Sorting drug conformers in enzyme active sites: the XTB way.

In the present study, we have used the MEI196 set of interaction energies to investigate low-cost computational chemistry approaches for the calculation of binding between a molecule and its environment. Density functional theory (DFT) methods, when used with the vDZP basis set, yield good agreement with the reference energies. On the other hand, semi-empirical methods are less accurate as expected. By examining different groups of systems within MEI196 that contain species of a similar nature, we find that chemical similarity leads to cancellation of errors in the calculation of relative binding energies. Importantly, the semi-empirical method GFN1-xTB (XTB1) yields reasonable results for this purpose. We have thus further assessed the performance of XTB1 for calculating relative energies of docking poses of substrates in enzyme active sites represented by cluster models or within the ONIOM protocol. The results support the observations on error cancellation. This paves the way for the use of XTB1 in parts of large-scale virtual screening workflows to accelerate the drug discovery process.

Hydration Structure of 102No2+: A Density Functional Theory-Molecular Dynamics Study.

The hydration structure of No2+, the divalent cation of nobelium in water, was investigated by ab initio molecular dynamics (MD) simulations. First, a series of benchmark calculations were performed to validate the density functional theory (DFT) calculation methods for a molecule containing a No atom. The DFT-MD simulation of the hydration structure of No2+ was conducted after the MD method was validated by simulating the hydration structures of Ca2+ and Sr2+, whose behavior was previously reported to be similar to that of No2+. The model cluster containing M2+ (M = Ca, Sr, or No) and 32 water molecules was used for DFT-MD simulation. The results showed that the hydration distance of No2+ was intermediate between those of Ca2+ and Sr2+. This trend in the hydration distance is in good agreement with the elution position trend obtained in a previous radiochemical experiment. The calculated No-O bond lengths in the optimized structure of [No(H2O)8]2+ was 2.59 Å, while the average No-O bond length of [No(H2O)8]2+ in water by DFT-MD was 2.55 Å. This difference implies the importance of dynamic solvent effects, considering the second (and further) coordination sphere in the theoretical calculation of solution chemistry for superheavy elements.

Cluster-in-Cluster Approach for Computing MP2-Level Vibrational Infrared Spectra of Large Molecular Clusters.

Constructing the Hessian matrix (HM) for large molecules demands huge computational resources. Here, we report a cluster-in-cluster (CIC) procedure for efficiently evaluating HM and dipole derivatives for large molecular clusters by employing the second-order Møller-Plesset perturbation (MP2) theory. The highlight of the proposal is the separation of the estimations of Hartree-Fock (HF) and post-HF components. The parent cluster with n molecules is divided (virtually) into n subclusters centering each monomer and accommodating its near neighbors decided by a distance cutoff. The HF-level HM is obtained by doing full calculation (FC), while the correlation part is approximated by the respective subclusters. A software automating the procedure [followed by calculating infrared (IR) frequencies and intensities] is applied to deduce the IR spectrum for a variety of molecular clusters, particularly water clusters of various sizes, containing up to ∼2000 basis functions. The accuracy of the IR spectrum constructed using CIC is remarkable, with a substantial time advantage (with respect to its FC counterpart). The reduced computational resources and the tractability of the computations are other major benefits of the procedure.

Imaging approaches for the diagnosis of genetic diseases affecting the female reproductive organs and beyond.

This review aims to provide an overview of neoplastic lesions associated with genetic diseases affecting the female reproductive organs. It seeks to enhance our understanding of the radiological aspects in diagnosing genetic diseases including hereditary breast and ovarian cancer syndromes, Lynch syndrome, Peutz-Jeghers syndrome, nevoid basal cell carcinoma syndrome, and Swyer syndrome, and explores the patterns and mechanisms of inheritance that require elucidation. Additionally, we discuss the imaging characteristics of lesions occurring in other regions due to the same genetic diseases.

Many-body Effects on Electronic Transport in Molecular Junctions: A Quantum Perspective.

This concept delves into quantum particle transport at the nanoscale, with a particular focus on how electrons move through molecular circuits. The thriving field of single molecular electronics benefits from the unique electrical and other properties of nanostructures. It concentrates on single molecular junctions that serve as bridges between electrodes. In this context, the electronic correlation-induced many-body effect gives rise to resonant states. These states, along with conductance, depend on electron spin. Thus, the field acts as a bridge between quantum and macroscopic worlds, unveiling unique behaviors of electrons. Additionally, external factors, such as magnetic fields and voltages, offer means to control the electron correlation in these junctions.

