Other Simulations

Clementi (1985) described ab initio computational chemistry as a global approach to simulations of complex chemical systems, derived directly from theory without recourse to empirical parametrizations. The intent is to break the computation into steps quantum mechanical computations for the elements of the system, construction of two-body potentials for the interactions between them, statistical mechanical simulations using the above potentials, and, finally, the treatment of higher levels of chemical complexity (e.g., dissipative behavior). This program has been followed for analysis of the hydration of DNA. Early work by Clementi et al. (1977) established intermolecular potentials for the interaction of lysozyme with water, given as maps of the energy of interaction of solvent water with the lysozyme surface. 

Bash et al. (1987) applied the thermodynamic perturbation method to complexes of thermolysin with a phosphonamidate [Cbz-Gly -(NH)-Leu-Leu] and the corresponding phosphonate inhibitor [Cbz-Gly -(0)-Leu-Leu]. The perturbation was carried out by using 20 windows, with 2-psec molecular dynamics simulations in each window. Computations were for the ligand in solution and bound to the enzyme. The solvation of the enzyme was represented by a spherical cap of 168 water molecules about the bound inhibitor. The difference in free energy of binding of the two inhibitors was calculated to be 4.38 kcal/mol, to be compared with the experimental value, 4.10 kcal/mol. These calculations point out the importance of solvation effects, which are seen in the 3.4 kcal/mol difference between the NH and O forms of the inhibitor. 

Kollman et al. (1987) summarized similar analyses, comparing transition states and preequilibrium complexes of native and mutant species of subtilisin, trypsin, and triose-phosphate isomerase. 

Warshel and collaborators (Warshel and Sussman, 1986 Warshel et al., 1988) developed the empirical valence bond method for obtaining free-energy differences and activation free energies. The effects of Gly-to-Ala mutations in trypsin were accurately simulated. This method was earlier applied to calculation of the potential surface for general acid catalysis of a disaccharide in solution and bound to lysozyme (Warshel and Weiss, 1980). 

Warshel et al. (1986) calculated protein pX values in solution by using a microscopic model and a reversible charging process. 

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In favourable contrast to molecular dynamics, BD allows molecular movements of realistically long duration to be simulated. Nevertheless, the practical number of protein molecules which can be simulated is only two since collective phenomena are often of crucial importance in detennining the course of interaction events, other simulation teclmiques, such as cellular automata [115], need to be used to capture the behaviour of large numbers of particles. 

How can we apply molecular dynamics simulations practically. This section gives a brief outline of a typical MD scenario. Imagine that you are interested in the response of a protein to changes in the amino add sequence, i.e., to point mutations. In this case, it is appropriate to divide the analysis into a static and a dynamic part. What we need first is a reference system, because it is advisable to base the interpretation of the calculated data on changes compared with other simulations. By taking this relative point of view, one hopes that possible errors introduced due to the assumptions and simplifications within the potential energy function may cancel out. All kinds of simulations, analyses, etc., should always be carried out for the reference and the model systems, applying the same simulation protocols. 

Monte Carlo simulations provide an alternate approach to the generation of stable conformations. As with HyperChem s other simulation methods, the effects of temperature changes and solvation are easily incorporated into the calculations. 

Tlie simulated value of Ts corresponding to T = 74 and Tb = 104 is the smaller of these two values (i.e., 74). Tlie other simulated values of Ts are obtained in similar fasliion and listed in column 7. The average of tlie simulated values of Ts, 83, is tlie estimated time to failure of tlie system. 

Optimisation may be used, for example, to minimise the cost of reactor operation or to maximise conversion. Having set up a mathematical model of a reactor system, it is only necessary to define a cost or profit functionOptimisation and then to minimise or maximise this by variation of the operational parameters, such as temperature, feed flow rate or coolant flow rate. The extremum can then be found either manually by trial and error or by the use of a numerical optimisation algorithms. The first method is easily applied with ISIM, or with any other simulation software, if only one operational parameter is allowed to vary at any one time. If two or more parameters are to be optimised this method however becomes extremely cumbersome. 

This analysis is limited, since it is based on a steady-state criterion. The linearisation approach, outlined above, also fails in that its analysis is restricted to variations, which are very close to the steady state. While this provides excellent information on the dynamic stability, it cannot predict the actual trajectory of the reaction, once this departs from the near steady state. A full dynamic analysis is, therefore, best considered in terms of the full dynamic model equations and this is easily effected, using digital simulation. The above case of the single CSTR, with a single exothermic reaction, is covered by the simulation examples, THERMPLOT and THERM. Other simulation examples, covering aspects of stirred-tank reactor stability are COOL, OSCIL, REFRIG and STABIL. 

