A Novel Comprehensive Evaluation Method for Estimating the Bank Profile Shape and Dimensions of Stable Channels Using the Maximum Entropy Principle

This paper presents an extensive and practical study of the estimation of stable channel bank shape and dimensions using the maximum entropy principle. The transverse slope (St) distribution of threshold channel bank cross-sections satisfies the properties of the probability space. The entropy of St is subject to two constraint conditions, and the principle of maximum entropy must be applied to find the least biased probability distribution. Accordingly, the Lagrange multiplier (λ) as a critical parameter in the entropy equation is calculated numerically based on the maximum entropy principle. The main goal of the present paper is the investigation of the hydraulic parameters influence governing the mean transverse slope (St¯) value comprehensively using a Gene Expression Programming (GEP) by knowing the initial information (discharge (Q) and mean sediment size (d50)) related to the intended problem. An explicit and simple equation of the St¯ of banks and the geometric and hydraulic parameters of flow is introduced based on the GEP in combination with the previous shape profile equation related to previous researchers. Therefore, a reliable numerical hybrid model is designed, namely Entropy-based Design Model of Threshold Channels (EDMTC) based on entropy theory combined with the evolutionary algorithm of the GEP model, for estimating the bank profile shape and also dimensions of threshold channels. A wide range of laboratory and field data are utilized to verify the proposed EDMTC. The results demonstrate that the used Shannon entropy model is accurate with a lower average value of Mean Absolute Relative Error (MARE) equal to 0.317 than a previous model proposed by Cao and Knight (1997) (MARE = 0.98) in estimating the bank profile shape of threshold channels based on entropy for the first time. Furthermore, the EDMTC proposed in this paper has acceptable accuracy in predicting the shape profile and consequently, the dimensions of threshold channel banks with a wide range of laboratory and field data when only the channel hydraulic characteristics (e.g., Q and d50) are known. Thus, EDMTC can be used in threshold channel design and implementation applications in cases when the channel characteristics are unknown. Furthermore, the uncertainty analysis of the EDMTC supports the model’s high reliability with a Width of Uncertainty Bound (WUB) of ±0.03 and standard deviation (Sd) of 0.24.

What sets river width?

One of the simplest questions in riverine science remains unanswered: “What determines the width of rivers?” While myriad environmental and geological factors have been proposed to control alluvial river size, no accepted theory exists to explain this fundamental characteristic of river systems. We combine analysis of a global dataset with a field study to support a simple hypothesis: River geometry adjusts to the threshold fluid entrainment stress of the most resistant material lining the channel. In addition, we demonstrate how changes in bank strength dictate planform morphology by exerting strong control on channel width. Our findings greatly extend the applicability of threshold channel theory, which was originally developed to explain straight gravel-bedded rivers with uniform grain size and stable banks. The parsimonious threshold-limiting channel model describes the average hydraulic state of natural rivers across a wide range of conditions and may find use in river management, stratigraphy, and planetary science.

Allosteric activation of an ion channel triggered by modification of mechanosensitive nano-pockets

Lipid availability within transmembrane nano-pockets of ion channels is linked with mechanosensation. However, the effect of hindering lipid-chain penetration into nano-pockets on channel structure has not been demonstrated. Here we identify nano-pockets on the large conductance mechanosensitive channel MscL, the high-pressure threshold channel. We restrict lipid-chain access to the nano-pockets by mutagenesis and sulfhydryl modification, and monitor channel conformation by PELDOR/DEER spectroscopy. For a single site located at the entrance of the nano-pockets and distal to the channel pore we generate an allosteric response in the absence of tension. Single-channel recordings reveal a significant decrease in the pressure activation threshold of the modified channel and a sub-conducting state in the absence of applied tension. Threshold is restored to wild-type levels upon reduction of the sulfhydryl modification. The modification associated with the conformational change restricts lipid access to the nano-pocket, interrupting the contact between the membrane and the channel that mediates mechanosensitivity.