Predicting potential SARS-CoV-2 mutations of concern via full quantum mechanical modelling.

Ab initio quantum mechanical models can characterize and predict intermolecular binding, but only recently have models including more than a few hundred atoms gained traction. Here, we simulate the electronic structure for approximately 13 000 atoms to predict and characterize binding of SARS-CoV-2 spike variants to the human ACE2 (hACE2) receptor using the quantum mechanics complexity reduction (QM-CR) approach. We compare four spike variants in our analysis: Wuhan, Omicron, and two Omicron-based variants. To assess binding, we mechanistically characterize the energetic contribution of each amino acid involved, and predict the effect of select single amino acid mutations. We validate our computational predictions experimentally by comparing the efficacy of spike variants binding to cells expressing hACE2. At the time we performed our simulations (December 2021), the mutation A484K which our model predicted to be highly beneficial to ACE2 binding had not been identified in epidemiological surveys; only recently (August 2023) has it appeared in variant BA.2.86. We argue that our computational model, QM-CR, can identify mutations critical for intermolecular interactions and inform the engineering of high-specificity interactors.

Imaging findings in inflammatory disease of the genital organs.

This review focuses on inflammatory diseases of female and male genital organs and discusses their epidemiology, pathogenesis, clinical presentation, and imaging findings. The female section covers pelvic inflammatory disease (PID) primarily caused by sexually transmitted infections (STIs) that affect the uterus, fallopian tubes, and ovaries. Unusual causes such as actinomycosis and tuberculosis have also been explored. The male section delves into infections affecting the vas deferens, epididymis, testes, prostate, and seminal vesicles. Uncommon causes such as tuberculosis, and Zinner syndrome have also been discussed. In addition, this review highlights other conditions that mimic male genital tract infections such as vasculitis, IgG4-related diseases, and sarcoidosis. Accurate diagnosis and appropriate management of these inflammatory diseases are essential for preventing serious complications and infertility. Imaging modalities such as ultrasound, magnetic resonance imaging, and computed tomography play a crucial role in diagnosis. Understanding the diverse etiologies and imaging findings is vital for the effective management of inflammatory diseases of the genital organs.

Hip and lumbosacral joint centre locations in asian population: Biases produced by existing regression equations and development of new equations.

The hip and lumbosacral joint centre (HJC and LSJC) predictions are required to analyse the lumbo-pelvic-hip dynamics during various human motions. Some HJC and LSJC regression equations based on pelvic dimension have been developed; however, the pre-existing methods need to be re-evaluated, and methodological reconsideration may improve the regression methods. Here we show that pre-existing methods produce biased predictions of the LSJC and HJC in 23 male and 24 female Japanese adults, and that the biases in the LSJC differ between sexes, using magnetic resonance imaging (MRI) around the pelvis. Compared with directly measured locations on MRI, the pre-existing regression equations predict LSJC to be more posterior in males and more inferior and posterior in females, and HJC to be more medial in both sexes. The better pre-existing regression equation for LSJC height differs between sexes, with pelvic-width-base better in males and pelvic-depth-base better in females, respectively. We suggest the unsuitability of pre-existing methods to our dataset consisting of Japanese adults and the importance of considering sex differences in regression methods. We propose regression equations to predict HJC and LSJC, considering soft-tissue thickness, sex differences, and a height-directional measure, using least absolute shrinkage and selection operator regression. We validate them using leave-one-out cross-validation (LOOCV). LOOCV shows that our model produces negligible biases and smaller absolute errors than the pre-existing regressions; in particular, the anteroposterior absolute error for LSJC is less than half that of the pre-existing regression. Our regression equation can be a powerful solution for accurate motion analysis.

The verification of delta SCF and Slater's transition state theory for the calculation of core ionization energy.

