Baixe Física de Biopolímeros: introdução e conceitos gerais e outras Notas de estudo em PDF para Engenharia de Produção, somente na Docsity! 1 CHAPTER 1 BIOPOLYMERS In this chapter, the basic properties of biopolymers will be briefly discussed. We will group them according to nucleic acids, proteins and polysaccharides and we will summarize their main biological functions. Biopolymers have the unique feature that they exhibit a hierarchy in their molecular structures. Associated with these structures, their biological functions emerge almost naturally. In the latter context, think about the importance of the double- helical structure of DNA for the replication process. It is important to realize that these biological functions are based on the way the building blocks (nucleotides, amino acids, carbohydrates, etc.) are assembled. We will subsequently present the primary, secondary and some tertiary structures of nucleic acids, proteins and polysaccharides and show how they are stabilized by interactions. However, a detailed discussion of the chemical composition of the various biopolymers and their biological functions is beyond the scope of this book and for this purpose the reader is referred to the dedicated literature (see, for instance, the textbooks of Mathews, van Holde and Ahern and Bloomfield, Crothers and Tinoco).1,2 1.1 Introduction Biopolymers or biomacromolecules can be roughly classified according to three different categories: nucleic acids, proteins and polysaccharides (carbohydrates). It should be born in mind that this classification is not strict and that there are important exceptions. An example is glycoprotein, which is a combination of protein and carbohydrate and plays a role in, among others, immune cell recognition and tissue adhesion. The biological functions of nucleic acids, proteins and polysaccharides are also different. Nucleic acids are 2 Introduction to Biopolymer Physics involved with the storage of the genetic code (DNA) and the translation of the genetic information into protein products (RNA). Proteins catalyze biochemical reactions (enzymes), have structural or mechanical functions or are important in cell signalling and immune responses. The structural components of plants are primarily composed of the polysaccharide cellulose. Bacteria excrete polysaccharides for adhesion to surfaces and to avoid dehydration. Examples of these polysaccharides are dextran, xanthan and pullulan, which have found wide-spread applications in pharmacy, biotechnology and the food industry. The classification according to the functioning of the biopolymers is also not unique. An important exception is the ribosome; an organelle on which proteins are assembled. A ribosome contains 65% RNA and 35% protein. It can be considered an enzyme, but its active site is made of RNA. However, the functioning and purpose of biopolymers in the machinery of life is beyond the scope of this book. Here, we intend to explore the extent to which their properties can be understood in terms of concepts from physics and mathematics. Like every polymer, biopolymers are strings or sequences of monomeric units or monomers for short. In many cases these strings are linear, but sometimes they are closed and circular, branched or even cross-linked. In the latter case, we are dealing with a gel. In this book, we will primarily focus on linear polymers, but we will also discuss star-branched polymers, spherical polymer brushes and closed circular, supercoiled DNA. The structure of any biopolymer is determined by the nature of the building blocks (i.e. the monomeric units) in combination with environmental conditions such as the temperature, the solvent (water) and the presence of salts and/or other molecular components. The monomeric units of nucleic acids, proteins and polysaccharides are largely different and will be discussed in the next section. A unique feature of biopolymers is that most of them are essentially heteropolymers, because they may contain a variety in monomeric units. The biological relevance of a biopolymer is ultimately based on the sequence of the monomers, i.e. the primary structure. In the case of DNA, the primary structure is the sequence of bases attached to the sugar rings, which determines the genetic code. For proteins, it is the amino acid sequence, which eventually determines, together with environmental conditions, their 3– dimensional shapes and biological functions. The properties of polysaccharides are also largely determined by the nature of the monomeric Chapter 1: Biopolymers 5 polymeric chain, in which the units are covalently linked by the phosphates. The monomeric units are the nucleotides. Each nucleotide is built around a five-carbon sugar; ribose in RNA and 2’–deoxyribose in DNA. In