The spin-Hamiltonian concept, as proposed by Van Vleck [79], was introduced to EPR spectroscopy by Pryce [50, 74] and others [75, 80, 81]. H. H. Wickmann was the first to simulate paramagnetic Mossbauer spectra [82, 83], and E. Miinck and P. Debmnner published the first computer routine for magnetically split Mossbauer spectra [84] which then became the basis of other simulation packages [85]. Concise introductions to the related modem EPR techniques can be found in the book by Schweiger and Jeschke [86]. Magnetic susceptibility is covered in textbooks on molecular magnetism [87-89]. An introduction to MCD spectroscopy is provided by [90-92]. Various aspects of the analysis of applied-field Mossbauer spectra of paramagnetic systems have been covered by a number of articles and reviews in the past [93-100]. 

Fig. 20. Excess compressibility yIS for a system of inelastic hard spheres, as function of the coefficient of normal restitution, for one solid fraction (as = 0.05). The excess compressibility has been normalized by the excess compressibility y is of the elastic hard spheres system. Other simulation parameters are as in Fig. 19.

Other simulation examples involving various safety aspects are HMT, THERM, REFRIG1, REFRIG2 and DSC. 

Stagewise and finite-differenced models involve changes with time and distance. When the model is written in array form the variable can be plotted as a function of the array index. This is done by choosing an index variable for the Y axis and the [ ] symbol for the X axis. The last value calculated is used in the plot, which means that if the steady-state has been reached then it is a steady-state profile with distance. An example is given in the Screenshot Guide in Section 2 of the Appendix and in many other simulation examples. 

Both routes have their limitations. The basic theory of complex structures, which are encountered with macromolecules, often does not allow analytic solutions. Incisive, though reasonable, approximations have to be introduced. On the other hand, rigorous simulations can be made by means of molecular dynamics, but this technique has the limitation that only rather small and fast moving objects can be treated within a reasonable time, even with the fastest computers presently available. This minute scale gives valuable information on the local structure and local dynamics, but no reliable predictions of the macro-molecular properties can be made by this technique. All other simulations have to start with some basic assumptions. These in turn are backed by results obtained from basic theories. Hence both approaches are complementary and are needed when constructing a reliable framework for macromolecules that reflects the desired relation to the materials properties. 

Once the initial and boundary conditions are specified, the classical equations of motion are integrated as in any other simulation. From the start of the trajectory, the atoms are free to move under the influence of the potential. One simply identifies reaction mechanisms and products during the dynamics. For the case of sputtering, the atomic motion is integrated until it is no longer possible for atoms and molecules to eject. The final state of ejected material above the surface is then evaluated. Properties of interest include the total yield per ion, energy and angular distributions, and the structure and... 

A second limiting physical/hydrodynamic case is the soil as a porous bed. Often others simulate undisturbed soils in the lab with soil columns, however we have chosen to use a slice of such a column a differential volume reactor (DVR)-as the experimental design (22). This approach offers advantages in the ability to develop a more spatially homogeneous system and also contributes to the perturbation/response analysis needed for systems identification. 

Other simulation studies reported on the differences between ATR and SR fuel processors for liquid hydrocarbons [82]. The results showed that a fuel processor based on the SR technology gives a higher power than an ATR-based fuel processor. However, this higher performance is counterbalanced by a much higher plant complexity, resulting in increased cost and an impact on system controllability and start-up time. 

MD simulations have provided a unique molecular description of cholesterol-phospholipid interactions [31]. Atomistic simulations have succeeded in reproducing the condensing effect of cholesterol on phospholipid bilayers [32-34], With atomistic detail, many properties can be determined, such as the effect of cholesterol on lipid chain ordering or on hydrogen bond formation. Other simulations have focused on the interaction of cholesterol and SM [35-37], Aittoniemi et al. [38] showed that hydrogen bonding alone cannot explain the preferential interaction between cholesterol and SM compared to cholesterol and POPC. 

Specific solute-solvent interactions, such as hydrogen bonds, undergo a significant change in the comse of SD. This was first observed by Fonseca and Ladanyi in the case of SD in methanoF and has since then been seen in a munber of other simulation studies. " ... 

Between 1955 and 1965, 147 human subjects underwent exposure to H at Edgewood. One hundred sixteen masked subjects had aerosol chamber exposures to test the effectiveness of various protective garments. Equipment was tested for leaks with chloropicrln exposures before H exposures. Subjects underwent up to 14 exposures to H on different days and were removed from the tests when dermal erythema indicated garment leakage. Some tests simulated tropical or windy conditions, and others simulated battlefield functions. Thirty-one subjects had cutaneous exposures to test the effectiveness of antidotes or treated cloths or for sensitization. 

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