The core ionization energies of second- and third-period elements of the molecules C2 H5 NO2 , SiF4 , Si(CH3 )4 , PF3 , POF3 , PSF3 , CS2 , OCS, SO2 , SO2 F2 , CH3 Cl, CFCl3 , SF5 Cl, and Cl3 PS are calculated by using Hartree-Fock (HF), and Kohn-Sham (KS) with BH&HLYP, B3LYP, and LC-BOP functionals. We used ΔSCF, Slater's transition state (STS), and two previously proposed shifted STS (1) and shifted STS (2) methods, which have been developed. The errors of ΔSCF and STS come mainly from the self-interaction errors (SIE) and can be corrected with a shifting scheme. In this study, we used the shifting parameters determined for each atom. The shifted STS (1) reproduces ΔSCF almost perfectly with mean absolute deviations (MAD) of 0.02 eV. While ΔSCF and STS vary significantly depending on the functional used, the variation of shifted STS (2) is small, and all shifted STS (2) values are close to the observed ones. The deviations of the shifted STS (2) from the experiment are 0.24 eV (BH&HLYP), 0.19 eV (B3LYP), and 0.23 eV (LC-BOP). These results further support the use of shifted STS methods for predicting the core ionization energies.

Special Topic on High Performance Computing in Chemical Physics.

Computational modeling and simulation have become indispensable scientific tools in virtually all areas of chemical, biomolecular, and materials systems research. Computation can provide unique and detailed atomic level information that is difficult or impossible to obtain through analytical theories and experimental investigations. In addition, recent advances in micro-electronics have resulted in computer architectures with unprecedented computational capabilities, from the largest supercomputers to common desktop computers. Combined with the development of new computational domain science methodologies and novel programming models and techniques, this has resulted in modeling and simulation resources capable of providing results at or better than experimental chemical accuracy and for systems in increasingly realistic chemical environments.

Development and validation of CT-based radiomics deep learning signatures to predict lymph node metastasis in non-functional pancreatic neuroendocrine tumors: a multicohort study.

Background: Lymph node status is an important factor for the patients with non-functional pancreatic neuroendocrine tumors (NF-PanNETs) with respect to the surgical methods, prognosis, recurrence. Our aim is to develop and validate a combination model based on contrast-enhanced CT images to predict the lymph node metastasis (LNM) in NF-PanNETs. Methods: Retrospective data were gathered for 320 patients with NF-PanNETs who underwent curative pancreatic resection and CT imaging at two institutions (Center 1, n = 236 and Center 2, n = 84) between January 2010 and March 2022. RDPs (Radiomics deep learning signature) were developed based on ten machine-learning techniques. These signatures were integrated with the clinicopathological factors into a nomogram for clinical applications. The evaluation of the model's performance was conducted through the metrics of the area under the curve (AUC). Findings: The RDPs showed excellent performance in both centers with a high AUC for predicting LNM and disease-free survival (DFS) in Center 1 (AUC, 0.88; 95% CI: 0.84-0.92; DFS, p < 0.05) and Center 2 (AUC, 0.91; 95% CI: 0.85-0.97; DFS, p < 0.05). The clinical factors of vascular invasion, perineural invasion, and tumor grade were associated with LNM (p < 0.05). The combination nomogram showed better prediction capability for LNM (AUC, 0.93; 95% CI: 0.89-0.96). Notably, our model maintained a satisfactory predictive ability for tumors at the 2-cm threshold, demonstrating its effectiveness across different tumor sizes in Center 1 (≤2 cm: AUC, 0.90 and >2 cm: AUC, 0.86) and Center 2 (≤2 cm: AUC, 0.93 and >2 cm: AUC, 0.91). Interpretation: Our RDPs may have the potential to preoperatively predict LNM in NF-PanNETs, address the insufficiency of clinical guidelines concerning the 2-cm threshold for tumor lymph node dissection, and provide precise therapeutic strategies. Funding: This work was supported by JSPS KAKENHI Grant Number JP22K20814; the Rare Tumor Research Special Project of the National Natural Science Foundation of China (82141104) and Clinical Research Special Project of Shanghai Municipal Health Commission (202340123).

Theoretical elucidation of the structure, bonding, and reactivity of the CaMn4Ox clusters in the whole Kok cycle for water oxidation embedded in the oxygen evolving center of photosystem II. New molecular and quantum insights into the mechanism of the O-O bond formation.