Fig. 1.1 the five carbon atoms of the sugar are counted from the one to which the base is attached at the right, down through the ring and then up to the fifth carbon at the upper left side. Besides a difference in bases, which will be discussed shortly, the chemical difference between RNA and DNA lies in the replacement of a hydroxyl group by a hydrogen atom at the 2’ position in DNA. The nucleotides are linked through the formation of a phosphodiester between the 5’ carbon of one nucleotide and the 3’ carbon of the next nucleotide. In this way, long nucleic acid chains sometimes contain millions of units which are attached to each other. It is important to realize that the string of nucleotides has a direction from the 3’ to the 5’ end. The phosphate group is a strong acid with a apK of around one. RNA and DNA are thus strong acids and under physiological conditions every phosphate moiety carries a negative charge. DNA and RNA are so-called polyelectrolytes and the presence of charge results in specific properties, such as an electrostatic contribution to the bending rigidity of the molecule. This and other effects of the presence of charge will be detailed in Chapter 3. The backbone of the nucleic acid molecule is a repetitive structure and by itself it cannot store information. It is clear that the information storage Sugar Sugar SugarSugar N N N NH N N NH O NH N N NH O HN NO O HN NO O N N Sugar 2 2 Guanine (G) DNA/RNA Adenine (A) DNA/RNA 2 Thymine (T) DNA Cytosine (C) DNA/RNA Uracil (U) RNA Figure 1.2 Pyrimidine (cytosine, C; thymine, T; uracil, U) and purine (adenine, A; guanine, G) bases in DNA and RNA. 6 Introduction to Biopolymer Physics capacity is derived from the sequence of bases, each of which is attached to the 1’ carbon of the sugar ring. There are two types of bases: the purines and pyrimidines. In the case of DNA, there are two purines, adenine (A) and guanine (G) and two pyrimidines, cytosine (C) and thymine (T). In the case of RNA, uracil (U) replaces thymine (see Fig. 1.2). DNA and RNA also contain a small fraction of chemically modified bases; some of these can induce alternate secondary structures, as will be discussed in Chapter 5. Note that the bases do not carry charge, but they can form hydrogen bonds. 1.2.2 Protein primary structure All proteins are polymers and their monomeric units are α− amino acids. The amino group is attached to the α− carbon, i.e. the carbon next to the carboxyl group. Under physiological conditions, the amino acid is in its zwitterionic form; the amino group has picked up a proton and has become positively charged and the carboxyl group has dissociated a proton and is negatively charged. Besides the amino group, a hydrogen atom and a side group are also attached to the α− carbon of every amino acid. The amino acids are distinguished by their different side groups. Twenty chemically different amino acids are incorporated in proteins; their structures are shown in Fig. 1.3. In the simplest case, glycine, the side group is just a hydrogen atom. The amino acids can be grouped according to the physical-chemical properties of the side group: aliphatic, hydroxyl or sulphur containing, cyclic (proline), aromatic, basic or acidic. It is clear that the higher order secondary and tertiary structures of proteins are intimately related to these properties, together with environmental factors such as the solvent quality. With the exception of glycine, there are always four different chemical groups attached to the α− carbon of every amino acid. Accordingly, amino acids are chiral and each one can occur in two different stereoisomers: the D– and L–forms. The L–form of alanine is displayed in Fig. 1.4; it has the amino, hydrogen, carboxyl and methyl groups arranged in a clockwise manner, when the α− carbon is viewed from the top with the amino and carboxyl groups pointing downwards and the hydrogen and methyl group pointing upwards. All amino acids incorporated by organisms into proteins are of the L–form. The chirality of the amino acids has an important consequence for the Chapter 1: Biopolymers 7 secondary structure. For instance, owing to the steric interactions among the side groups, only right-handed α−helixes are possible. Left-handed helixes can be obtained by using synthetic amino acids in the D–form. Amino acids can be covalently linked by the formation of a peptide bond between the α− carboxyl group and the α− amino group. This is illustrated in Fig. 1.4 for the link between alanine and glycine in order to form C COOH N H 3 - H C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - CH CH CH3 2 CH3CH3 CH CH3CH3 + + + + Glycine Alanine Valine Leucine Isoleucine Aliphatic OH NH C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - HCOH CH2 CH3 H C2 CH2 + + + + + Serine