Liquid water (expanded scale, right panel) has a maximum density at around 4 °C.

Figure 1.13

The density of ice and liquid water as a function of temperature (at atmospheric pressure). Solid ice has a much lower density (0.915 g cm−3) than water (left panel). Liquid water (expanded scale, right panel) has a maximum density at around 4 °C.

Close modal

The survival of life on Earth is often attributed to these anomalous volumetric properties. During winter, ice floats on the lake surface acting as a thermal insulator to prevent further freezing. Meanwhile, the bottom of the lake remains comfortably liquid at 4 °C.

All of these anomalous properties can be attributed to the polarity and hydrogen bonding ability of the water molecule. Because of the molecular structure, and the ability to act as both hydrogen bond donor and acceptor, the most favourable interactions occur in a tetrahedral arrangement in which one water molecule may interact with up to four neighbouring water molecules. Consequently, the normal structure of crystalline ice involves a quite open tetrahedral lattice linked by hydrogen bonding (Figure 1.14).

Figure 1.14

The tetrahedral crystal structure of ordinary ice.

Figure 1.14

The tetrahedral crystal structure of ordinary ice.

Close modal

Most substances expand on heating because the increased thermal motion leads to larger average intermolecular distances. However when ice melts (at 0 °C), some of the hydrogen bonds break and the lattice becomes more flexible and dynamic, and some of the molecules can fall into the interstitial gaps to give a denser structure. This continues until around 4 °C where the gradually increasing thermal motion takes over, and the more usual thermal expansion occurs.

However, hydrogen bonding and residual tetrahedral structure persist in the liquid, although now in a much more dynamic and less ordered fashion, and to a lesser extent as the temperature rises. This residual hydrogen bonding contributes to the high heat capacity of liquid water. The heat capacity of a substance represents the energy required to raise the temperature of the substance by a given amount. In the case of liquid water, some of the energy goes into breaking intermolecular hydrogen bonds rather than molecular kinetic energy, so it takes more energy to bring about a rise in temperature than would otherwise be the case.

‘Temperature’ is a measure of how we feel the kinetic energy of the random movements of atoms and molecules in any substance. The higgledy-piggledy rotational, vibrational, and translational motions of atoms and molecules increase with temperature.

The high surface tension of water and its inability to wet greasy surfaces is also a consequence of this residual hydrogen-bonded structure. Water molecules at air–water interfaces or non-polar surfaces are less able to adopt the energetically preferred tetrahedral arrangement. Soaps and detergents can overcome this by forming an amphiphilic layer at the interface.

The dielectric constant or relative permittivityr) of a substance is a measure of its polarizability in an electric field. For water at room temperature, εr≈80 (compared to one for a vacuum). This very high value arises because the dipolar water molecules tend to reorient and align parallel to the electric field. This has the effect of partially cancelling the electric field and results in a weakening of electrostatic interactions between charged groups. Figure 1.15 

Figure 1.15

Molecular dipoles tend to align parallel to an electric field. Thermal motion will tend to disrupt this reorientation.

Figure 1.15

Molecular dipoles tend to align parallel to an electric field. Thermal motion will tend to disrupt this reorientation.

Close modal

Remember that the electrostatic (Coulomb) potential energy between two charges, q1 and q2, separated by a distance r, is given by:

graphic

Consequently, the high value of εr has a significant effect on interactions between charges in water.

This is why salts are soluble and tend to dissociate into ions in water, but not in less polar solvents.

Because water molecules have such a high affinity for each other, non-polar molecules have difficulty fitting in to aqueous solutions. This is known as the hydrophobic effect. We know from experience that oil and water do not mix. Non-polar molecules are unable to form hydrogen bonds, so they cannot be accommodated easily within the partially hydrogen-bonded structures of liquid water. This leads to an apparent repulsion between water and non-polar molecules, such that the non-polar groups tend to be insoluble in the water and form separate phases or aggregates with other non-polar groups.