This paper reviews our historical developments of broken-symmetry (BS) and beyond BS methods that are applicable for theoretical investigations of metalloenzymes such as OEC in PSII. The BS hybrid DFT (HDFT) calculations starting from high-resolution (HR) XRD structure in the most stable S1 state have been performed to elucidate structure and bonding of whole possible intermediates of the CaMn4Ox cluster (1) in the Si (i = 0 ~ 4) states of the Kok cycle. The large-scale HDFT/MM computations starting from HR XRD have been performed to elucidate biomolecular system structures which are crucial for examination of possible water inlet and proton release pathways for water oxidation in OEC of PSII. DLPNO CCSD(T0) computations have been performed for elucidation of scope and reliability of relative energies among the intermediates by HDFT. These computations combined with EXAFS, XRD, XFEL, and EPR experimental results have elucidated the structure, bonding, and reactivity of the key intermediates, which are indispensable for understanding and explanation of the mechanism of water oxidation in OEC of PSII. Interplay between theory and experiments have elucidated important roles of four degrees of freedom, spin, charge, orbital, and nuclear motion for understanding and explanation of the chemical reactivity of 1 embedded in protein matrix, indicating the participations of the Ca(H2O)n ion and tyrosine(Yz)-O radical as a one-electron acceptor for the O-O bond formation. The Ca-assisted Yz-coupled O-O bond formation mechanisms for water oxidation are consistent with recent XES and very recent time-resolved SFX XFEL and FTIR results.

REAlgo: Rapid and efficient algorithm for estimating MP2/CCSD energy gradients for large molecular clusters.

This work reports the development of an algorithm for rapid and efficient evaluation of energy gradients for large molecular clusters employing correlated methods viz. second-order Møller-Plesset perturbation theory (MP2) theory and couple cluster singles and doubles (CCSD). The procedure segregates the estimation of Hartree-Fock (HF) and correlation components. The HF energy and gradients are obtained by performing a full calculation. The correlation energy is approximated as the corresponding two-body interaction energy. Correlation gradients for each monomer are approximated from the respective monomer-centric fragments comprising its immediate neighbours. The programmed algorithm is explored for the geometry optimization of large molecular clusters using the BERNY optimizer as implemented in the Gaussian suite of software. The accuracy and efficacy of the method are critically probed for a variety of large molecular clusters containing up to 3000 basis functions, in particular large water clusters. The CCSD level geometry optimization of molecular clusters containing ∼800 basis functions employing a modest hardware is also reported.

Distal muscle cross-sectional area is correlated with shot put performance.

Shot putters throw a heavy shot by "pushing". Pushing involves the coordinated extension of multiple joints and is a common motor task for both upper and lower limbs. In lower limb musculature, proximal-specific development and association with motor performance have been shown in athletes. However, as the upper limb is not mechanically loaded to support the body during daily locomotion, it may develop differently from the lower limb. We investigated the cross-sectional area of the prime movers of the upper limb and upper trunk (pectoralis major, deltoid, triceps brachii, and palmar flexors) in eleven male shot put athletes and fourteen untrained males by obtaining magnetic resonance images and manually tracing the muscles on the images. All target muscles were significantly larger in athletes than non-athletes (p < 0.01), with "huge" effect sizes for the pectoralis major and palmar flexors (d = 2.74, 2.04). All target muscle cross-sectional areas were positively correlated with season best record (r ≥ 0.62, p ≤ 0.04), with a particularly strong correlation for the palmar flexors (r = 0.96). These results suggest that the distal muscles of the upper limb are also expected to develop and are strongly associated with motor performance. This is especially true for the distal upper limb muscles (palmar flexors) in shot putters. These findings provide insight into potential training interventions for athletic performance in forceful upper limb movements.

Single-cell dissection, hdWGCNA and deep learning reveal the role of oxidatively stressed plasma cells in ulcerative colitis.

Ulcerative colitis (UC) develops as a result of complex interactions between various cell types in the mucosal microenvironment. In this study, we aim to elucidate the pathogenesis of ulcerative colitis at the single-cell level and unveil its clinical significance. Using single-cell RNA sequencing and high-dimensional weighted gene co-expression network analysis, we identify a subpopulation of plasma cells (PCs) with significantly increased infiltration in UC colonic mucosa, characterized by pronounced oxidative stress. Combining 10 machine learning approaches, we find that the PC oxidative stress genes accurately distinguish diseased mucosa from normal mucosa (independent external testing AUC=0.991, sensitivity=0.986, specificity=0.909). Using MCPcounter and non-negative matrix factorization, we identify the association between PC oxidative stress genes and immune cell infiltration as well as patient heterogeneity. Spatial transcriptome data is used to verify the infiltration of oxidatively stressed PCs in colitis. Finally, we develop a gene-immune convolutional neural network deep learning model to diagnose UC mucosa in different cohorts (independent external testing AUC=0.984, sensitivity=95.9%, specificity=100%). Our work sheds light on the key pathogenic cell subpopulations in UC and is essential for the development of future clinical disease diagnostic tools.

