Ideas of Quantum Chemistry P92 pot

876
15. Information Processing – the Mission of Chemistry
Claude Elwood Shannon
(1916–2001), American math-
ematician, professor at the
Massachusetts Institute of
Technology, his professional
life was associated with the
Bell Laboratories. His idea,
now so obvious, that informa-
tion may be transmitted as a
sequence of “0” and “1” was
shocking in 1948. It was said
that Shannon used to under-
stand problems ‘
in zero time
’.
where p stands for the probability of
the event the information reports. How
much information is contained in the
news that in a single trial coin came
down tails? Well, it is I =−log
2
1
2
= 1
bit. The news “there is air in Paris”isof
no use in a TV news service,
39
because
in this case I =−log

2
1 =0
Claude Shannon introduced the no-
tion of the average information associ-
ated with all possible N results of an
event in the usual way
H =
N

i=1
p
i
I
i
=−
N

i=1
p
i
log
2
p
i
 (15.15)
where H is called the entropy of information, because a similar formula works ininformation
entropy
thermodynamics for entropy.
The quantity H (a measure of our ignorance) is largest, if all p
i

are equal.
At a given instant we estimate the probabilities of all possible results of an event
(we compute H
o
), then reliable information arrives and the estimation changes
(we compute the information entropy in the new situation H
f
). Then, according
to Shannon the measure of the information received is
I =H
o
−H
f
 (15.16)
Example 1. Information flow in transcription. The sequence of three DNA bases
(there are four bases possible: A, T,G,C), or a codon, codes for a single amino
codon
acid (there are 20 possible amino acids) in protein. Why three? Maybe three is too
many? Let us see, what the problem looks like from the point of view of informa-
tion flow.
A single codon carries the following information (in bits)
I
codon3
=−log
2

1
4
·
1

4
·
1
4

=6
39
Now we know why the everyday TV news is full of thefts, catastrophes and unbridled crimes
Although it apparently looks upsetting, in fact it represents an optimistic signal: this is just incredibly
rare.
15.15 The mission of chemistry
877
while a single amino acid in a protein
I
aa
=−log
2

1
20

=423
Thus, the codon information is sufficient to choose a particular amino acid from
20 possibles.
If nature designed the two-base codons, then such a codon would contain only
I
codon2
=−log
2
(

1
4
·
1
4
) =4 bits, which would be insufficient to code the amino acid.
Thus, the protein coding that uses the information from the DNA sequence,
takes place with the information excess of 6 −423 =177 bits per amino acid.
15.15 THE MISSION OF CHEMISTRY
There is an impression that chemistry in biology is only a kind of substitute, a pre-
text, no more than a material carrier of the mission of the whole organism. Text-
books of biochemistry do not say much about chemistry, they talk about molecular
functions to perform, in a sense about metachemistry. A particular molecule seems
not to be so important. What counts is its function. A good example are enzymes.
One type of enzyme may perform the same or similar functions in many different
organisms (from fungi to man). The function is the same, but the composition of
the enzyme changes from species to species: two species may differ by as much
as 70% of the amino acids. However, those amino acids that are crucial for the
enzyme function are preserved in all species.
We may perceive chemistry as a potential medium for information processing.
This unbelievable chemical task would be collecting, transporting, changing, dis-
patching and transferring of information.
Chemistry, as we develop it, is far from such a masterpiece. What we are doing
currently might be compared to chemical research by a Martian with a beauti-
fully edited “Auguries of Innocence” by William Blake. The little green guy would
perform a chemical analysis of the paper (he probably would even make a whole
branch of science of that), examine the chemical composition of the printing dye;
with other Martian Professors he would make some crazy hypotheses on the pos-
sible source of the leather cover, list the 26 different black signs as well as their
perpendicular and horizontal clusters, analyze their frequencies, etc. He would,

however, be very far from the information the book contains, including the boring
matrix of black marks:
To see a world in a grain of sand
And heaven in a wild flower
Hold infinity in the palm of your hand
And eternity in an hour
and most importantly he could not even imagine his heart
40
beating any faster
40
Ifany
878
15. Information Processing – the Mission of Chemistry
after reading this passage, because of thousands of associations he could never have
had We are close to what the Martian Professor would do. We have wonderful
matter in our hands from which we could make chemical poems, but so far we are
able to do only very little.
Molecules could play much more demanding roles than those, we have foreseen
for them: they can process information. The first achievement in this direction came
from Leonard Adleman – a mathematician.
15.16 MOLECULAR COMPUTERS BASED ON SYNTHON
INTERACTIONS
Computers have changed human civilization. Their speed doubles every year or
so, but the expectations are even greater. A possible solution is parallel process-
ing, or making lots of computations at the same time, another is miniaturization.
As will be seen in a moment, both these possibilities could be offered by mole-
cular computers, in which the elementary devices would be the individual mole-
cules chemists work with all the time. This stage of technology is not yet achieved.
The highly elaborated silicon lithographic technology makes it possible to create
Leonard M. Adleman (b. 1945),

