Part II Construction and comparison with the structure of DNA

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1 Part II Construction and comparison with the structure of DNA

2 Desired functional properties 1) We look for a stable structure (stable enough to account for the permanency of biological structures on geological time scales). 2) This structure must contain information. 3) This structure can be duplicated and transported efficiently to daughter cells. 4) This structure is able to change (mutate) in order to account for the phenomenon of evolution.

3 Efficiency and economy of matter We want to use as little matter as possible Miniaturization Use atoms and molecules (the energy required at the subatomic level is beyond biological reach)

4 Stability Stability and chemical bonds: We want to use the strongest chemical bond, which are covalent bonds. Therefore we want to build a molecule.

5 Information A small molecule contains little information. Therefore to carry information, the desired structure must be a macromolecule. The simplest structure for a macromolecule is that of a linear polymer. A homopolymer (made of identical monomers) does not contain information. We need at least two types of monomers A and B. This discrete structure is compatible with a mutation process involving A A A B B particulate changes in the sequence. A B Suggests a binary code with 0 and 1 B

6 Structure of the heteropolymer This heteropolymer must be transported efficiently to the daughter cells during cell division. This implies the existence of microscopic machines able to move efficiently along it (or to transport the polymer if they remain immobile). To increase the symmetry of the polymer and the efficiency of the transport process, one can ask that the movements occur in a regular manner (by translation and rotation). Therefore, the heteropolymer must be able to exist in a helical conformation. Two reasons

7 The helical structure (1) All monomers must contain an identical chemical group used for the interactions with the microscopic machine. These identical groups are used to connect the monomers between themselves and adopt a helical structure. The heteropolymer contains therefore a helical backbone on which are attached as side groups the specific groups of the monomers. B B A B A A

8 The helical structure (2) A helical structure is as a rule a chiral structure (except for the singular case of a degenerate helix). It is therefore reasonable to except the helical backbone to be built from identical chiral components, making the heteropolymer an isotactic (Natta) chain. Another argument comes from the elastic properties of helical structures: chirality will favor the compaction of the polymer, and compaction is associated with transport efficiency. Still another argument comes from the efficiency of chiral catalysis (below)

9 θ λ R In a helix, the tangent to the curve makes a constant angle with the helical axis. This is equivalent to a constant ratio between the curvature (κ) of the curve and its torsion (τ)

10 τ / κ ~ λ / R λ τ κ Infinite torsion for a finite value of the curvature A degenerate helix: a straight line No curvature for a finite value of the torsion NO CHIRALITY NO POSSIBILITY OF COMPACTION

11 Polarity of the backbone We want the microscopic machines to be able to move efficiently in a given direction: this implies that the backbone has a polar structure. This also gives a direction to the information. The microscopic machine dissipates chemical energy in a polar and a chiral environment. Both asymmetries contribute to the efficiency. B B CH A CH A

12 Duplication of a structure: Pauling s insight (1) In general, the use of a gene as a template would lead to the formation of a molecule not with identical structure but with complementary structure + linear (inefficient) amplification

13 Duplication of a structure (2) If the structure that serves as a template (the gene molecule) consists of, say, two parts, which are themselves complementary in structure, then each of these parts can serve as the mold for the production of a replica of the other part, and the complex of two complementary parts thus can serve as the mold for the production of duplicates of itself. Pauling Molecular architecture and the processes of life. 21st Sir Jesse Boot Foundation lecture, 28 May Nottingham. + exponential (efficient) amplification

14 Duplication of a structure (3) The structure of the genetic material must be such that it contains its own complement. Again a symmetry argument brought up for two reasons (efficiency and a priori considerations: C2 axis, see below)

15 Duplication of a structure (4) The desired structure contains two complementary parts. The replication process is semiconservative. This is an efficient process, leading to an exponential amplification. The chemical bonds between the complementary parts should preferentially be weak (non covalent) bonds (since they must be broken during the duplication process). Weak bonds and preferred directions: Rather H bonds than vdw or electrostatic bonds (isotropic)

16 Duplication of the structure (5) A

17 The double helix The helix that we have built up to now is only half the desired structure: the final structure is made of two helices, with the same helical backbone. In the double helix, the genetic information is present twice because of the complementary rules We have to choose between a pair of helices side by side (a paranemic structure), and a pair of plectonemic (intertwined) helices.

18 The plectonemic double helix (1) A paranemic structure is irregular, but a plectonemic structure can still be a helix. To maximize symmetry, we therefore choose the plectonemic structure.

19 The plectonemic double helix (2) Given the polarity of the backbone, the two strands of the double helix can have either a parallel or an antiparallel orientation. We can further increase the symmetry of this structure by giving opposite polarities to the complementary strands, so as to introduce a C2 (dyad) rotation axis for the backbones of the two complementary strands.

20 The plectonemic double helix (3) We can restore the translational symmetry through cyclization of the linear polymer. The energetic (bending) cost will be low if the polymer is long enough This generates cyclic polymers with characteristic topologies: The two complementary strands are catenated. The double-stranded polymer can be knotted (the unknotted form being preferred for symmetry considerations).

22 Final structure for the genetic A helical, chiral structure: material (1) The plectonemic double helix is made of two heteropolymers complementary of one another, and whose backbones are related by a C2 symmetry. The monomers are made up of: 1) identical chiral groups that connect monomers and adopt a helical structure; 2) (at least two) specific lateral groups which need not be chiral.