Core-Level 2s and 2p Binding Energies of Third-Period Elements (P, S, and Cl) Calculated by Hartree-Fock and Kohn-Sham ΔSCF Theory.

In the present study, we investigate the use of the ΔSCF method and Slater's transition state (STS) theory to calculate the binding energies of the 2s and 2p electrons of third-period elements (P, S, and Cl). Both the Hartree-Fock (HF) and Kohn-Sham (KS) approximations are examined. The STS approximation performs well in reproducing the ΔSCF values. However, for the ΔSCF method itself, while the binding energy of the 2p electrons is accurately predicted, the results for 2s are fairly sensitive to the functional, exhibiting significant variations due to self-interaction errors (SIE). Nonetheless, the variations in chemical shifts between different species remain relatively small, and the values agree with experiments due to the cancellation of SIE. A notable observation is that the chemical shifts of the 2s and 2p electrons are similar, indicating a perturbation caused by the valence electrons. The error in the absolute binding energy of KS ΔSCF against the experiment is nearly constant for the same element in different molecules, and it depends largely on the functional owing to SIE. A shifting scheme previously developed can be employed to reproduce the experimental 2s and 2p binding energies, with dependence on the functional and atom but not on the molecule even for 2s KS ΔSCF binding energies. Upon obtaining the corrected binding energies, we find that the gap between 2s and 2p binding energy is nearly independent of chemical environment for a given element: 57.5, 63.9, and 70.9 eV for the elements P, S, and Cl, respectively.

Identification of antigen-presentation related B cells as a key player in Crohn's disease using single-cell dissecting, hdWGCNA, and deep learning.

Crohn's disease (CD) arises from intricate intercellular interactions within the intestinal lamina propria. Our objective was to use single-cell RNA sequencing to investigate CD pathogenesis and explore its clinical significance. We identified a distinct subset of B cells, highly infiltrated in the CD lamina propria, that expressed genes related to antigen presentation. Using high-dimensional weighted gene co-expression network analysis and nine machine learning techniques, we demonstrated that the antigen-presenting CD-specific B cell signature effectively differentiated diseased mucosa from normal mucosa (Independent external testing AUC = 0.963). Additionally, using MCPcounter and non-negative matrix factorization, we established a relationship between the antigen-presenting CD-specific B cell signature and immune cell infiltration and patient heterogeneity. Finally, we developed a gene-immune convolutional neural network deep learning model that accurately diagnosed CD mucosa in diverse cohorts (Independent external testing AUC = 0.963). Our research has revealed a population of B cells with a potential promoting role in CD pathogenesis and represents a fundamental step in the development of future clinical diagnostic tools for the disease.

Differences in the position of endometriosis-associated and non-associated ovarian cancer relative to the uterus.

BACKGROUND: Preoperative assessment of the histological type of ovarian cancer is essential to determine the appropriate treatment strategy. Tumor location may be helpful in this regard. The purpose of this study was to compare the position of endometriosis-associated (EAOCs) and non-associated (non-EAOCs) ovarian cancer relative to the uterus using MRI. METHODS: This retrospective study included patients with pathologically confirmed malignant epithelial ovarian tumors who underwent MRI at our hospital between January 2015 and January 2023. T2-weighted images of the sagittal and axial sections of the long axis of the uterine body were used for the analysis. Three blinded experienced radiologists independently interpreted the images and assessed whether the ovarian tumor was attached to the uterus, and the angle between the uterus and the tumor was measured. The presence of attachment and the measured angles were compared for each histology. In addition, the angles between EAOCs, including endometrioid carcinomas (ECs) and clear cell carcinomas (CCCs), were compared with non-EAOCs. RESULTS: In total, 184 women (mean age, 56 years; age range, 20-91 years) were evaluated. High-grade serous carcinomas (HGSCs) were significantly smaller than the others and had significantly less uterine attachment than CCCs (p < 0.01 for all readers). According to the mean of the measured angles, CCCs were positioned significantly more posteriorly than HGSCs and mucinous carcinomas (p < 0.02), and EAOCs were positioned significantly more posteriorly to the uterus than non-EAOCs (p < 0.01). CONCLUSION: HGSCs are often not attached to the uterus, and EAOCs are positioned more posteriorly to the uterus than non-EAOCs. CRITICAL RELEVANCE STATEMENT: High-grade serous carcinomas were often not attached to the uterus, and endometriosis-associated ovarian cancers were positioned more posteriorly to the uterus than non-endometriosis-associated ovarian cancers. KEY POINTS: • The position of the ovarian tumor can be determined using MRI. • High-grade serous carcinomas had less attachment to the uterus. • Endometriosis-associated cancers were positioned more posteriorly to the uterus. • The location of ovarian tumors is helpful in estimating histology.

