There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

BIOE 402. Medical Technology Assessment. 2 or 3 hours. Bioentrepreneur course. Assessment of medical technology in the context of commercialization. Objectives, competition, market share, funding, pricing, manufacturing, growth, and intellectual property; many issues unique to biomedical products. Course Information: 2 undergraduate hours. 3 graduate hours. Prerequisite(s): Junior standing or above and consent of the instructor.

“Bioinformatics” 특집을 내면서

N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

https://iopscience.iop.org/article/10.1088/0031-9112/34/4/040/pdf

Stochastic Processes in Physics and Chemistry

We present a feature functional theory - binding predictor (FFT-BP) for the protein-ligand binding affinity prediction. The underpinning assumptions of FFT-BP are as follows: i) representability: there exists a microscopic feature vector that can uniquely characterize and distinguish one protein-ligand complex from another; ii) feature-function relationship: the macroscopic features, including binding free energy, of a complex is a functional of microscopic feature vectors; and iii) similarity: molecules with similar microscopic features have similar macroscopic features, such as binding affinity. Physical models, such as implicit solvent models and quantum theory, are utilized to extract microscopic features, while machine learning algorithms are employed to rank the similarity among protein-ligand complexes. A large variety of numerical validations and tests confirms the accuracy and robustness of the proposed FFT-BP model. The root mean square errors (RMSEs) of FFT-BP blind predictions of a benchmark set of 100 complexes, the PDBBind v2007 core set of 195 complexes and the PDBBind v2015 core set of 195 complexes are 1.99, 2.02 and 1.92 kcal/mol, respectively. Their corresponding Pearson correlation coefficients are 0.75, 0.80, and 0.78, respectively.

Feature functional theory - binding predictor (FFT-BP) for the blind prediction of binding free energies

Protein flexibility is an intrinsic property and plays a fundamental role in protein functions. Computational analysis of protein flexibility is crucial to protein function prediction, macromolecular flexible docking, and rational drug design. Most current approaches for protein flexibility analysis are based on Hamiltonian mechanics. We introduce a stochastic model to study protein flexibility. The essential idea is to analyze the free induction decay of a perturbed protein structural probability, which satisfies the master equation. The transition probability matrix is constructed by using probability density estimators including monotonically decreasing radial basis functions. We show that the proposed stochastic model gives rise to some of the best predictions of Debye-Waller factors or B factors for three sets of protein data introduced in the literature.

/pdf/stochastic-model-for-protein-flexibility-analysis-4m3d2t1pob.pdf

Stochastic model for protein flexibility analysis.

Packing interaction is a critical driving force in the folding of helical membrane proteins. Despite the importance, packing defects (i.e., cavities including voids, pockets, and pores) are prevalent in membrane-integral enzymes, channels, transporters, and receptors, playing essential roles in function. Then, a question arises regarding how the two competing requirements, packing for stability vs. cavities for function, are reconciled in membrane protein structures. Here, using the intramembrane protease GlpG of Escherichiacoli as a model and cavity-filling mutation as a probe, we tested the impacts of native cavities on the thermodynamic stability and function of a membrane protein. We find several stabilizing mutations which induce substantial activity reduction without distorting the active site. Notably, these mutations are all mapped onto the regions of conformational flexibility and functional importance, indicating that the cavities facilitate functional movement of GlpG while compromising the stability. Experiment and molecular dynamics simulation suggest that the stabilization is induced by the coupling between enhanced protein packing and weakly unfavorable lipid desolvation, or solely by favorable lipid solvation on the cavities. Our result suggests that, stabilized by the relatively weak interactions with lipids, cavities are accommodated in membrane proteins without severe energetic cost, which, in turn, serve as a platform to fine-tune the balance between stability and flexibility for optimal activity.

https://www.pnas.org/content/pnas/117/36/22146.full.pdf

Structural cavities are critical to balancing stability and activity of a membrane-integral enzyme

Protein-nucleic acid complexes are important for many cellular processes including the most essential functions such as transcription and translation. For many protein-nucleic acid complexes, flexibility of both macromolecules has been shown to be critical for specificity and/or function. The flexibility-rigidity index (FRI) has been proposed as an accurate and efficient approach for protein flexibility analysis. In this article, we introduce FRI for the flexibility analysis of protein-nucleic acid complexes. We demonstrate that a multiscale strategy, which incorporates multiple kernels to capture various length scales in biomolecular collective motions, is able to significantly improve the state of art in the flexibility analysis of protein-nucleic acid complexes. We take the advantage of the high accuracy and O(N) computational complexity of our multiscale FRI method to investigate the flexibility of ribosomal subunits, which are difficult to analyze by alternative approaches. An anisotropic FRI approach, which involves localized Hessian matrices, is utilized to study the translocation dynamics in an RNA polymerase.

Flexibility-rigidity index for protein-nucleic acid flexibility and fluctuation analysis.

In this work, a systematic protocol is proposed to automatically parametrize the non-polar part of implicit solvent models with polar and non-polar components. The proposed protocol utilizes either the classical Poisson model or the Kohn-Sham density functional theory based polarizable Poisson model for modeling polar solvation free energies. Four sets of radius parameters are combined with four sets of charge force fields to arrive at a total of 16 different parametrizations for the polar component. For the non-polar component, either the standard model of surface area, molecular volume, and van der Waals interactions or a model with atomic surface areas and molecular volume is employed. To automatically parametrize a non-polar model, we develop scoring and ranking algorithms to classify solute molecules. The their non-polar parametrization is obtained based on the assumption that similar molecules have similar parametrizations. A large database with 668 experimental data is collected and employed to validate the proposed protocol. The lowest leave-one-out root mean square (RMS) error for the database is 1.33 kcal/mol. Additionally, five subsets of the database, i.e., SAMPL0-SAMPL4, are employed to further demonstrate that the proposed protocol. The optimal RMS errors are 0.93, 2.82, 1.90, 0.78, and 1.03 kcal/mol, respectively, for SAMPL0, SAMPL1, SAMPL2, SAMPL3, and SAMPL4 test sets. The corresponding RMS errors for the polarizable Poisson model with the Amber Bondi radii are 0.93, 2.89, 1.90, 1.16, and 1.07 kcal/mol, respectively.

Guo-Wei Wei

Papers

Feature functional theory - binding predictor (FFT-BP) for the blind prediction of binding free energies

Stochastic model for protein flexibility analysis.

Structural cavities are critical to balancing stability and activity of a membrane-integral enzyme

Flexibility-rigidity index for protein-nucleic acid flexibility and fluctuation analysis.

Automatic parametrization of non-polar implicit solvent models for the blind prediction of solvation free energies.