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. . 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. 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. 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