Triple modal treatment comprising with proton beam radiation, hyperthermia, and gemcitabine/nab-paclitaxel for locally advanced pancreatic cancer: a phase I/II study protocol (TT-LAP trial).

BACKGROUND: Locally advanced pancreatic ductal adenocarcinoma (PDAC), accounting for about 30% of PDAC patients, is difficult to cure by radical resection or systemic chemotherapy alone. A multidisciplinary strategy is required and our TT-LAP trial aims to evaluate whether triple-modal treatment with proton beam therapy (PBT), hyperthermia, and gemcitabine plus nab-paclitaxel is a safe and synergistically effective treatment for patients with locally advanced PDAC. METHODS: This trial is an interventional, open-label, non-randomized, single-center, single-arm phase I/II clinical trial organized and sponsored by the University of Tsukuba. Eligible patients who are diagnosed with locally advanced pancreatic cancer, including both borderline resectable (BR) and unresectable locally advanced (UR-LA) patients, and selected according to the inclusion and exclusion criteria will receive triple-modal treatment consisting of chemotherapy, hyperthermia, and proton beam radiation. Treatment induction will include 2 cycles of chemotherapy (gemcitabine plus nab-paclitaxel), proton beam therapy, and 6 total sessions of hyperthermia therapy. The initial 5 patients will move to phase II after adverse events are verified by a monitoring committee and safety is ensured. The primary endpoint is 2-year survival rate while secondary endpoints include adverse event rate, treatment completion rate, response rate, progression-free survival, overall survival, resection rate, pathologic response rate, and R0 (no pathologic cancer remnants) rate. The target sample size is set at 30 cases. DISCUSSION: The TT-LAP trial is the first to evaluate the safety and effectiveness (phases1/2) of triple-modal treatment comprised of proton beam therapy, hyperthermia, and gemcitabine/nab-paclitaxel for locally advanced pancreatic cancer. ETHICS AND DISSEMINATION: This protocol was approved by the Tsukuba University Clinical Research Review Board (reference number TCRB22-007). Results will be analyzed after study recruitment and follow-up are completed. Results will be presented at international meetings of interest in pancreatic cancer plus gastrointestinal, hepatobiliary, and pancreatic surgeries and published in peer-reviewed journals. TRIAL REGISTRATION: Japan Registry of Clinical Trials, jRCTs031220160. Registered 24 th June 2022, https://jrct.niph.go.jp/en-latest-detail/jRCTs031220160 .

Analytical quadrature method using recurrence formulas for two-electron integrals of frequency-dependent Breit interaction.

A recursive scheme was proposed to calculate two-electron integrals of frequency-dependent Breit interactions in electronic structure calculations using Gaussian basis functions. As shown in a previous study [R. Ahlrichs, Phys. Chem. Chem. Phys. 8 (2006) 3072-3077], the vertical recurrence relation for the two-electron integrals of the general two-body potential is valid. In addition, the authors have shown that the horizontal case is also valid. Explicit expressions for generalized molecular incomplete gamma function corresponding to the frequency-dependent Gaunt and gauge potentials were then derived, along with their asymptotic formulas. In addition, an implementation for computing the generalized molecular incomplete gamma function was proposed. Through numerical calculations, the shape of the curves of the generalized molecular incomplete gamma functions were found to vary significantly from that of the zero-energy case with the increase in the energy variable.