American mathematician, pro-
fessor of computer science
and of molecular biology at
the University of California,
Los Angeles. As a young boy
he dreamed of becoming a
chemist, then a medical doc-
tor. These dreams led him to
the discovery described here.
electronic devices of size of the order of
1000 Å. Chemists would be able to go
down to the hundreds or even tens of Å.
Besides, the new technology would be
based on self-organization (supramole-
cular chemistry) and self-assembling. In
1cm
3
we could store the information
of a huge number of todays CD-ROMs.
People thought a computer had to have
the form of a box with metallic and non-
metallic tools inside, as it is now. However, .
In 1994 mathematician Leonard M. Adleman
41
began his experiments in one
of the American genetics labs, while learning the biological stuff in the evenings.
polymerase
Once, reading in bed Watson’s textbook “The Molecular Biology of the Gene”, he
recognized that the features of the polymerase molecule interacting with the DNA
strand described in the textbook perfectly match the features of what is called

Turing machine, or, an abstract representation of a computing device,madejustbe-
Turi ng m ac hi ne
fore the Second World War by Alan Turing.
Therefore, it was certain that the polymerase and the DNA (and certainly some
other molecules) could be used as computers. If we think about it now,thecom-
puter in our head is more similar to excusez le mot water, than to a box with hard
disks, etc. The achievement of Adleman was that he was able to translate a known
and important mathematical problem into the language of laboratory recipes, and
then using a chemical procedure he was able to solve the mathematical prob-
lem.
41
L. Adleman, Science 266 (1994) 1021.
15.16 Molecular computers based on synthon interactions
879
Alan Mathison Turing (1912–1954), British
mathematical genius, in a paper in
Proc. Lon-
don Math. Soc
. 42 (1937) 230), defined a sim-
ple device (known now as the Turing machine).
The machine consists of a read/write head that
scans a 1D tape divided into squares, each
of which contains a “0” or “1”. The behaviour
of the machine is completely characterized by
the current state of the machine, the content
of the square it is just reading, and a table of
instructions. Such a theoretical concept was of
importance in considering the feasibility of any
program coded on the tape. During the Second
World War Turing continued Polish achieve-

ments by decoding further versions of the Ger-
man Enigma code at Bletchley Park, the British
wartime cryptanalytic headquarter. He was re-
membered for his eccentric habits. People saw
him riding his bicycle with a gas mask on (he
claimed it relieved his allergies). Alan Turing
was found dead in his bed with a half eaten
poisoned apple.
Fig. 15.10. A graph of airplane flights. Is the graph of the Hamilton type? This was a question for the
molecular computer. (a) The graph from the Adleman’s experiment. (b) A simplified graph described
in this book.
Fig. 15.10 shows the original problem of Adleman: a graph with 14 airplane
flights involving seven cities.
The task is called the travelling salesman problem, notorious in mathematics as
travelling
salesman
problem
extremely difficult.
42
The salesman begins his journey from the city START and
wants to go to the city GOAL, visiting every other city precisely once. This is fea-
sible only for some flight patterns. Those graphs for which it is feasible are called
the Hamilton graphs. When the number of cities is small, such a problem may be
Hamilton graphs
quite effectively solved by the computer in our head. For seven cities it takes on
average 56 s, as stated by Adleman, for a little larger number we need a desk com-
puter, but for a hundred cities all the computers of the world would be unable to
provide the answer. But, . a molecular computer would have the answer within a
second.
42

The problem belongs to what is called NP-hard (NP from non-polynomial), in which the difficulties
increase faster than any polynomial with the size of the problem.
880
15. Information Processing – the Mission of Chemistry
William Rowan Hamilton (1805–1865) was a
Astronomer Royal in Ireland. At the age of
17 he found an error in the famous “Celes-
tial Mechanics” by Laplace. This drew the at-
tention of scientists and was the beginning of
the Hamilton’s scientific career. In the present
book his name is repeated many times (be-
cause of Hamiltonian).
How does a molecular computer work?
Let us recall two important examples of complementary synthons: guanine and
cytosine (GC) and adenine with tymine, see p. 751.
Let us repeat Adleman’s algorithm for a much simpler graph (Fig. 15.10.b).
What Adleman did was the following.
1. He assigned for every city some particular piece of DNA (sequence) composed
of eight nucleic bases:
City A A C T T G C A G
City B T C G G A C T G
City C G G C T A T G T
City D C C G A G C A A
2. Then to each existing flight X→Y, another eight-base DNA sequence was as-
signed: composed of the second half of the sequence of X and the first part of
thesequenceofY:
Flight A→BGCAGTCGG
Flight A→DGCAGCCGA
Flight B→C ACTGGGCT
Flight B→DACTGCCGA

