The computed electrostatic and proton transfer properties are studied for 20 enzymes that represent all six major enzyme commission classes and a variety of different folds. The properties of aspartate, glutamate, and lysine residues that have been previously experimentally determined to be catalytically active are reported. The catalytic aspartate and glutamate residues studied here are strongly coupled to at least one other aspartate or glutamate residue and often to multiple other carboxylate residues with intrinsic pK a differences less than 1 pH unit. Sometimes these catalytic acidic residues are also coupled to a histidine residue, such that the intrinsic pK a of the acidic residue is higher than that of the histidine. All catalytic lysine residues studied here are strongly coupled to tyrosine or cysteine residues, wherein the intrinsic pK a of the anion-forming residue is higher than that of the lysine. Some catalytic lysines are also coupled to other lysines with intrinsic pK a differences within 1 pH unit. Some evidence of the possible types of interactions that facilitate nucleophilicity is discussed. The interactions reported here provide important clues about how side chain functional groups that are weak Brønsted acids or bases for the free amino acid in solution can achieve catalytic potency and become strong acids, bases or nucleophiles in the enzymatic environment.

There is a growing interest in measuring the cell wall mechanical property at different locations in single walled cells. We present an inference scheme that maps relative surface elastic modulus distributions along the cell wall based on tracking the location of material marker points along the turgid and relaxed cell wall outline. A primary scheme is developed to provide a step-function inference of surface elastic moduli by computing the tensions and elastic stretches between material marker points. We perform analysis to investigate the stability of the primary scheme against perturbations on the marker-point locations, which may occur due to image acquisition and processing from experiments. The perturbation analysis shows that the primary scheme is more stable to noise when the spacing between the marker points is coarser, and has been confirmed by the numerical experiments where we apply the primary scheme to

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The computed electrostatic and proton transfer properties are studied for 20 enzymes that represent all six major EC classes and a variety of different folds. The properties of aspartate, glutamate, and lysine residues that have been previously experimentally determined to be catalytically active are reported. All catalytic aspartate and glutamate residues studied here are strongly coupled to at least one other aspartate or glutamate residue and often to multiple other carboxylate residues with intrinsic pKa differences less than 1 pH unit. Sometimes these catalytic acidic residues are also coupled to a histidine residue, such that the intrinsic pKa of the acidic residue is higher than that of the histidine. All catalytic lysine residues studied here are strongly coupled to tyrosine or cysteine residues, wherein the intrinsic pKa of the anion‐forming residue is higher than that of the lysine. Some catalytic lysines are also coupled to other lysines with intrinsic pKa differences within 1 pH unit. Some evidence of the possible types of interactions that facilitate nucleophilicity is discussed. The interactions reported here provide important clues about how side chain functional groups that are weak Br⊘nsted acids or bases for the free amino acid in solution can become strong acids, bases or nucleophiles in the enzymatic environment. Such interactions are important considerations in enzyme design.