Sampling the Variational Posterior with Local Refinement

Variational inference is an optimization-based method for approximating the posterior distribution of the parameters in Bayesian probabilistic models. A key challenge of variational inference is to approximate the posterior with a distribution that is computationally tractable yet sufficiently expressive. We propose a novel method for generating samples from a highly flexible variational approximation. The method starts with a coarse initial approximation and generates samples by refining it in selected, local regions. This allows the samples to capture dependencies and multi-modality in the posterior, even when these are absent from the initial approximation. We demonstrate theoretically that our method always improves the quality of the approximation (as measured by the evidence lower bound). In experiments, our method consistently outperforms recent variational inference methods in terms of log-likelihood and ELBO across three example tasks: the Eight-Schools example (an inference task in a hierarchical model), training a ResNet-20 (Bayesian inference in a large neural network), and the Mushroom task (posterior sampling in a contextual bandit problem).     

Modeling the amide I bands of small peptides

In this paper different floating oscillator models for describing the amide I band of peptides and proteins are compared with density functional theory (DFT) calculations. Models for the variation of the frequency shifts of the oscillators and the nearest-neighbor coupling between them with respect to conformation are constructed from DFT normal mode calculations on N-acetyl-glycine-N(')-methylamide. The calculated frequencies are compared with those obtained from existing electrostatic models. Furthermore, a new transition charge coupling model is presented. We suggest a model which combines the nearest-neighbor maps with long-range interactions accounted for using the new transition charge model and an existing electrostatic map for long-range interaction frequency shifts. This model and others, which account for the frequency shifts by electrostatic maps exclusively, are tested by comparing the predicted IR spectra with those from DFT calculations on the pentapeptide [Leu]-enkephalin. The new model described above gives the best agreement and, after a systematic blueshift is accounted for, reproduces the DFT frequencies to within 3.5 cm(-1). The correlation of the intensities for this model with intensities from DFT calculations is 0.94.     

Orally administered bismuth drug together with N-acetyl cysteine as a broad-spectrum anti-coronavirus cocktail therapy

The emergence of SARS-CoV-2 variants of concern compromises vaccine efficacy and emphasizes the need for further development of anti-SARS-CoV-2 therapeutics, in particular orally administered take-home therapies. Cocktail therapy has shown great promise in the treatment of viral infection. Herein, we reported the potent preclinical anti-SARS-CoV-2 efficacy of a cocktail therapy consisting of clinically used drugs, e.g. colloidal bismuth subcitrate (CBS) or bismuth subsalicylate (BSS), and N-acetyl-l-cysteine (NAC). Oral administration of the cocktail reduced viral loads in the lung and ameliorated virus-induced pneumonia in a hamster infection model. The mechanistic studies showed that NAC prevented the hydrolysis of bismuth drugs at gastric pH via the formation of the stable component [Bi(NAC)₃], and optimized the pharmacokinetics profile of CBS in vivo. Combination of bismuth drugs with NAC suppressed the replication of a panel of medically important coronaviruses including Middle East respiratory syndrome-related coronavirus (MERS-CoV), Human coronavirus 229E (HCoV-229E) and SARS-CoV-2 Alpha variant (B.1.1.7) with broad-spectrum inhibitory activities towards key viral cysteine enzymes/proteases including papain-like protease (PL^pro), main protease (M^pro), helicase (Hel) and angiotensin-converting enzyme 2 (ACE2). Importantly, our study offered a potential at-home treatment for combating SARS-CoV-2 and future coronavirus infections.

A cocktail therapy comprising bismuth drugs and N-acetyl-l-cysteine is reported to suppress the replication of SARS-CoV-2 via the oral route. The broad-spectrum inhibitory activities of the combination upon key viral cysteine enzymes are verified.     

Necessary conditions for the compensation approach for a random walk in the quarter-plane

Queueing Systems - We consider the invariant measure of homogeneous random walks in the quarter-plane. In particular, we consider measures that can be expressed as a countably infinite sum of...     