Flight B→AACTGACTT
Flight C→DATGTCCGA
3. Then, Adleman ordered the synthesis of the DNA sequences of the flights and
the DNA sequences complementary to the cities, i.e.
co-City A T G A A C G T C
co-City B A G C C T G A C
co-City C C C G A T A C A
co-City D G G C T C G T T
4. All these substances are to be mixed together, dissolved in water, add a bit of
salt and an enzyme called ligase.
43
43
To be as effective as Nature, we want to have conditions similar to those in living cells.
15.16 Molecular computers based on synthon interactions
881
How to read the solution
What happened in the test tube? First of all matching and pairing of the corre-
sponding synthons took place. For example, the DNA strand that codes the AB-
flight (i.e. GCAGTCGG) found in the solution the complementary synthon of city
B (i.e. the co-City AGCCTGAC) and because of the molecular recognition mech-
anism made a strong intermolecular complex:
GCAGTCGG













AGCCTGAC
where the upper part is flights, and the lower part is co-Cities. Note that the flights
are the only feasible ones, because only feasible flights’ DNA sequences were syn-
thesized. The role of a co-City’s DNA is to provide the information that there is
the possibility to land and take-off in this particular city.
In the example just given, the complex will also find the synthon that corre-
sponds to flight B → C, i.e. ACTGGGCT, and we obtain a more extended strand
GCAGTCGG|ACTGGGCT

























AGCC T GAC
In this way from the upper part
44
of the intermolecular complexes we can read
a particular itinerary. The ligase was needed, because this enzyme binds the loose
ends of the DNA strands (thus removing the perpendicular separators above).
Therefore, every possible itinerary is represented by a DNA oligomer. If the graph were
Hamiltonian, then in the solution there would be the DNA molecule composed of 24
nucleotides that codes the proper itinerary:
GCAGTCGGACTGGGCTATGTCCGA.
Eliminating wrong trajectories. . .
Practically, independent of how large N is, after a second the solution to the travelling
salesman problem is ready. The only problem now is to be able to read the solution.
This will currently take much more than a second, but in principle only depends
linearly on the number of cities.
To get the solution we use three techniques: polymerase chain reaction (PCR),
electrophoresis and separation through affinity. The machinery behind all this is
recognition of synthons and co-synthons (known in biochemistry as hybridization,
it has nothing to do with hybridization described in Chapter 8).
44
From the lower part as well.
882
15. Information Processing – the Mission of Chemistry
The itineraries coded by the hybridization are mostly wrong. One of the reasons

is that they do not start from the START CITY (A) and do not end up at the GOAL
CITY (D). Using the PCR technique
45
it is possible to increase the concentration
of only those itineraries, which start from START and end at GOAL to such an
extent that all other concentrations may be treated as marginal.
Still there are a lot of wrong itineraries. First of all there are a lot of itineraries
that are too long or too short. This problem may be fixed by electrophoresis,
46
which allows the separation of DNA strands of a given length, in our case the 24-
city itineraries. In this way we have itineraries starting from START and ending at
GOAL and having 24 cities. They can be copied again by PCR.
Now we have to eliminate more wrong itineraries: those which repeat some
transit cities and leave others unvisited. This is done by the affinity separation
method.
47
First, the co-synthon for the first transit city (in our case: C) on the
list of transit cities (in our case: C and D) is prepared and attached to the surface
of iron balls. The iron balls are then added to the solution and after allowing a
second to bind to those itineraries that contain the city, they are picked out using
a magnet. The balls are then placed in another test tube, the attached “itineraries”
released from the surface of the iron balls and the empty iron balls are separated.
Thus, we have in a test tube the “itineraries” that begin and end correctly, have the
correct number of 24 nucleotides and certainly go through the first transit city (C)
on our list of transit cities.
The process is repeated for the second etc. transit cities. If, in the last test tube,
there is an “itinerary”, the answer to the salesman problem is positive and the cor-
responding “itinerary” is identified (after copying by PCR and sequencing). Oth-
erwise the answer is negative.
Thus, a mathematical problem was solved using a kind of molecular biocom-

