Biological systems, forces

Algorithmic and computational solutions for model (or design) equations, combined with chemical/biological modeling, are the main subjects of this book. We shall learn that the complexities for generally nonlinear chemical/biological systems force us to use mainly numerical techniques, rather than being able to find analytical solutions. 

A major advance in force measurement was the development by Tabor, Win-terton and Israelachvili of a surface force apparatus (SFA) involving crossed cylinders coated with molecularly smooth cleaved mica sheets [11, 28]. A current version of an apparatus is shown in Fig. VI-4 from Ref. 29. The separation between surfaces is measured interferometrically to a precision of 0.1 nm the surfaces are driven together with piezoelectric transducers. The combination of a stiff double-cantilever spring with one of a number of measuring leaf springs provides force resolution down to 10 dyn (10 N). Since its development, several groups have used the SFA to measure the retarded and unretarded dispersion forces, electrostatic repulsions in a variety of electrolytes, structural and solvation forces (see below), and numerous studies of polymeric and biological systems. 

Interactions between macromolecules (protems, lipids, DNA,.. . ) or biological structures (e.g. membranes) are considerably more complex than the interactions described m the two preceding paragraphs. The sum of all biological mteractions at the molecular level is the basis of the complex mechanisms of life. In addition to computer simulations, direct force measurements [98], especially the surface forces apparatus, represent an invaluable tool to help understand the molecular interactions in biological systems. 

J. N. Israelachvih, Intermolecular and Suface Forces, With Applications to Colloidal and Biological Systems, Academic Press, Inc., San Diego, 1985. 

Electroultrafiltration (EUF) combines forced-flow electrophoresis (see Electroseparations,electrophoresis) with ultrafiltration to control or eliminate the gel-polarization layer (45—47). Suspended colloidal particles have electrophoretic mobilities measured by a zeta potential (see Colloids Elotation). Most naturally occurring suspensoids (eg, clay, PVC latex, and biological systems), emulsions, and protein solutes are negatively charged. Placing an electric field across an ultrafiltration membrane faciUtates transport of retained species away from the membrane surface. Thus, the retention of partially rejected solutes can be dramatically improved (see Electrodialysis). 

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

Equations (l)-(3) in combination are a potential energy function that is representative of those commonly used in biomolecular simulations. As discussed above, the fonn of this equation is adequate to treat the physical interactions that occur in biological systems. The accuracy of that treatment, however, is dictated by the parameters used in the potential energy function, and it is the combination of the potential energy function and the parameters that comprises a force field. In the remainder of this chapter we describe various aspects of force fields including their derivation (i.e., optimization of the parameters), those widely available, and their applicability. 

It should also be noted that a force field for a wide variety of small molecules, CHARMm (note the small m, indicating the commercial version of the program and parameters), is available [39] and has been applied to protein simulations with limited success. Efforts are currently under way to extend the CHARMm small molecule force field to make the nonbonded parameters consistent with those of the CHARMM force fields, thereby allowing for a variety of small molecules to be included in computational smdies of biological systems. 

The specific protein-DNA interactions described in this book are all with DNA in its regular B-form, or, in some cases with distorted B-DNA. In biological systems DNA appears not to adopt the A conformation, although double-stranded RNA does preferentially adopt this conformation in vivo. Whether or not Z-DNA occurs in nature is a matter of controversy. However, the formation of A-DNA and Z-DNA in vitro does illustrate the large structural changes that DNA can be forced to undergo. 

Mass transfer Irreversible and spontaneous transport of mass of a chemical component in a space with a non-homogeneous field of the chemical potential of the component. The driving force causing the transport can be the difference in concentration (in liquids) or partial pressures ( in gases) of the component. In biological systems. 

Many experimental results have been published, which deal with shear stress in biological systems. Most of them use laminar flow systems such as viscosimeters, flow channels or flasks and very small agitated vessels which are not relevant to technical reactor systems with fully developed turbulent flow. On the other hand the geometric and technical parameters are often not sufficiently described. Therefore it is not possible to explain the complex mechanism of force in bioreactors only on the basis of existing results from biological systems. 

The susceptibility of biological systems, including procaryotic and eucaryo-tic cultures and enzyme solutions, to the forces prevailing under normal processing conditions has been extensively studied and is the subject of comprehensive reviews [12-16], including other chapters in this volume. Downstream processing operations, as well as routine pumping, will expose cell suspensions... 

This strnctnring of liqnids into discrete layers when confined by a solid surface has been more readily observable in liquid systems other than water [1,55]. In fact, such solvation forces in water, also known as hydration forces, have been notoriously difficult to measure due to the small size of the water molecule and the ease with which trace amounts of contamination can affect the ordering. However, hydration forces are thought to be influential in many adhesive processes. In colloidal and biological systems, the idea that the hydration layer mnst be overcome before two molecules, colloidal particles, or membranes can adhere to each other is prevalent. This implies that factors affecting the water structure, such as the presence of salts, can also control adhesive processes. 

Patel S, Brooks CL (2006) Fluctuating charge force fields recent developments and applications from small molecules to macromolecular biological systems. Mol Simul 32(3 1). 231—249... 

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