Most recent experiments have indicated that distal pocket polarity rather than steric hindrance is the major factor governing the distribution of FeCO stretching frequencies (ν C-O , ν Fe-CO ) in myoglobins and hemoglobins. Hydrogen bonding and other polar interactions have also been shown to play a key role in regulating O 2 and CO binding. To quantify the effects of polarity on ν C-O , ν Fe-CO , and ligand binding, we calculated electrostatic potential field distributions in the distal pockets of 18 different mutants and two wild-type forms of recombinant pig and sperm whale MbCO. The results were obtained using linearized Poisson-Boltzmann methods with coordinates from high-resolution structures determined experimentally by X-ray crystallography. The computed potential fields at the ligand atoms vary from +30 to -12 kcal/mol depending on the protein structure at the distal site. The electrostatic fields correlate inversely with ν C-O and directly with ν Fe-CO . In all our calculations, the distal histidine is modeled as the neutral N -H tautomer, regardless of which ferrous ligand is bound. If the neutral Nδ-H tautomer is used, the computed potentials at the bound ligand atoms are uniformly negative and show no correlation with ν C-O , ν Fe-C , and any ligand binding parameters. Although calculated using primarily MbCO structures, there is a linear, inverse relationship between the electrostatic field at the ligand binding site and the logarithm of the rate constant for O 2 dissociation. As a result, high O 2 affinity can be predicted semiquantitatively from a large positive potential field or from an experimentally low value of ν C-O . Thus, the stretching frequency of bound CO serves as an empirical voltmeter that can be used to measure the polarity of the distal pocket and to predict the extent of electrostatic stabilization of bound O 2 .

Molecular dynamics simulations have been used to investigate the relationship between the coordinating residues of the EF-hand calcium binding loop of parvalbumin and the overall plasticity and flexibility of the protein. The first simulation modeled the transition from Ca(2+) to Mg(2+) coordination by varying the van der Waals parameters for the bound metal ions. The glutamate at position 12 could be accurately and reversibly seen to be a source of selective bidentate ligation of Ca(2+) in the simulations. A second simulation correlated well with the experimental observation that an E101D substitution at EF loop position 12 results in a dramatically less tightly bound monodentate Ca(2+) coordination by aspartate. A final set of simulations investigated Ca(2+) binding in the E101D mutant loop in the presence of applied external forces designed to impose bidentate coordination. The results of these simulations illustrate that the aspartate is capable of attaining a suitable orientation for bidentate coordination, thus implying that it is the inherent rigidity of the loop that prevents bidentate coordination in the parvalbumin E101D mutant.

This work shows how to decrease the complexity of modeling exibility in proteins by reducing the number of dimensions necessary to model important macromolecular motions such as the induced-t process. Induced t occurs during the binding of a protein to other proteins, nucleic acids, or small molecules (ligands) and is a critical part of protein function. It is now widely accepted that conformational changes of proteins can affect their ability to bind other molecules and that any progress in modeling protein motion and exibility will contribute to the understanding of key biological functions. However, modeling protein exibility has proven a very dif cult task. Experimental laboratory methods, such as x-ray crystallography, produce rather limited information, while computational methods such as molecular dynamics are too slow for routine use with large systems. In this work, we show how to use the principal component analysis method, a dimensionality reduction technique, to transform the original high-dimensional representation of protein motion into a lower dimensional representation that captures the dominant modes of motions of proteins. For a medium-sized protein, this corresponds to reducing a problem with a few thousand degrees of freedom to one with less than fty. Although there is inevitably some loss in accuracy, we show that we can obtain conformations that have been observed in laboratory experiments, starting from different initial conformations and working in a drastically reduced search space.

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Proteins are involved either directly or indirectly in all biological processes in living organisms. It is now widely accepted that conformational changes of proteins can critically affect their ability to bind other molecules and that any progress in modeling protein motion and flexibility will contribute to the understanding of key biological functions. However, modeling protein flexibility has proven a very difficult task. Experimental laboratory methods such as X-ray crystallography produce rather few structures, while computational methods such as Molecular Dynamics are too slow for routine use with large systems. A medium sized protein typically has a few thousands of degrees of freedom. This paper shows how to obtain a reduced basis representation of protein flexibility. We use the Principal Component Analysis method, a dimensionality reduction technique, to transform the original high dimensional representation of protein motion into a lower dimensional representation that captures the dominant modes of motions of the protein. Although there is inevitably some loss in accuracy, we show that we can obtain conformations that have been observed in laboratory experiments, starting from different initial conformations and working in a drastically reduced search space.