The Hastings algorithm is a key tool in computational science. While mathematically justified by detailed balance, it can be conceptually difficult to grasp. Here, we present two complementary and intuitive ways to derive and understand the algorithm. In our framework, it is straightforward to see that the celebrated Metropolis-Hastings algorithm has the highest acceptance probability of all Hastings algorithms.
We applied coherence analysis�used by engineers to identify linear interactions in stochastic systems�to molecular dynamics simulations of crambin, a thionin storage protein found in Abyssinian cabbage. A key advantage of coherence over other analyses is that it is robust, independent of the properties, or even the existence of probability distributions often relied on in statistical mechanics. For frequencies between 0.391 and 5.08 GHz (corresponding reciprocally to times of 2.56 and 0.197 ns), the displacements of oxygen and nitrogen atoms across α-helix H-bonds are strongly correlated, with a coherence greater than 0.9; the secondary structure causes the Hbonds to effectively act as a spring. Similar coherence behavior is observed for covalent bonds and other noncovalent interactions including H-bonds in β-sheets and salt bridges. In contrast, arbitrary pairs of atoms that are physically distant have uncorrelated motions and negligible coherence. These results suggest that coherence may be used to objectively identify atomic interactions without subjective thresholds such as H-bond lengths angles and angles. Strong coherence is also observed between the average position of adjacent leaves (groups of atoms) in an α-helix, suggesting that the harmonic analysis of classical molecular dynamics can successfully describe the propagation of allosteric interactions through the structure.
Layer sampling is an algorithm for generating variates from a non-normalized multidimensional distribution p (•). It empirically constructs a majorizing function for p (•) from a sequence of layers. The method first selects a layer based on the previous variate. Next, a sample is drawn from the selected layer, using a method such as Rejection Sampling. Layer sampling is regenerative. At regeneration times, the layers may be adapted to increase mixing of the Markov chain. Layer sampling may also be used to estimate arbitrary integrals, including normalizing constants.
The Front Cover shows an antitumor agent CAB‐NE3TA (green) and a fluorescent dye IR800 (cyan) conjugated to an antibody (panitumumab, PAN) bound to epidermal growth factor receptor (EGFR). Rapidly dividing cancers require more iron than normal cells and are sensitive to depletion of cellular iron. The therapeutic antibody–drug conjugate (CAB‐NE3TA‐PAN) built on the cytotoxic iron chelator CAB‐NE3TA was effective in tumor suppression in human‐skin‐cancer‐bearing mice. This work demonstrates the potential of the therapeutic and theranostic conjugates for antibody‐targeted iron chelation therapy and fluorescent optical imaging of cancers. Cover artwork by David D. L. Minh et al. More information can be found in the Full Paper by Hyun‐Soon Chong et al. on page 2606 in Issue 24, 2018 (DOI: 10.1002/cmdc.201800598).
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