Excitons in tubular molecular aggregates

We present a brief overview of recent work on the optical properties of molecular aggregates with a tubular (cylindrical) shape. The exciton states responsible for these properties can be distinguished with regard to a transverse wave number, which directly relates to optical selection rules and polarization direction of the associated absorption line. We discuss two types of analytical solutions for the exciton wave functions and the associated absorption and dichroism spectra.     

Multiscale modeling of molecular structure and optical properties of complex supramolecular aggregates

Supramolecular aggregates of synthetic dye molecules offer great perspectives to prepare biomimetic functional materials for light-harvesting and energy transport. The design is complicated by the fact that structure–property relationships are hard to establish, because the molecular packing results from a delicate balance of interactions and the excitonic properties that dictate the optics and excited state dynamics, in turn sensitively depend on this packing. Here we show how an iterative multiscale approach combining molecular dynamics and quantum mechanical exciton modeling can be used to obtain accurate insight into the packing of thousands of cyanine dye molecules in a complex double-walled tubular aggregate in close interaction with its solvent environment. Our approach allows us to answer open questions not only on the structure of these prototypical aggregates, but also about their molecular-scale structural and energetic heterogeneity, as well as on the microscopic origin of their photophysical properties. This opens the route to accurate predictions of energy transport and other functional properties.

Multiscale modeling resolves the molecular structure of a synthetic light-harvesting complex, unraveling the microscopic origin of its photophysical properties.

Supramolecular structures may self-assemble from a variety of building blocks, resulting in a wide range of advanced materials with attractive biomimetic, sensing, catalytic, optoelectronic and photonic functionalities.^1–10 The close-packed nanoscale organization of the individual molecules within a supramolecular system, held together via noncovalent interactions, gives rise to the aggregate''s (collective) properties. Assemblies consisting of dye molecules often exhibit unique collective optical properties and are of interest for opto-electronic applications as well as artificial light-harvesting complexes that mimic natural antenna systems of photosynthetic bacteria and plants.^11–13 For example, chlorosomal antenna complexes of photosynthetic green sulfur bacteria are self-assembled into multilayer tubular structures having bacteriochlorophyll pigments as building blocks.^14–16 The structure of these antenna complexes and the underlying molecular arrangement ensures that the process of light-harvesting and excitation energy transport is very efficient, even under extremely low light conditions.^17,18 The quest to recreate such efficiency under laboratory conditions has sparked numerous studies of synthetic self-assembled systems mimicking natural chlorosomes, e.g. using porphyrins,¹⁹ zinc chlorin,²⁰ and cyanine dyes.²¹ Of particular interest are the tubular aggregates of 3,3′-bis(2-sulfopropyl)-5,5′,6,6′-tetrachloro-1,1′-dioctylbenzimidacarbocyanine (C8S3).^22–25 Cryo-TEM reveals a hierarchy of supramolecular architectures, including double-walled nanotubes; under certain conditions, bundles of nanotubes arise.²⁶ Thus, this system allows for the occurrence of electronic excitation energy transport at various levels: within one wall, between walls of one tube, and between different tubes, similar to the situation in natural systems.^27,28To understand how such supramolecular systems work, as well as propose design rules for new materials, it is essential to determine the relationship between molecular structure and optical properties. Current experimental techniques, however, are unable to resolve the structure at the molecular level. This, in combination with the sensitivity of spectral properties to the details of the molecular packing, leads to a crucial role for theoretical modeling.²⁹ For example, molecular dynamics (MD) simulations have been used to predict the molecular packing within a variety of supramolecular assemblies.^30–34 However, synthetic amphiphiles with aromatic groups, such as cyanine dyes—often used to prepare aggregates with optical functionality—tend to fall into kinetic traps during spontaneous self-assembly simulations and the packing of the aromatic chromophores remains highly disordered on the accessible time scale, leading to predicted (optical) spectra that are not consistent with experimental data.³⁵ This problem can be overcome by building assemblies based upon proposed architectures and assessing their stability in relatively short MD simulations.^36–38 The drawback of this approach is the requirement of a thorough understanding of what to use as a starting point and how to validate the structure. In any case, proper validation requires the modeling of the optical spectra of the obtained structure, and finally, comparing it to the experiment. The demanding character of such methods explains why an important role is played by phenomenological modeling, in which a molecular packing is guessed and the optics is obtained from parametrizing an exciton model that describes the collective excited states of the assembly with interactions dictated by the guessed packing. By comparing the calculated spectra to experimental ones, the structure and exciton model may be fine-tuned. While this method has been successful in describing spectra,^23,39 it is limited in its predictive power and also lacks access to essential microscopic parameters, such as tuning of the optical excitation energies imposed by the environment, disorder in these energies and structural heterogeneity.In this work, we use an advanced multiscale approach to determine structure–optical property relationships for the C8S3 double-walled nanotubes, guided by comparison to experiments. The optical spectrum of these aggregates, in which multiple exciton peaks may be discerned, suggests a rather complex underlying molecular packing. This fact, combined with their sheer size going up to many thousands of molecules, makes these systems exceptionally challenging to resolve and leaves important questions concerning structure–function relationships unanswered or under debate, for instance the origin of the splitting between the two lowest-energy spectral bands.^23,38 Here, we answer these questions by iteratively combining MD simulations to capture the details of molecular packing and structural disorder, an exciton Hamiltonian approach to calculate optical signatures, and explicit microelectrostatic calculations to estimate energetic disorder and solvent shifts. Previous attempts to reveal the structure of cyanine-based nanotubes were limited to small-scale system sizes,^37,38 modeling optical features phenomenologically rather than using atomistic information³⁸ or featuring simpler, single-walled systems.³⁷ In addition to answering important questions for the C8S3 double-walled nanotubes, our study opens the way to explain and predict at an unprecedented level of detail the functional properties of other highly complex molecular materials.     