puter. From the information processing point of view, this was possible because
parallel processing was under way – a lot of DNA oligomers interacted with them-
selves at the same time. The number of such molecular processors was of the order
of 10
23
. This number is so huge, that such a biocomputer is able to check (virtually)
all possibilities and to find the solution.
45
The PCR technique is able to copy a chosen DNA sequence and to grow its population even from a
single molecule to a high concentration by using the repeated action of an enzyme, a polymerase.
The reaction was invented by Kary B. Mullis (b. 1944), American technical chemist in an industrial
company. In 1983 Mullis was driving to his favourite California surfing area, when the idea of a DNA
copying molecular machine struck him suddenly. He stopped the car and made a note of the reaction.
His company gave him a prize of $10 000 and sold the patent to another company for $300000 000.
In 1993 Kary Mullis received the Nobel Prize in chemistry “for his invention of the polymerase chain
reaction (PCTR) method”.
46
Electrophoresis is able to physically separate DNA sequences according to their length. It is based
on the electrolysis of a gel. Since DNA is an anion, it will travel through the gel to anode. The shorter
the molecule, the longer distance it will reach. The DNA molecules of a given length can then be picked
out by cutting the particular piece of gel and then they can be multiplied by PCR.
47
Affinity separation method makes possible to separate particular sequences from a mixture of DNA
sequences. This is achieved by providing its co-synthon attached to iron spheres. The particular se-
quence we are looking for binds to the surface of the iron ball, which may afterwards be separated from
the solution using a magnet.
Summary
883
Summary
Chemistry has attained such a stage that soon a new quality can be achieved:

• chemistry entered the second half of the twentieth century with detailed knowledge of
the main building blocks of molecular structures: atoms, chemical bonds, bond angles
and intermolecular interactions;
• the accumulated knowledge now serves to build more and more complex molecular ar-
chitectures;
• in these architectures we may use chemical bonds (with energy of the order of 50–
150 kcal/mol) to build the molecules as well as intermolecular interactions (with energy
of about 1–20 kcal/mol) to construct supramolecular structures from them;
• in supramolecular chemistry we operate with synthons, i.e. some special systems of func-
tional groups that fit together perfectly when rigid (“key-lock” mechanism) or flexible
(“hand-glove” mechanism), giving rise to molecular recognition;
• the interaction leads to a molecular complex that facilitates further evolution of the sys-
tem: either by a chemical reaction going on selectively at such a configuration of the
molecules, or by further self-organization due to next-step molecular recognition of the
newly formed synthons;
• this may result in forming complex systems of multilevel architecture, each level charac-
terized by its own stability;
• the self-organization may take place with significant interaction non-additivity effects
(“non-linearity” in mathematical terms) that may lead to cooperation in forming the mul-
tilevel structure;
• high cooperation may lead to spontaneous transformation of the structure, called collec-
tive transformation, to another state (“domino effect”);
• the self-organized structures may interact with other such structures (chemical reactions
or association);
• in particular they may create the autocatalytic cycle which represents chemical feed back;
• such cycles may couple in a higher-order cycle forming hypercycles;
• a dynamic system with hypercycles, when perturbed by an external stimulus, reacts in a
complex and non-linear way;
• one of the possibilities in non-equilibrium conditions are the limit cycles, which lead to
dissipative structures, which may exhibit periodicity (in space and time) as well as chaotic

behaviour;
• some dynamic systems may represent molecular libraries with the proportions of species
strongly depending on external conditions (cf. the immune system);
• molecules may act (e.g., transfer photon, electron, proton, ion, conformational change,
etc.) thus performing a function;
• several functions may cooperate exhibiting a space/time organization of the individual
functions;
• some molecules may serve for effective information processing;
• information processing seems to represent the ultimate goal of the future chemistry.
Main concepts, new terms
complex systems (p. 852)
self-organization (p. 853)
cooperativity (p. 854)
combinatorial chemistry (p. 855)
molecular libraries (p. 855)
non-linearity (p. 857)
attractors (p. 858)
repellers (p. 858)
884
15. Information Processing – the Mission of Chemistry
fixed point (p. 858)
limit cycle (p. 858)
logistic equation (p. 860)
chaos (p. 860)
bifurcation (p. 861)
catastrophe (p. 862)
domino (p. 863)
renormalization (p. 863)
collectivity (p. 863)
decimation (p. 865)