Cysteine Threonine Methionine Proline CH2 OH CH2 SH CH2 CH3 S CH C COOH N H 3 - CHCH3 CH2 + CH3 2 Hydroxyl or Sulphur Cyclic Phenylalanine Tyrosine Tryptophan Histidine Lysine Arginine 2CH 2CH 2CH HN N H + + + + + + + 2CH 2 CH2 N H3 CH CH2 CH2 + 2 CH2 C 2 CH CH2 NH + N H 2NH Aromatic Basic C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - C COOH N H 3 - 2 C NH2O + + + + Aspartic acid Glutamic acid Asparagine Glutamine Acidic CH2 - 2 CH COO - 2 CH 2CH CH C NH2O 2CH COO Figure 1.3 The twenty standard α− amino acids found in proteins. Note that they have been arranged according to the properties of the side group. In organisms, more different amino acids are present, but those are not incorporated in proteins. 10 Introduction to Biopolymer Physics polymer of maltotriose units. Three glucose units in maltotriose are connected by an ,1 4α− bond; whereas consecutive maltotriose units are connected by ,1 6α− bonds (see Fig. 1.6). Dextran is a branched polysaccharide made of many glucose molecules joined into chains of varying lengths. The linear chain sections are linked by ,1 6α− bonds between glucose units, while branches begin from ,1 3α− linkages (and in some cases, ,1 2α− and ,1 4α− linkages as well). Polysaccharides are never as complex as proteins or nucleic acids; they usually contain no more than two kinds of residues. Furthermore, polysaccharide chains have a random degree of polymerisation, in contrast with proteins and nucleic acids which are almost always of a defined length. OH O CH OH2 OH O OH O CH OH2 OH O OH O CH 2 OH O OH OH O CH 2 OH OH O OH O CH 2 OH O OH O CH 2 OH OH O OH O CH 2 OH OH O Pullulan Dextran Figure 1.6 Primary structures of pullulan and dextran. Pullulan is a linear polymer with a repeating maltotriose unit of three glucose units. Dextran has a branched structure with on average about 100 monomers between the branch points. Chapter 1: Biopolymers 11 In their basic form, polysaccharides are uncharged. However, they are often functionalized with carboxyl groups, phosphate groups and/or sulphuric ester groups. The monomeric units contain many hydroxyl groups, which can engage in intra- and inter-molecular formation of hydrogen bonds. This hydrogen bonding keeps the chains together and contributes to the high tensile strength of the polymeric material. In this context, it is interesting to note that other forms of functionalization also occur. For instance, chitin, which is a major component of the exoskeletons of crustaceans and insects, can be described as cellulose with one hydroxyl group on carbon 2 of each glucose unit substituted by an acetylated amino (acetylamine) group. This substitution allows for increased hydrogen bonding, which gives the matrix formed by the polymer increased strength. Some polysaccharides such as cellulose are insoluble in water, whereas for others (e.g. dextran or pullulan) water is a moderate to excellent solvent. 1.3 Secondary structures 1.3.1 Secondary structures of nucleic acids The bases of DNA and RNA can form base-pairs stabilized with hydrogen bonds. As shown in Fig. 1.7, adenine can form two hydrogen bonds with thymine, whereas guanine can form three hydrogen bonds with cytosine. With these pairing arrangements between the purines and pyrimidines, the distances between the 1’ carbons of the attached sugars are the same (1.08 nm). In this way, two opposing single strands with a complementary base sequence can form a double helix, which is regular in diameter. This would not be possible if purines pair with purines and/or pyrimidines with pyrimidines. Besides hydrogen bonding, the double helix is stabilized by dispersion forces resulting from correlated electron charge fluctuations in the stack of base-pairs. RNA is usually single-stranded, but most RNA molecules can form hair- pin structures by base-pairing of self-complementary regions within the same molecule. Single-stranded DNA with self-complementary base sequences can also fold back on itself and form single-chain stacked base structures. At elevated temperature and/or in the presence denaturing agents, the single- 12 Introduction to Biopolymer Physics stranded DNA molecule will take a random coil configuration. However, the canonical form of DNA is the double helix made of two complementary strands in an anti-parallel direction (the duplex). In the double helix, each strand can serve as a template for a complementary strand of DNA in the case of replication or for a complementary strand of messenger RNA in the case of the transcription of the genome for the synthesis of protein products. The bases from the two opposing DNA strands in the duplex are stacked in the interior of the helix, whereas the two anti-parallel sugar-phosphate backbones are extended along the outside. The helix has a