A Novel Mathematical Approach for Analysis of Integrated Cell-Patient Data Uncovers a 6-Gene Signature Linked to Endocrine Therapy Resistance.

A significant number of breast cancers develop resistance to hormone therapy. This progression, while posing a major clinical challenge, is difficult to predict. Despite important contributions made by cell models and clinical studies to tackle this problem, both present limitations when taken individually. Experiments with cell models are highly reproducible but do not reflect the indubitable heterogenous landscape of breast cancer. On the other hand, clinical studies account for this complexity but introduce uncontrolled noise due to external factors. Here, we propose a new approach for biomarker discovery that is based on a combined analysis of sequencing data from controlled MCF7 cell experiments and heterogenous clinical samples that include clinical and sequencing information from The Cancer Genome Atlas. Using data from differential gene expression analysis and a Bayesian logistic regression model coupled with an original simulated annealing-type algorithm, we discovered a novel 6-gene signature for stratifying patient response to hormone therapy. The experimental observations and computational analysis built on independent cohorts indicated the superior predictive performance of this gene set over previously known signatures of similar scope. Together, these findings revealed a new gene signature to identify patients with breast cancer with an increased risk of developing resistance to endocrine therapy.

BayFlux: A Bayesian method to quantify metabolic Fluxes and their uncertainty at the genome scale.

Metabolic fluxes, the number of metabolites traversing each biochemical reaction in a cell per unit time, are crucial for assessing and understanding cell function. 13C Metabolic Flux Analysis (13C MFA) is considered to be the gold standard for measuring metabolic fluxes. 13C MFA typically works by leveraging extracellular exchange fluxes as well as data from 13C labeling experiments to calculate the flux profile which best fit the data for a small, central carbon, metabolic model. However, the nonlinear nature of the 13C MFA fitting procedure means that several flux profiles fit the experimental data within the experimental error, and traditional optimization methods offer only a partial or skewed picture, especially in "non-gaussian" situations where multiple very distinct flux regions fit the data equally well. Here, we present a method for flux space sampling through Bayesian inference (BayFlux), that identifies the full distribution of fluxes compatible with experimental data for a comprehensive genome-scale model. This Bayesian approach allows us to accurately quantify uncertainty in calculated fluxes. We also find that, surprisingly, the genome-scale model of metabolism produces narrower flux distributions (reduced uncertainty) than the small core metabolic models traditionally used in 13C MFA. The different results for some reactions when using genome-scale models vs core metabolic models advise caution in assuming strong inferences from 13C MFA since the results may depend significantly on the completeness of the model used. Based on BayFlux, we developed and evaluated novel methods (P-13C MOMA and P-13C ROOM) to predict the biological results of a gene knockout, that improve on the traditional MOMA and ROOM methods by quantifying prediction uncertainty.

A High-Quality Genome-Scale Model for Rhodococcus opacus Metabolism.

Rhodococcus opacus is a bacterium that has a high tolerance to aromatic compounds and can produce significant amounts of triacylglycerol (TAG). Here, we present iGR1773, the first genome-scale model (GSM) of R. opacus PD630 metabolism based on its genomic sequence and associated data. The model includes 1773 genes, 3025 reactions, and 1956 metabolites, was developed in a reproducible manner using CarveMe, and was evaluated through Metabolic Model tests (MEMOTE). We combine the model with two Constraint-Based Reconstruction and Analysis (COBRA) methods that use transcriptomics data to predict growth rates and fluxes: E-Flux2 and SPOT (Simplified Pearson Correlation with Transcriptomic data). Growth rates are best predicted by E-Flux2. Flux profiles are more accurately predicted by E-Flux2 than flux balance analysis (FBA) and parsimonious FBA (pFBA), when compared to 44 central carbon fluxes measured by 13C-Metabolic Flux Analysis (13C-MFA). Under glucose-fed conditions, E-Flux2 presents an R2 value of 0.54, while predictions based on pFBA had an inferior R2 of 0.28. We attribute this improved performance to the extra activity information provided by the transcriptomics data. For phenol-fed metabolism, in which the substrate first enters the TCA cycle, E-Flux2's flux predictions display a high R2 of 0.96 while pFBA showed an R2 of 0.93. We also show that glucose metabolism and phenol metabolism function with similar relative ATP maintenance costs. These findings demonstrate that iGR1773 can help the metabolic engineering community predict aromatic substrate utilization patterns and perform computational strain design.

On the interfacial lithium dynamics in Li7La3Zr2O12:poly(ethylene oxide) (LiTFSI) composite polymer-ceramic solid electrolytes under strong polymer phase confinement.