Direct measurement of the energy thresholds to conformational isomerization in tryptamine: experiment and theory

The methods of stimulated emission pumping-hole filling spectroscopy (SEP-HFS) and stimulated emission pumping population transfer spectroscopy (SEP-PTS) were applied to the conformation-specific study of conformational isomerization in tryptamine [TRA, 3-(2-aminoethyl)indole]. These experimental methods employ stimulated emission pumping to selectively excite a fraction of the population of a single conformation of TRA to well-defined ground-state vibrational levels. This produces single conformations with well-defined internal energy, tunable over a range of energies from near the zero-point level to well above the lowest barriers to conformational isomerization. When the SEP step overcomes a barrier to isomerization, a fraction of the excited population isomerizes to form that product. By carrying out SEP excitation early in a supersonic expansion, these product molecules are subsequently cooled to their zero-point vibrational levels, where they can be detected downstream with a third tunable laser that probes the ground-state population of a particular product conformer via a unique ultraviolet transition using laser-induced fluorescence. The population transfer spectra (recorded by tuning the SEP dump laser while holding the pump and probe lasers fixed) exhibit sharp onsets that directly determine the energy thresholds for conformational isomerization in a given reactant-product conformer pair. In the absence of tunneling effects, the first observed transition in a given X-Y PTS constitutes an upper bound to the energy barrier to conformational isomerization, while the last transition not observed constitutes a lower bound. The bounds for isomerizing conformer A of tryptamine to B(688-748 cm(-1)), C(1)(860-1000 cm(-1)), C(2)(1219-1316 cm(-1)), D(1219-1282 cm(-1)), E(1219-1316 cm(-1)), and F(688-748 cm(-1)) are determined. In addition, thresholds for isomerizing from B to A(<1562 cm(-1)), B to F(562-688 cm(-1)), and out of C(2) to B(<747 cm(-1)) are also determined. The A-->B and B-->A transitions are used to place bounds on the relative energies of minima B relative to A, with B lying at least 126 cm(-1) above A. The corresponding barriers have been computed using both density functional and second-order many-body perturbation theory methods in order to establish the level of theory needed to reproduce experimental results. While most of the computed barriers match experiment well, the barriers for the A-F and B-F transitions are too high by almost a factor of 2. Possible reasons for this discrepancy are discussed.