A theoretical construction of
the genetic material (2)
Jean-Louis Sikorav
EPFL September 25 2008
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.
Stability
• Stability and chemical bonds:
We want to use the strongest chemical
bond, which are covalent bonds.
Therefore we want to build a molecule.
Cf. Schrödinger What is Life (1944):
Molecule = solid = crystal
Gas = liquid = amorphous
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.
This discrete structure is compatible with a
mutation process involving particulate
changes in the sequence.
A
B
A
B
A
Cf. Schrödinger What is Life (1944): “The
gene is an aperiodic solid/crystal, a complicated
organic molecule in which every group of atoms
plays an individual role, not entirely equivalent to
that of others”.
A
B
B
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.
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
A
B
B
A
A
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.
• An other argument comes from the elastic properties
of helical structures: chirality will favor the compaction
of the polymer, and compaction is associated with
transport efficiency.
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)
τ/κ~λ/R
Infinite torsion for a
finite value of the
curvature
λ →∞
A degenerate
helix: a straight
line
τ
→∞
κ
No curvature for a
finite value of the
torsion
NO CHIRALITY
NO POSSIBILITY OF COMPACTION
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.
B
CH
B
A
CH
A
Duplication of a structure:
Pauling’s insight (1)
“The detailed mechanism by means of which a
gene produces replicas of itself is not yet known. 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. It might
happen, of course, that a molecule could be at the
same time identical with and complementary to the
template on which it is molded. However, this case
seems to me to be too unlikely to be valid in general,
except in the following way:”
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 1948. Nottingham.
Duplication of a structure (3)
The structure of the genetic material
must be such that it contains its own
complement.
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).
Duplication of the structure (5)
A
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.
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.
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.
Final structure for the genetic
material (1)
A helical, chiral structure:
• 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.
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
• Four lateral groups, called
bases (A, T, G, C): Adenine,
Thymine, Guanine and
Cytosine
• Planar, achiral see (also the
amino acids of proteins)
The structure of DNA:
2) polar, antiparallel strands
The structure of DNA:
3) Base pairing and C2 axis A-T
Crick et Watson, Proc. Roy. Soc. London A (1954), vol. 223, pp.
80-96.
The structure of DNA:
3) Base pairing and C2 axis G-C
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
B-DNA projection parallel to
the helical axis
B DNA Sugar
Symmetry and asymmetry in
the structure of DNA
Symmetry elements
Helical symmetry
C2 rotation axis
Commensurability
(in the fiber B form)
Redundancy
(von Neumann)
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)
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).
• The main 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, 376-389.
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.
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))
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
The discovery of the structure
of DNA (2)
Theory
X-ray experiments
• The notion of a
• Astbury (1947)
molecular helix
• Wilkins et al. (1951-)
Pauling et al. (1951).
• Franklin and
• X-ray diffraction of
Gosling:
helices
1952 B form of
Cochran, Crick and
DNA, C2 axis
Vand (1952)
1953-54
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!
DNA replication as a symmetry
breaking event
• Antiparallel strands
plus polar
replicating
machines (DNA
polymerases) lead
to an asymmetry in
the replication of
the leading and
lagging strands
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.
Conclusions (2)
Physics and biology
“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