It is not that the individual water molecules repel the non-polar groups (they don't), but that the collective affinity of the water molecules for each other tends to exclude others that do not have similar hydrogen bonding tendencies.

Due to dipole : induced-dipole interactions, the attractive force between an isolated water molecule and a nearby non-polar molecule in a vacuum is probably greater than between two non-polar molecules under similar circumstances. That is why the build-up of static electricity tends to attract dust.

One peculiar property of hydrophobic interactions is that they appear to get stronger with increasing temperature, at least at low temperatures. This is illustrated by the observation that the solubility in water of many non-polar compounds becomes smaller as the temperature is raised.2 

Although oil and water do not mix of their own accord, this can be done if we are willing to put work into it or use some means of circumventing the hydrophobic tendencies. Foams and emulsions are examples of dispersions of small air bubbles or fatty globules in water, and such materials play significant roles in food technology, cosmetics and related industries. They are normally produced by ‘whipping’ (mechanical agitation) or ‘sparging’ (blowing bubbles). It requires a lot of energy to overcome the water surface tension but this can be reduced by adding detergents or other surfactant molecules that reduce the effective surface tension by forming an amphiphilic layer at the interface—like a micelle (see Section 1.5), with the polar groups in contact with water and the non-polar tails towards the more hydrophobic air or oily globule.

This will be familiar from everyday experience with soaps, shampoos and other domestic cleaning products. But foams and emulsions are inherently unstable and will tend to collapse over time (see Box 1.2). Because of the high surface area to volume ratio, small bubbles or globules have a higher surface energy (more hydrophobic area exposed to water) and will merge to form larger bubbles or droplets. Denatured (unfolded) proteins often have good surfactant properties. Conversely, foaming will tend to denature proteins in solution and is best avoided.

Molecules with detergent-like properties are relatively rare in biology because of their tendency to disrupt biological membranes. However, there are some examples of proteins that have evolved to have biocompatible surfactant activities in specific instances.3  Latherin is a protein from horse sweat that allows the sweat to spread better on the oily horsehair. Ranaspumins are proteins involved in constructing the foam nests of some tropical frogs. Hydrophobins are proteins produced by fungi to reduce surface tension and help them grow in thin water films. And our lungs contain specific phospholipid and carbohydrate-associated proteins that reduce surface tension forces between alveolar surfaces to help us breath more easily.

Box 1.2 Surface Tension and the Pressure Inside a Bubble

Surface tension (γ) can be defined as the force per unit length at a line or edge in the liquid interface. (γ=0.073 N m−1 for water at an air interface.)

A bubble of radius r will have an excess pressure, ΔP, that can be estimated by considering the balance of forces indicated in Figure 1.16. At mechanical equilibrium, the force exerted by the excess pressure on the circular cross-section area (area×pressure=πr2ΔP) is balanced by the surface tension force in the perimeter (circumference×surface tension=2πrγ).

graphic

Figure 1.16

The balance of forces in a bubble.

Figure 1.16

The balance of forces in a bubble.

Close modal

Consequently, the excess pressure inside a bubble is inversely proportional to its radius. Smaller bubbles will tend to coalesce or gas (air) will diffuse from one to the other to form larger bubbles. Solitary bubbles or bubbles at the surface of a foam will tend to burst if they can.

Similar principles apply to dispersions of fatty droplets in aqueous emulsions.

The acid–base properties of water, together with its solvent polarity, mean that free charged groups (ions) are common and that most biological macromolecules must be regarded as polyelectrolyes, i.e. large molecules with multiple charges.

To summarize:

graphic

The equilibrium constant for this (remembering the thermodynamic convention that the activity of H2O(l)=1) is KW=[H+][OH]=10−14 mol2 dm−6 at 25 °C.

The bare proton (H+ ion) does not really exists as a free entity in solution, but is better represented as H3O+, [H9O4]+, or other complex species. However, H+ is a convenient shorthand.

For hypothetically pure water at 25 °C, [H+]=[OH]=10−7 mol dm−3.

