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This paper presents a novel fuzzy energy minimization method for simultaneous segmentation and bias field estimation of medical images. We first define an objective function based on a localized fuzzy c-means (FCM) clustering for the image intensities in a neighborhood around each point. Then, this objective function is integrated with respect to the neighborhood center over the entire image domain to formulate a global fuzzy energy, which depends on membership functions, a bias field that accounts for the intensity inhomogeneity, and the constants that approximate the true intensities of the corresponding tissues. Therefore, segmentation and bias field estimation are simultaneously achieved by minimizing the global fuzzy energy. Besides, to reduce the impact of noise, the proposed algorithm incorporates spatial information into the membership function using the spatial function which is the summation of the membership functions in the neighborhood of each pixel under consideration. Experimental results on synthetic and real images are given to demonstrate the desirable performance of the proposed algorithm.

It is a grand attraction for contemporary biochemists to computationally design enzymes for novel chemical transformation or improved catalytic efficiency. Rosetta by Baker et al. is no doubt the leading software in the protein design society. Generally, optimization of the transition state (TS) is part of the Rosetta’s protocol to enhance the catalytic efficiency of target enzymes, since TS stabilization is the determining factor for catalytic efficiency based on the TS theory (TST). However, it is confusing that optimization of the reactant state (RS) also results in significant improvement of catalytic efficiency in some cases, such as design of gluten hydrolase (Kuma030). Therefore, it is interesting to uncover underlying reason why a better binding in the RS leading to an increased kcat. In this study, the combined quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) and free energy (PMF) simulations, pKa calculation, and the statistical analysis such as the ANOVA test were carried out to shed light on the interesting but elusive question. By integration of our computational results and general acid/base theory, we answered the question why optimization of RS stabilization leads to a better TS stabilization in the general acid/base catalysis. In addition, a new and simplified protein-design strategy is proposed for the general acid/base catalysis. The idea, that application of traditional well-defined enzyme mechanism to protein design strategy, would be a great help for methodology development of protein design.

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