self-similarity (p. 865)
fractals (p. 865)
feed-back (p. 866)
autocatalysis (p. 868)
brusselator (p. 868)
nodes (stable and unstable, p. 872)
saddle point of reaction (p. 872)
stellar nodes (stable and unstable, p. 872)
focus (stable and unstable, p. 872)
reaction centre (p. 872)
dissipative structures (p. 873)
hypercycles (p. 873)
molecular function (p. 875)
information (p. 876)
information entropy (p. 876)
DNA computing (p. 878)
Turing machine (p. 878)
Hamilton graph (p. 879)
travelling salesman problem (p. 879)
NP-hard problem (p. 879)
DNA hybridization (p. 881)
PCR (p. 882)
separation by affinity (p. 882)
From the research front
To say that organic chemists are able to synthesize almost any molecule one may think of
is certainly an exaggeration, but the statement seems sometimes to be very close to real-
ity. Chemists were able to synthesize the five-olympic-ring molecule, the three interlocked
Borromean rings, the football made of carbon atoms, the “cuban” – a hydrocarbon cube,
“basketan” – in the form of an apple basket, the rotaxans shown in Fig. 13.2, a molecular
in the form of Möbius band, etc. Now we may ask why the enormous synthetic effort was

undertaken and what these molecules were synthesized for. Well, the answer seems to be
that contemporary chemists are fascinated by their art of making complex and yet perfect
and beautiful molecular objects. The main goal apparently was to demonstrate the master-
ship of modern chemistry. However, high symmetry does not necessarily means a particular
usefulness. The synthetic targets should be identified by the careful planning of molecular
functions, rather than molecular beauty.
Ad futurum. . .
We may expect that more and more often chemical research will focus on molecular func-
tion, and (later) on the space/time cooperation of the functions. Research projects will be
formulated in a way that will highlight the role of the molecular function, and will consist of
several (interrelated) steps:
• first, the technical goal will be defined,
• the molecular functions will be identified which will make this goal achievable,
• theoreticians will design and test in computers (“in silico”) the molecules which will ex-
hibit the above functions,
• synthetic chemists will synthesize the molecules designed,
• physicochemists will check whether the molecular functions are there,
• finally, the material will be checked against the technical goal.
We will be able to produce “smart” materials which will respond to external conditions
in a previously designed, complex, yet we hope, predictable way. The materials that will
be created this way will not resemble the materials of today, which are mostly carrying out
Additional literature
885
one primitive function. The drugs of today are usually quite simple molecules, which enter
the extremely complex system of our body. The drugs of tomorrow will involve much larger
molecules (like proteins). Will we be clever enough to avoid unpredictable interactions with
our body? What in principle do we want to achieve?
What will the motivation of our work be? Will we take into account the psychological
needs of the human being, equilibrium of their minds?
What will the future of the human family be, which was able in the past to create such

wonderful music, Chartres cathedral, breathtaking painting, moving poetry, abstract math-
ematics, proudly landed on other celestial bodies? In the past nothing could stop their cu-
riosity and ingeniousness, they were able to resist the harshest conditions on their planet.
Humans have reached nowadays the technical level that probably will assure avoiding the
next glaciation,
48
maybe allow a small asteroid be pushed off the target by nuclear war-
heads if it were aimed dangerously at the Earth, also . erasing in nuclear war most of its
own population together with the wonders of our civilization.
What is the goal of these beings and what will be the final limit of their existence? What
are they aiming at? Do we want to know the smell of fresh bread, to be charmed by Chartres
cathedral with all it has in it, to use our knowledge to cherish the friendship of the human
family, or will it be sufficient to pack a newborn into a personal container and make com-
puters inject substances that will make his neural system as happy as in Seventh Heaven?
Which of the goals we do want, as chemists, to participate in?
Additional literature
M. Eigen, P. Schuster, “The Hypercycle. A Principle of Natural Organization”, Springer
Verlag, Berlin, 1979.
An excellent, comprehensible book, written by the leading specialists in the domain of
molecular evolution.
I. Prigogine, “From Being to Becoming. Time and Complexity in Physical Sciences”, Free-
man, San Francisco, 1980.
A book written by the most prominent specialist in the field.
A. Babloyantz, “Molecules, Dynamics and Life”, Wiley, New York, 1987.
The author describes the scientific achievements of Prigogine and his group, which she
participated in. An excellent, competent book, the most comprehensible among the first
three recommended books.
J M. Lehn, “Supramolecular chemistry: Concept and Perspectives”, VCH, 1995.
A vision of supramolecular chemistry given by one of its founders.
Questions

1. Decimation means:
a) bifurcation; b) renormalization of the Hamiltonian and reaching self-similarity;
c) scaling all the distances by a factor of ten; d) taking explicitly every tenth electron
in a wave function.
2. A dissipative structure in a complex system:
a) appears in a system far from equilibrium;
b) means the largest molecular complex in the system;
48
Well, it is expected within the next 500 years.