Hydrogen ion concentration is more conveniently expressed using the logarithmic pH scale, in which pH=−log10[H+].

Strictly speaking, we should talk in terms of ‘activity’ rather than ‘concentration’ here. The thermodynamic activity of a solute is its concentration multiplied by a fudge factor (called ‘activity coefficient’) that takes account of some of the intermolecular interactions in solution. For dilute solutions, the difference is rarely significant.

Worked Problem 1.5
  • Q: The measured pH of ‘ultrapure’ laboratory water is frequently below pH 7. Why might this be?

  • A: Several reasons:

    1. Dissolved atmospheric CO2 (carbonic acid) if the water has been left standing for a while

    2. pH not measured at 25 °C (H+ dissociation increases with temperature)

    3. Contamination from an unwashed pH electrode

    4. pH meter wrongly calibrated

Acidic and basic groups in solution can take part in this equilibrium exchange of protons:

graphic
with the acid dissociation constant, KA=[A][H+]/[AH] and pKA=−log10KA.

The pKA of any group is most conveniently viewed as that pH at which the conjugate acid is 50% dissociated ([A]=[AH], so that KA=[H+] in these circumstances).

In proteins, the relevant groups are the acidic and basic amino acid side chains, and the N- and C-terminal peptide groups (Table 1.2). As a consequence, the overall charge on a protein molecule will depend on pH.

Table 1.2

Typical pKA and charge state for protein amino acid residues and other groups in water (see Figure 1.2 for amino acid structures and abbreviations)

GrouppH<pKATypical pKApH > pKA
C-terminus –COOH -COO 
Glu, Asp –COOH -COO 
His –Im–H+ –Im 
N-terminus –NH3+ –NH2 
Cys –SH –S 
Lys –NH3+ 11 –NH2 
Tyr –ϕ–OH 11 –ϕ–O 
Arg –C(NH2)2+ 12.5 –C(NH)(NH2
Phosphoglycerol R=CH2(OH)CH(OH)CH2-O R–P(OH)O2 5.6 R–PO32− 
GrouppH<pKATypical pKApH > pKA
C-terminus –COOH -COO 
Glu, Asp –COOH -COO 
His –Im–H+ –Im 
N-terminus –NH3+ –NH2 
Cys –SH –S 
Lys –NH3+ 11 –NH2 
Tyr –ϕ–OH 11 –ϕ–O 
Arg –C(NH2)2+ 12.5 –C(NH)(NH2
Phosphoglycerol R=CH2(OH)CH(OH)CH2-O R–P(OH)O2 5.6 R–PO32− 

Interactions with other groups and change in solvent environment in folded proteins can affect actual pK values.

Worked Problem 1.6
  • Q: Lysozyme is a small globular protein with antibiotic activity found in a variety of biological fluids. Typically it consists of a single polypeptide chain of around 129 amino acids (RMM 14 300), containing two glutamic acid (Glu), seven aspartic acid (Asp), six lysine (Lys), 11 arginine (Arg), three tyrosine (Tyr) and one histidine (His) residues, in addition to numerous other groups. What total charge might this protein have at pH 2, pH 7 or pH 12?

  • At pH 7 (pH > pKA for Asp, Glu, His and C-terminal groups, but pH<pKA for others), total charge=−2(Glu)–7(Asp)–1(C-terminal)+6(Lys)+11(Arg)+1(N-terminus)=+8.

    At pH 12 (pH > pKA for all groups other than Arg), total charge=−2(Glu) – 7(Asp) – 1(C-terminal) – 3(Tyr)+11(Arg)=−2.

    Note that these are only approximate estimates, since actual pKa values will depend on local environments within the protein.

Typical pH values for biological and other fluids are as follows:

  • blood pH 7.3–7.5

  • gastric juices pH 1–3

  • saliva pH 6.5–7.5

  • urine pH 5–8

  • milk pH 6.3–6.7

  • beer pH 4–5

  • wine pH 2–4

  • soft drinks pH 2–4

  • citrus fruits pH 1.8–4.

