Computational Molecules in the Cell

Clearly, such a projection is fanciful. Although it is widely believed that computer power will continue to grow at current rates for about the next decade or so, it is not possible to predict how long such a growth rate can continue. On the other hand, it is not necessary to simulate the hill life cyde of an intad bacterium. Such a simulation would be extreme overkill, since it would describe the synthesis and folding of every molecule in the cell, with atomic detail. 

Here a is the differential cross-section, and depends only on Pi Pi = l/>3 Pa and on (/U - p2) p2 Pa)-The precise number of molecules in the cell fluctuates around the value given by the Boltzmann equation, because the collisions occur at random, and only their probability is given by the Stosszahlansatz. Our aim is to compute these fluctuations. If / differs little from the equilibrium distribution one may replace the Boltzmann equation by its linearized version. It is then possible to include the fluctuations by adding a Langevin term, whose strength is determined by means of the fluctuation-dissipation theorem.510 As demonstrated in IX.4, however, the Langevin approach is unreliable outside the linear domain. We shall therefore start from the master equation and use the -expansion. The whole procedure consists of four steps. 

The average concentration of species X at time t is given by Cx t) = "xTCwx, t). If diffusion is sufficiently rapid to maintain the system in local equilibrium so that the distribution of molecules in the cells is Poissonian, characterized by the instantaneous value of the chemical concentration, we may replace P( x, t) in Eq. [22] by P nx, Cx t)) and compute the time rate of change of the average value of the concentration of species X as... 

From X-ray measurements in the liquid crystalline phase it is impossible to determine the conformation of the molecules in the condensed state. Computer simulations give us information about the molecules internal freedom in vacuum, but the conformations of the molecules in the condensed state can be different because of intermolecular repulsion or attraction. But it may be assumed that the molecular conformations in the solid state are among the most stable conformations of the molecules in the condensed matter and therefore also among the most probable conformations in the liquid crystalline state. Thus, as more crystallo-graphically independent molecules in the unit cell exist, the more we can learn about the internal molecular freedom of the molecules in the condensed state. 

As a molecule passes from tissue to tissue via the blood, it is exposed to hxmdreds of possible metabolic sites it can be bound to protein, fat, or other molecules in the serum it can be sequestered in certain organs or excreted via the kidneys, the colon, or even the breath, at rates and by mechanisms that we simply do not completely xmderstand. Faced with these facts, how can anyone state dogmatically that we can replace intact animals with computers, bacteria, cell cultures, etc. ... 

The prospective applications ofmolecular assemblies seem so wide that their limits are difficult to set. The sizes of electronic devices in the computer industry are close to their lower limits. One simply cannot fit many more electronic elements into a cell since the walls between the elements in the cell would become too thin to insulate them effectively. Thus further miniaturization of today s devices will soon be virtually impossible. Therefore, another approach from bottom up was proposed. It consists in the creation of electronic devices of the size of a single molecule or of a well-defined molecular aggregate. This is an enormous technological task and only the first steps in this direction have been taken. In the future, organic compounds and supramolecular complexes will serve as conductors, as well as semi- and superconductors, since they can be easily obtained with sufficient, controllable purity and their properties can be fine tuned by minor adjustments of their structures. For instance, the charge-transfer complex of tetrathiafulvalene 21 with tetramethylquinodimethane 22 exhibits room- temperature conductivity [30] close to that of metals. Therefore it could be called an organic metal. Several systems which could serve as molecular devices have been proposed. One example of such a system which can also act as a sensor consists of a basic solution of phenolophthalein dye 10b with P-cyciodextrin 11. The purple solution of the dye not only loses its colour upon the complexation but the colour comes back when the solution is heated [31]. 

An optical scanner precisely measures the position and the intensity of each reflection and transmits this information in digital form to a computer for analysis. The position of a reflection can be used to obtain the direction in which that particular beam was diffracted by the crystal. The intensity of a reflection is obtained by measuring the optical absorbance of the spot on the film, giving a measure of the strength of the diffracted beam that produced the spot. The computer program that reconstructs an image of the molecules in the unit cell requires these two parameters, the beam intensity and direction, for each diffracted beam. 

Each reflection is the result of diffraction from complicated objects, the molecules in the unit cell, so the resulting wave is complicated also. Before considering how the computer represents such an intricate wave, let us consider mathematical descriptions of the simplest waves. 

The Fourier transform describes precisely the mathematical relationship between an object and its diffraction pattern. In Figs. 2.7-2.10, the diffraction patterns are the Fourier transforms of the corresponding objects or arrays of objects. To put it another way, the Fourier transform is the lens-simulating operation that a computer performs to produce an image of molecules (or more precisely, of electron clouds) in the crystal. This view of p(x,y,z) as the Fourier transform of the structure factors implies that if we can measure three parameters— amplitude, frequency, and phase — of each reflection, then we can obtain the function p(x,y,z), graph the function, and "see" a fuzzy image of the molecules in the unit cell. 

ORIG and SCALE lines, containing instructions for computing the positions of symmetry-related molecules in the unit cell. 

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