major and minor groove. Three secondary structures of the double-stranded DNA molecule have been identified: the A–, B– and Z–forms. The average values of the most important structural parameters are collected in Table I.I and space-filling representations are shown in Fig. 1.8. The main distinguishing features of these different secondary structures of DNA are2 • The A– and B–forms are right-handed and can be found in any sequence. B is the dominant form under physiological conditions. The A–form is H H H H Sugar Sugar N N N N N N N O N N N N O Sugar N N O O N N Sugar Guanine Cytosine H H H Adenine Thymine H Figure 1.7 Base-pairing of thymine with adenine and cytosine with guanine. Chapter 1: Biopolymers 15 hydrogen on the fourth residue up the chain (separated by two residues). The hydrogen bonds are almost parallel to the helix axis. There is little or no steric interaction among the side groups, because they are pointing outwards away from the central axis of the helix. The α−helix has 3.6 residues per turn, which results in a rise of 0.15 nm per residue and a pitch of 0.54 nm per turn. In the less abundant 103 − helix, there is a hydrogen bond between the carbonyl oxygen and the amide hydrogen of the third residue up the chain. Accordingly, the 103 − helix is less compressed in the longitudinal direction with 3.0 residues per turn and a rise of 0.20 nm per residue. In the β− sheet, each residue is flipped by 180 degrees with respect to its preceding one and the polypeptide chain (β− strand) is folded in a zigzag fashion. As illustrated in Fig. 1.10, the linear hydrogen bonds are now formed R C N C O O O O O O O O C C C C C C C C N N N N N C C C C C C C N N C N O R R R R R R R R C C O C C C C C C N N N N C C C C C C N N C N N C C N C Figure 1.9 Left: Irregular α− helical secondary structure of polypeptides. The hydrogen bonds between the carbonyl oxygen and the amide hydrogen are within a single polypeptide chain and almost parallel to the helix axis. The side groups point outwards. Right: Schematic helical ribbon representation showing the atoms of the backbone atoms only. 16 Introduction to Biopolymer Physics between adjacent chains almost perpendicular to the strand axis. Due to the consecutive flipping of the residues by 180 degrees, the side groups alternately point upwards and downwards away from the sheet. The β− sheet can be formed in two ways: parallel and anti-parallel. In the parallel configuration, the β− strands are all running in the same direction from the N– to the C– terminus. In the anti-parallel configuration, adjacent strands are running in opposite directions (as in Fig. 1.10). In the β− strand there are just two residues per turn, but the rise per residue differs between the parallel and anti- parallel configuration: 0.32 and 0.34 nm, respectively. The geometrical attributes of a number of secondary protein structures are collected in Table I.II. C N N N N N N N N N N N N N C C C C C C C C C C C C C C C C C C C C C C C C C C C C CN N O O O O O O OO O C N R R R R R R R R R R R R R R N N N N N N N N N N N N C C C C C C C C C C C C C C C C C C C C C O O O O C C R C C C C C CN N O Figure 1.10 Left: Irregular anti-parallel β− sheet secondary structure of polypeptides. The hydrogen bonds between the carbonyl oxygen and the amide hydrogen are between adjacent chains and almost perpendicular to the chain axis. The side groups alternately point upwards and downwards along the chain. Right: Schematic representation showing the atoms of the backbone atoms only and the coarse-grained arrows which show the directions from the N– to the C–terminus. Chapter 1: Biopolymers 17 In proteins, the secondary structures may be deformed by the presence of the side groups. The α−helix and β− strand structures are often depicted by the coarse-grained helical ribbon and deformed arrow shapes as shown in Figs. 1.9 and 1.10, respectively. The arrow heads at the ends of the β− strands point in the direction from the N– to the C–terminus. 1.3.3 Secondary structures of polysaccharides Polysaccharides with a complex and/or branched primary structure, such as pullulan and dextran respectively, take a random coil conformation when dissolved in a suitable solvent (water). If the primary structure is simple and regular, polysaccharides may exhibit a regular secondary structure. In amylose, the regular orientation of successive glucose residues results in a right-handed helix with six residues per turn. Cellulose can exist as fully extended chains with each residue flipped by 180 degrees with respect to its neighbour in the chain. The cellulose chains form ribbons that are packed side-by-side with hydrogen bonds within and between them; a structure which is reminiscent of the β− sheet. Xanthan is a linear polysaccharide with a repeating unit made of 5 sugar units. To every repeating unit of the main chain a small side-chain is attached consisting of three modified sugar units. Two of these xanthan chains are thought to form a double helix, which gives the molecule a high bending rigidity and accounts for its surprisingly high solution viscosity. 