At low pH, most proteins will carry a net positive charge, whereas their overall charge will be negative at very high pH. The intermediate pH at which the net charge is zero is called the isoelectric point, pI. At this pH, the numbers of positively and negatively charged groups just balance. This will depend on the actual composition and conformation of the protein, and will determine its behaviour (mobility) in an electric field or in certain chromatographic processes (see Chapter 7) as well as its functional properties.

DNA and RNA will carry a net negative charge at neutral pH because of the phosphate backbone. (The purine and pyrimidine bases themselves are uncharged.)

Many lipids and carbohydrates may contain acidic or basic groups, so their charges may also depend on pH.

Because of the way in which molecular charge can affect biological properties, it is usually necessary to control the pH. Buffer solutions contain mixtures of conjugate acids and bases that can tolerate addition of H+ or OH without great change in pH. Buffering power is greatest when the desired pH is close to the pKA of the buffer components.

Oxygen binding by haemoglobin is very sensitive to pH. This is one of the reasons why pH control in the bloodstream and other tissues is particularly important.

Aqueous buffer solutions are frequently made up by adding similar amounts of a weak acid and its salt with a strong base (e.g. ethanoic acid and sodium ethanoate) to water (Table 1.3). Alternatively, one may start with a solution of weak acid (say) and titrate to the desired pH by addition of base.

Table 1.3

Typical buffers and their useful pH ranges

BufferpKAAHApH range
[AH]/[A]=10[AH]/[A]=1[AH]/[A]=0.1
Ethanoic acid/ sodium ethanoate 4.8 CH3COOH CH3COO 3.8 4.8 5.8 
Carbonic acid/ sodium carbonate 6.4 H2CO3 HCO3 5.4 6.4 7.4 
NaH2PO4/ Na2HPO4 7.2 H2PO4 HPO42− 6.2 7.7 8.2 
Ethylamine/ ethylamine-HCl C2H5NH3+ C2H5NH2 10 
    lowest useful pH best buffering pH highest useful pH 
BufferpKAAHApH range
[AH]/[A]=10[AH]/[A]=1[AH]/[A]=0.1
Ethanoic acid/ sodium ethanoate 4.8 CH3COOH CH3COO 3.8 4.8 5.8 
Carbonic acid/ sodium carbonate 6.4 H2CO3 HCO3 5.4 6.4 7.4 
NaH2PO4/ Na2HPO4 7.2 H2PO4 HPO42− 6.2 7.7 8.2 
Ethylamine/ ethylamine-HCl C2H5NH3+ C2H5NH2 10 
    lowest useful pH best buffering pH highest useful pH 

The equivalent for basic buffers is to mix the weak base and its salt with a strong acid (e.g. ethylamine and ethylamine-HCl), or to titrate the weak base solution with strong acid.

Box 1.3 How to Estimate Buffer pH

Buffering in aqueous solution is based on a weak acid–base equilibrium:

graphic

Buffering capacity is best around pH=pKA since there is likely to be sufficient [AH] and [A] in solution to accommodate addition of small amounts of strong base or acid without the pH straying outside this range.

Scientists are (mostly) human. Although we try to be systematic, logical, and consistent, we do have occasional lapses—sometimes for sheer laziness, sometimes for practical convenience. Consequently, and especially in an interdisciplinary subject such as this, you will encounter non-standard units and different terminologies. Although you will be familiar with SI units (and this book tries to be consistent in their use), you will already know that they are not always used elsewhere. For example, despite metrication, we still buy petrol in litres (or even gallons) and not cubic decimetres (dm3).

