Simulation approaches, general

The previous chapters taught us how to ask questions about specific enzymatic reactions. In this chapter we will attempt to look for general trends in enzyme catalysis. In doing so we will examine various working hypotheses that attribute the catalytic power of enzymes to different factors. We will try to demonstrate that computer simulation approaches are extremely useful in such examinations, as they offer a way to dissect the total catalytic effect into its individual contributions. 

Evans and Baranyai [51, 52] have explored what they describe as a nonlinear generalization of Prigogine s principle of minimum entropy production. In their theory the rate of (first) entropy production is equated to the rate of phase space compression. Since phase space is incompressible under Hamilton s equations of motion, which all real systems obey, the compression of phase space that occurs in nonequilibrium molecular dynamics (NEMD) simulations is purely an artifact of the non-Hamiltonian equations of motion that arise in implementing the Evans-Hoover thermostat [53, 54]. (See Section VIIIC for a critical discussion of the NEMD method.) While the NEMD method is a valid simulation approach in the linear regime, the phase space compression induced by the thermostat awaits physical interpretation even if it does turn out to be related to the rate of first entropy production, then the hurdle posed by Question (3) remains to be surmounted. 

The alternate approach to developing interaction potentials is to consider the solid surface as a very large molecule. One can then apply theoretical techniques based on gas-phase reaction ideas. The simulation of real systems, however, often requires that both reactive adsorbed atoms as well as a large number of substrate atoms be explicitly treated, and so these techniques rapidly become computationally infeasible. It is apparent that to simulate the general situation, bonding ideas from both regimes should be used. This breakdown does, however, provide a useful format within which to discuss intermediate-range interaction potentials, and so it will be used to illustrate potentials which are in current use in simulations of gas-surface interactions. 

We have presented a general reaction-diffusion model for porous catalyst particles in stirred semibatch reactors applied to three-phase processes. The model was solved numerically for small and large catalyst particles to elucidate the role of internal and external mass transfer limitations. The case studies (citral and sugar hydrogenation) revealed that both internal and external resistances can considerably affect the rate and selectivity of the process. In order to obtain the best possible performance of industrial reactors, it is necessary to use this kind of simulation approach, which helps to optimize the process parameters, such as temperature, hydrogen pressure, catalyst particle size and the stirring conditions. 

In order to improve MD simulations, a number of specific areas should be addressed in the area of basic molecular dynamics theory. These include (1) development of full quantum mechanical calculations on complex molecules and more robust ways to incorporate quantum mechanical calculations within larger-scale classical mechanics or statistical mechanics approaches (2) development and refinement of transferable force fields between arbitrary atoms and molecules, which are necessary building blocks for MD simulations of general systems and (3) development of multiscale theories and techniques for understanding systems. Moreover, the community must develop toolkits that allow general users to perform such simulations. 

The crystallization of 3D-ordered crystalline phases from thermotropic mesophases, envisaged as stable pre-crystalline partially ordered intermediates, is an additional interesting issue which should be considered with care experimentally, theoretically, and with appropriate simulation approaches. Depending upon the nature of the mesophase it can be seen as a crystal-crystal transition or, for conformationally disordered, columnar mesophases, it approaches a true crystallization process. It is quite clear that the preexisting order will play a major role for example if the mesophase is chain-extended, bundle equilibria and chain-folding should not play any role. Indeed available experimental evidence supports this idea. Mechanistic and kinetic features should in general differ widely from the standard chain-folded crystallization processes yielding thin lamellar structures. In a number of cases (polyphosphazenes, polysiloxanes, see below) the crystalline polymorphs obtained from the chain-extended precursor differ from those obtained from solution. 

COMPUTER-SIMULATION APPROACHES TO IONIC SOLVATION 2.17.1. General... 

It is generally accepted (e.g., Ref. 1) that many enzymes have evolved by optimizing kCat/-KM, where Km — ( -i + kcaX)/k and can be approximated as Km % k- /k — K l. However, this observation, and related findings, has not identified the factors responsible for the actual catalytic effect. As will be shown below, the key question is to determine how the activation barrier in the chemical step is reduced. In order to proceed further in a meaningful way, we need a reliable tool to quantify the activation barrier and to relate that with the structure and function of the enzyme. We also need to determine the individual contributions to the overall catalytic effect. Gradually it is becoming clear that this is best accomplished by computer simulation approaches. 

Numeric simulation is used to testify the proposed PCA methods. The reason of using numeric simulation instead of experimental data is the generality and flexibility of the simulation approach. With the aid of simulation, one can easily investigate purposefully various situations that are not likely be encountered in a few experiments. The examples based on experimental data for cluster analysis, however, will be presented in the chapter Classification of materials . 

An optimal choice of weights can be found by measuring the local dif-fusivity of a random walk along the reaction coordinates and applying the feedback method to shift weight towards the bottlenecks in the simulation. This generalized ensemble optimization approach has recently been illustrated for the simulation of dense Lennard-Jones fluids close to the vapor-liquid equilibrium [21]. The interaction between particles in the fluid is described by a... 

Here, we focus on recent developments in modeling SOFCs that have been attained with KMC simulations. This general modeling approach has been very successful when applied to predict surface deposition processes [33-38] and heterogeneous catalysis [39-48], and it has now become a valuable tool for... 

In general, previous experimental values and computational data can be used to estimate the kinetic parameters needed for a KMC-based simulation. These parameters may be improved and adjusted after KMC simulation, if an initially identified reaction mechanism is shown to be insufficient to capture the experimental behavior. Most importantly, the DFT+KMC multiscale simulation approach establishes a well-defined pathway for taking atomistic-level details and reaching lab-level experimental results, which can be used to accelerate the discovery process and enhance engineering design. 

As both approaches require a generalized, detailed, and (in case of the simulation approach) formal model of the work process, they can only be realized in the long term. Several iterations of the modeling procedure are required to construct the required models. So far, models of two concrete projects have been created on a medium level of detail. The flrst model deals with a rather small project it was planned as a demonstration of our methodology and was used by Air Products to assess the suitability of the methodology for their needs. The second model describes a rather complex design process with more than a dozen roles, several dozens actors, and more than one hundred activities. The project is continued as part of the transfer project described in Sect. 7.3. 

Once the selectivity is optimized, a system optimization can be performed to improve resolution or to minimize the separation time. Unlike selectivity optimization, system optimization is usually predictable, since only kinetic parameters are generally considered. Typical experimental variables include column length, particle size, flow rate, instrument configuration, sample injection size, etc. Many of these parameters are connected to the chromatogram through reliable equations, and therefore, computer simulation approaches have been successful in providing a stmctured approach to this problem [375,557,558]. 

Figure 4 shows the comparison carried out between the measured and simulated pressures. The general shape of the curves obtained with hydraulic simulation is quite similar to measurement results, except there is a constant difference of about 1 bar between the P4 measurements and the simulation. This point will be discussed in Section 4.5 below. Our simulation approach (a hydraulic steady flow analysis with four steady-state steps) was not able to reproduce pore pressure increase (led to a higher horizontal stress than vertical stress) as excavation neared the monitored borehole intervals and as post-tunnel face dissipation was completed. 

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