A better molecular-level understanding of Li+ diffusion through ceramic/polymer interfaces is key to design high-performance composite solid-state electrolytes for all-solid-state batteries. By considering as a case study a composite electrolyte constituted by Li+ conductive Ga3+ doped-Li7La3Zr2O12 (LLZO) garnet fillers embedded within a poly(ethylene oxide) and lithium bis(trifluoromethanesulfonyl) imide polymer matrix (PEO(LiTFSI)), we investigate Li+ interfacial dynamics at conditions of high polymer confinement, with large filler particles in a fully amorphous polymer phase. Such confinement scenario is aimed to capture the conditions near the percolation threshold, at which conductivity enhancement is often reported. Using molecular dynamics simulations combined with the generalized shadow hybrid Monte Carlo method and umbrella sampling calculations, we explain why the hopping towards the polymer phase of the Li+ sitting on the LLZO surface is thermodynamically hindered, while hopping of Li+ from the polymer to the LLZO is kinetically slowed-down by rigidified polymer near the interface. In addition, we demonstrate how the overlap of LLZO-bound polymer chains at high confinement leads to a decrease of Li+ diffusivity within the interstitial space. We put forward that these insights are relevant to interpret the variation of ionic conductivity as a function of volume fraction and filler particle sizes also below the glass transition temperature of the polymer, at the typical operating conditions of lithium ion batteries.

Unveiling Interfacial Li-Ion Dynamics in Li7La3Zr2O12/PEO(LiTFSI) Composite Polymer-Ceramic Solid Electrolytes for All-Solid-State Lithium Batteries.

Unlocking the full potential of solid-state electrolytes (SSEs) is key to enabling safer and more-energy dense technologies than today's Li-ion batteries. In particular, composite materials comprising a conductive, flexible polymer matrix embedding ceramic filler particles are emerging as a good strategy to provide the combination of conductivity and mechanical and chemical stability demanded from SSEs. However, the electrochemical activity of these materials strongly depends on their polymer/ceramic interfacial Li-ion dynamics at the molecular scale, whose fundamental understanding remains elusive. While this interface has been explored for nonconductive ceramic fillers, atomistic modeling of interfaces involving a potentially more promising conductive ceramic filler is still lacking. We address this shortfall by employing molecular dynamics and enhanced Monte Carlo techniques to gain unprecedented insights into the interfacial Li-ion dynamics in a composite polymer-ceramic electrolyte, which integrates polyethylene oxide plus LiN(CF3SO2)2 lithium imide salt (LiTFSI), and Li-ion conductive cubic Li7La3Zr2O12 (LLZO) inclusions. Our simulations automatically produce the interfacial Li-ion distribution assumed in space-charge models and, for the first time, a long-range impact of the garnet surface on the Li-ion diffusivity is unveiled. Based on our calculations and experimental measurements of tensile strength and ionic conductivity, we are able to explain a previously reported drop in conductivity at a critical filler fraction well below the theoretical percolation threshold. Our results pave the way for the computational modeling of other conductive filler/polymer combinations and the rational design of composite SSEs.

Atomistic Insight into Ion Transport and Conductivity in Ga/Al-Substituted Li7La3Zr2O12 Solid Electrolytes.

Garnet-structured Li7La3Zr2O12 is a promising solid electrolyte for next-generation solid-state Li batteries. However, sufficiently fast Li-ion mobility required for battery applications only emerges at high temperatures, upon a phase transition to cubic structure. A well-known strategy to stabilize the cubic phase at room temperature relies on aliovalent substitution; in particular, the substitution of Li+ by Al3+ and Ga3+ ions. Yet, despite having the same formal charge, Ga3+ substitution yields higher conductivities (10-3 S/cm) than Al3+ (10-4 S/cm). The reason of such difference in ionic conductivity remains a mystery. Here, we use molecular dynamic simulations and advanced sampling techniques to precisely unveil the atomistic origin of this phenomenon. Our results show that Li+ vacancies generated by Al3+ and Ga3+ substitution remain adjacent to Ga3+ and Al3+ ions, without contributing to the promotion of Li+ mobility. However, while Ga3+ ions tend to allow limited Li+ diffusion within their immediate surroundings, the less repulsive interactions associated with Al3+ ions lead to a complete blockage of neighboring Li+ diffusion paths. This effect is magnified at lower temperatures and explains the higher conductivities observed for Ga-substituted systems. Overall, this study provides a valuable insight into the fundamental ion transport mechanism in the bulk of Ga/Al-substituted Li7La3Zr2O12 and paves the way for rationalizing aliovalent substitution design strategies for enhancing ionic transport in these materials.

Adaptive Splitting Integrators for Enhancing Sampling Efficiency of Modified Hamiltonian Monte Carlo Methods in Molecular Simulation.