1.4 Tertiary structure and stabilizing interactions Naked double-stranded DNA, that is DNA not complexed with proteins, behaves as a charged polymer and takes a random coil conformation in water or an aqueous buffer. However, the biological relevance of naked DNA is limited. Inside the capsid of certain bacteriophages, double-stranded DNA is compacted and essentially protein-free, except for the proteins which make up the structure of the capsid itself. In the nucleoid region of bacterial cells, the genome is thought to be compacted by specific interactions with proteins as well as by osmotic, depletion effects exerted by non-binding proteins dispersed in the cytoplasm (the latter effects will be discussed in Chapter 6). In eukaryotic cells, DNA is wrapped around histone proteins and looks like 20 Introduction to Biopolymer Physics • Van der Waals interaction. The interior of globular proteins is closely packed with many uncharged side groups. The weak attraction resulting from dipole and induced dipole interactions between these side groups adds up and results in a significant stabilizing force. • Disulfide bonding. If the protein is meant to function in an external, oxidizing environment, as opposed to the reducing environment inside most cells, significant stabilization of the folded structure can come from the formation of disulfide bonds between cysteine residues. • Hydrophobic interaction. Despite the fact that the aforementioned interactions stabilize the native state to a significant extent, the main contribution to the stability of the protein comes from the hydrophobic effect. If the hydrophobic side groups are buried in the interior of the globular protein, water molecules that were first restricted in their translational and rotational motions due to the interaction with the protein are released. This release of hydration water molecules results in an increase of the entropy of the whole system including protein and solvent, which partially offsets the tremendous loss in configurational entropy associated with the folding process. Relatively small proteins fold spontaneously into their 3–dimensional, native tertiary structures. For longer polypeptide sequences, the folding process may be assisted with helper proteins called chaperones, thereby avoiding misfolded states and possibly amorphous aggregation. We will further discuss the scientifically challenging folding problem in Sec. 5.4. Finally, one should bear in mind that many, if not all proteins are multi-unit assemblies and that they form higher order complexes with other biopolymers, such as DNA and RNA in the machinery of life. 1.5 Questions 1. What are the differences between DNA and RNA from a primary structural point of view? 2. Describe the difference in molecular structure of amylose and cellulose. 3. Give a reason why water is a good solvent for dextran and not a good Chapter 1: Biopolymers 21 solvent for cellulose. 4. Why does dextran not have a regular secondary structure as is found for amylose? 5. Why is the right-handed α−helix much more abundant than the left- handed α−helix in polypeptides of biological origin? Under which condition would the left-handed helix be more abundant? 6. Describe the differences between the parallel and the anti-parallel β− sheets of polypeptides. Why do they have a slightly different rise per residue? 7. Give a reason why a single-stranded DNA molecule does not take such an intricate tertiary structure as can be found in transfer RNA. 8. What happens to the 3–dimensional tertiary structure of a closed circular and supercoiled DNA molecule when one of the strands of the duplex is cleaved by an enzyme or accidentally cut (nicked)? 9. Why is purine or pyrimidine base-pairing not suitable for the formation of a double helix of two opposing strands of nucleic acid? 10. A protein made of 101 residues in its random coil state can exist in 3 to the power 100 conformations, if each link between residues has three equally probable configurations (see Sec. 5.4). a. Estimate the change in configurational entropy if the protein folds into a native structure with only one conformation. b. Suppose that the protein folds into a single α−helix. Calculate the stabilization energy pertaining to the formation of the intra- molecular hydrogen bonds between carbonyl oxygen and amide hydrogen. Assume that each hydrogen bond contributes 5 kJ/mol to the stabilization energy. c. Is the α−helix stable at 298 K?