23 Final structure for the genetic material (2) The complementarity between the two chains results from weak (non covalent) bonds between the lateral groups, and is such that it is compatible with the helical structure. The replication of the genetic material is a semi-conservative process in which each of the two chains is used as a template for the synthesis of the complementary one. Miniature motors assist the replication process. They could help to disrupt the non covalent interactions between the two chains. The order of the monomers defines a polar sequence which contains the genetic information. Mutations in the genetic material correspond to changes in the sequence defined by the monomers. Three asymmetry elements : Chirality, Polarity and Sequence

The structure of DNA: 1) single-stranded DNA (Kornberg and Baker) A polar backbone A polyester (phosphodiester) connected to a chiral sugar (deoxyribose) with 3 asymmetric carbons, each

24 The structure of DNA: 1) single-stranded DNA (Kornberg and Baker) A polar backbone A polyester (phosphodiester) connected to a chiral sugar (deoxyribose) with 3 asymmetric carbons, each with a specific function 4 in RNA: less stable Four lateral groups, called bases (A, T, G, C): Adenine, Thymine, Guanine and Cytosine Planar, achiral see (also the amino acids of proteins)

25 The structure of DNA: 2) polar, antiparallel strands

26 The structure of DNA: 3) Base pairing and C2 axis A-T Crick et Watson, Proc. Roy. Soc. London A (1954), vol. 223, pp

27 The structure of DNA: 3) Base pairing and C2 axis G-C

28 The structure of DNA: 4) B DNA A commensurate double helix: 10 bases every 34 Å (pitch) Diameter of 20 Å Bases paired and stacked

29 B-DNA projection parallel to the helical axis

30 B DNA Sugar

31 Symmetry and asymmetry in the structure of DNA Symmetry elements Helical symmetry C2 rotation axis Commensurability (in the fiber B form) Redundancy (von Neumann) Translational symmetry in circular DNA Asymmetries Chirality of the sugar Polarity of the backbones Asymmetry of the sequence Chirality of the helix (right for B, left for Z DNA) Major/minor grooves (in B DNA)

32 Nature of our approach (1) We have constructed the structure to describe it (process description versus state description) We have used functional considerations to construct the structure We have used no detailed information coming from the actual structure of DNA (1953). Key arguments come from Pauling and Delbrück (1940), Schrödinger (1944), Pauling (1948) and Crane (1950) Principles and problems of biological growth, The Scientific Monthly, June 1950, 70, Plus: basic facts/concepts on: 1 Theory of Evolution 2 Cell 3 Heredity 4 Chirality. 5 Brownian motion and life.

33 Nature of our approach (2) No chemical details. We have built a geometrical structure (plus energetic considerations: strong versus weak bonds) compatible with the desired functional properties. However, chemical details matter (drug design). We have built a plausible (ideal) structure. Nature produced this ideal structure! The discovery of the structure of DNA took a different path: Cf. J. D. Watson, The Double Helix (1968)

34 The discovery of the structure of DNA (1) DNA as the material basis of heredity : Morgan (chromosomal location of the gene) Griffith (1928) Avery et al. (1944) Boivin et al. (1948) Hershey et Chase (1952) Chemistry of DNA: Miescher (1868) Levene, Sevag, Todd et al. primary structure Gulland et al. (1946) Chargaff (1950-2) A = T, G = C Donohue (1952): Tautomeric forms of the bases

35 The discovery of the structure of DNA (2) Theory The notion of a molecular helix Pauling et al. (1951). X-ray diffraction of helices Cochran, Crick and Vand (1952) X-ray experiments Astbury (1947) Wilkins et al. (1951-) Franklin and Gosling: 1952 B form of DNA, C2 axis Bijvoet Absolute configuration

36 The discovery of the structure of DNA (3) Again multidisciplinary in nature Cytology Microbiology (Bio)chemistry Design (molecular helix) X-Ray theory and experiments

37 DNA replication as a symmetry breaking event (1) The replication of circular DNA chains (or very long linear chains) creates a topological problem since the two complementary strands become separated. Delbrück (PNAS, 1954) proposed a mechanism to remove the topological constraint, in which one of the two strands is transiently cleaved by an enzyme, allowing the passage of the complementary strand through it. He observed that if a covalent bond is established between the cleaved strand and the hypothetic enzyme, there would be no need to consume energy to perform the cleavage-resealing reaction. Delbrück rejected this mechanism, because it introduces an asymmetry between the two chains (only one of them being broken) which is contrary to the symmetry of the structure. In 1971 J. C. Wang described an enzyme - later called DNA topoisomerase - which works exactly as described by Delbrück!

38 DNA replication as a symmetry Antiparallel strands plus polar replicating machines (DNA polymerases) lead to an asymmetry in the replication of the leading and lagging strands breaking event

39 Conclusions (1) The construction requires the introduction of numerous facts and concepts about life. Asymmetry, Brownian motion, chance, chirality, chiral catalysis, complementarity, contingency, efficiency, evolution, fitness, helices, information, invariance, metabolism, motor, necessity, polarity, sequence, symmetry, transport.

40 Conclusions (2) Physics and biology: an apparent conflict Evolution is not the key to world understanding: The experience of science accumulated in her own history has led to the recognition that evolution is far from being the basic principle of the world understanding. It is the end rather than the beginning of an analysis of nature. Explanation of a phenomenon is to be sought not in its origin but in its immanent law. H. Weyl 1949 In biology nothing makes sense except in the light of evolution. Dobzhansky 1979 The structure of DNA is partially invariant (for the last 3.5 billion years). The explanation of this invariance requires physical (and chemical) laws.

A construction of the genetic material. Cargese, June

A construction of the genetic material Cargese, June 19 2006 Summary The goal of this course is to provide an introduction to the structure of the genetic material. There exist two complementary approaches