The modified Hamiltonian Monte Carlo (MHMC) methods, i.e., importance sampling methods that use modified Hamiltonians within a Hybrid Monte Carlo (HMC) framework, often outperform in sampling efficiency standard techniques such as molecular dynamics (MD) and HMC. The performance of MHMC may be enhanced further through the rational choice of the simulation parameters and by replacing the standard Verlet integrator with more sophisticated splitting algorithms. Unfortunately, it is not easy to identify the appropriate values of the parameters that appear in those algorithms. We propose a technique, that we call MAIA (Modified Adaptive Integration Approach), which, for a given simulation system and a given time step, automatically selects the optimal integrator within a useful family of two-stage splitting formulas. Extended MAIA (or e-MAIA) is an enhanced version of MAIA, which additionally supplies a value of the method-specific parameter that, for the problem under consideration, keeps the momentum acceptance rate at a user-desired level. The MAIA and e-MAIA algorithms have been implemented, with no computational overhead during simulations, in MultiHMC-GROMACS, a modified version of the popular software package GROMACS. Tests performed on well-known molecular models demonstrate the superiority of the suggested approaches over a range of integrators (both standard and recently developed), as well as their capacity to improve the sampling efficiency of GSHMC, a noticeable method for molecular simulation in the MHMC family. GSHMC combined with e-MAIA shows a remarkably good performance when compared to MD and HMC coupled with the appropriate adaptive integrators.

Assessment of van der Waals inclusive density functional theory methods for layered electroactive materials.

The discovery of computationally driven materials requires efficient and accurate methods. Density functional theory (DFT) meets these two requirements for many classes of materials. However, DFT-based methods have limitations. One significant shortcoming is the inadequate treatment of weak van der Waals (vdW) interactions, which are crucial for layered materials. Here we assess the performance of various vdW-inclusive DFT approaches for predicting the structure and voltage of layered electroactive materials for Li-ion batteries, considering a set of 20 different compounds. We find that the so-called optB86b-vdW density functional improves the agreement with the experimental data, closely followed by the latest generation of dispersion correction methods. These approaches yield average relative errors for the structural parameters smaller than 3%. The average deviations for redox potentials are below 0.15 V. Looking ahead, this study identifies accurate methods for Li-ion vdW bound systems, providing enhanced predictive power to DFT-assisted design for developing new types of electroactive materials in general.

Constant pressure hybrid Monte Carlo simulations in GROMACS.

Adaptation and implementation of the Generalized Shadow Hybrid Monte Carlo (GSHMC) method for molecular simulation at constant pressure in the NPT ensemble are discussed. The resulting method, termed NPT-GSHMC, combines Andersen barostat with GSHMC to enable molecular simulations in the environment natural for biological applications, namely, at constant pressure and constant temperature. Generalized Hybrid Monte Carlo methods are designed to maintain constant temperature and volume and extending their functionality to preserving pressure is not trivial. The theoretical formulation of NPT-GSHMC was previously introduced. Our main contribution is the implementation of this methodology in the GROMACS molecular simulation package and the evaluation of properties of NPT-GSHMC, such as accuracy, performance, effectiveness for real physical systems in comparison with well-established molecular simulation techniques. Benchmarking tests are presented and the obtained preliminary results are promising. For the first time, the generalized hybrid Monte Carlo simulations at constant pressure are available within the popular open source molecular dynamics software package.

Multiscale simulations of the antimicrobial peptide maculatin 1.1: water permeation through disordered aggregates.

The antimicrobial peptide maculatin 1.1 (M1.1) is an amphipathic α-helix that permeabilizes lipid bilayers. In coarse-grained molecular dynamics (CG MD) simulations, M1.1 has previously been shown to form membrane-spanning aggregates in DPPC bilayers. In this study, a simple multiscale methodology has been applied to allow sampling of important regions of the free energy surface at higher resolution. Thus, by back-converting the CG configurations to atomistic representations, it is shown that water is able to permeate through the M1.1 aggregates. Investigation of aggregate stoichiometry shows that at least six peptides are required for water permeation. The aggregates are dynamically disordered structures, and water flux occurs through irregular, fluctuating channels. The results are discussed in relation to experimental data and other simulations of antimicrobial peptides.

Improved sampling for simulations of interfacial membrane proteins: application of generalized shadow hybrid Monte Carlo to a peptide toxin/bilayer system.

The computational costs associated with performing molecular dynamics (MD) simulations are still somewhat prohibitive and therefore limit the time and length scales that can be currently achieved. One approach to overcoming the limited size and duration of a simulation is to reduce the amount of detail when representing a system of interest, generally termed "coarse-graining". An alternative approach is via more efficient sampling methods that offer an enhanced search of a complex multidimensional energy landscape. One could also combine enhanced sampling methods with a coarse-grained (CG) force field. Here, we apply generalized shadow hybrid Monte Carlo (GSHMC), a recently proposed simulation protocol, to a biomolecular system of moderate size and show that GSHMC offers improved sampling compared to standard MD simulation. Our test system is a CG representation of a small peptide toxin interacting with a phospholipid bilayer. Specifically, we show that GSHMC allows for a quicker localization of the toxin to its equilibrium location of interaction at the headgroup/water interface of the bilayer. GSHMC therefore potentially allows for future exploration of larger and more complex systems over longer periods, which would otherwise be impractical to perform using conventional simulation methodology.