Here is a (partial) list of commonly used units and terms, together with their more consistent (SI) equivalents:

Non-standardStandard (SI)
Length micron (μ) 10−6 m 
 Angstrom unit, Å 10−10 m 
Volume litre, L dm3 
 mL cm3 
 μL, microlitre μdm3 
Concentration mg per mL, mg mL−1 mg cm−3 
 M, molar, molarity, moles per litre mol dm−3 
Relative molecular mass ‘molecular weight’ RMM 
 1 Dalton (1 Da) 1 amu 
Heat energy calorie (cal) Joule (J) 
 1 cal 4.184 J 
Non-standardStandard (SI)
Length micron (μ) 10−6 m 
 Angstrom unit, Å 10−10 m 
Volume litre, L dm3 
 mL cm3 
 μL, microlitre μdm3 
Concentration mg per mL, mg mL−1 mg cm−3 
 M, molar, molarity, moles per litre mol dm−3 
Relative molecular mass ‘molecular weight’ RMM 
 1 Dalton (1 Da) 1 amu 
Heat energy calorie (cal) Joule (J) 
 1 cal 4.184 J 

Summary of Key Points
  1. Biological systems are made up of structured macromolecules of specific sequence (proteins, nucleic acids, polysaccharides) and of smaller molecules (lipids, etc.) that self-assemble into larger structures.

  2. Secondary, tertiary, quaternary structures, assembly and interactions involve non-covalent forces.

  3. Water plays a dominant role in these interactions.

  • 1.1. Serum albumin (RMM approx. 65 000) is present in blood at a concentration of around 45 mg cm−3. Roughly how far apart are the protein molecules and how might this compare to their size?

  • 1.2. (a) How many possible conformers are there for a polypeptide made up of 100 amino acids? (b) Assuming that these conformers may switch on a femtosecond timescale (about the fastest possible for bond rotations), how long might it take to explore all possible conformers?

  • 1.3. How high might an average 70 kg person climb (or jump) on the energy provided by (a) 10 g of sugar; (b) 10 g of fat? Is this realistic? [Reminder: ‘calorific values’ are around 39 kJ g−1 for fat and 17 kJ g−1 for carbohydrate.]

  • 1.4. The average resting male produces about 7000 kJ of heat energy per day. How much fat might he therefore lose by just sitting around and doing nothing? [Reminder: the ‘calorific value’ of fat is around 39 kJ g−1.]

  • 1.5. Why is the water temperature at the bottom of a (partially) frozen lake usually around 4 °C?

  • 1.6. (a) List some of the anomalous properties of water that can be ascribed to hydrogen bonding. (b) Is this the bond that sank the Titanic?

  • 1.7. What is the electrostatic potential energy between a pair of Na+ and Cl ions, 0.5 nm (5 Å) apart: (a) in vacuum; (b) in water?

  • 1.8. (a) Why does the relative permittivity (dielectric constant) of water decrease with temperature? (b) How might this affect the strength of electrostatic interactions between opposite charges in water? (c) Are such interactions endothermic or exothermic?

  • 1.9. Popular newspapers sometimes state that the DNA molecule in a human cell is about 1.8 metres long or the height of Craig Venter (one of the scientists who led the Human Genome Project). Why might this differ from the estimate given in Worked Problem 1.4?

  • J. M. Berg, J. L. Tymoczko and L. Stryer, Biochemistry, Freeman, San Francisco, 6th edn, 2006.

  • S. Doonan, Peptides and Proteins, RSC Tutorial Chemistry Text, Royal Society of Chemistry, Cambridge, 2002.

  • S. Mitchell and P. Carmichael, Biology for Chemists, RSC Tutorial Chemistry Text, Royal Society of Chemistry, Cambridge, 2004.

  • N. C. Price, R. A. Dwek, R. G. Ratcliffe and M. R. Wormald, Physical Chemistry for Biochemists, Oxford University Press, Oxford, 3rd edn, 2001.

  • D. Sheehan, Physical Biochemistry: Principles and Applications, Wiley, New York, 2nd edn, 2009.

  • K. E. van Holde, W. C. Johnson and P. S. Ho, Principles of Physical Biochemistry, Prentice Hall, New York, 1998.

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