Scholarly Works - Chemistry
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Item Open Access Accepted version Peer-reviewed Pressure gradients fail to predict diffusio-osmosis.(IoP, 2018-04-25) Liu, Yawei; Ganti, Raman; Frenkel, Daan; Frenkel, Daan [0000-0002-6362-2021]We present numerical simulations of diffusio-osmotic flow, i.e. the fluid flow generated by a concentration gradient along a solid-fluid interface. In our study, we compare a number of distinct approaches that have been proposed for computing such flows and compare them with a reference calculation based on direct, non-equilibrium molecular dynamics simulations. As alternatives, we consider schemes that compute diffusio-osmotic flow from the gradient of the chemical potentials of the constituent species and from the gradient of the component of the pressure tensor parallel to the interface. We find that the approach based on treating chemical potential gradients as external forces acting on various species agrees with the direct simulations, thereby supporting the approach of Marbach et al (2017 J. Chem. Phys. 146 194701). In contrast, an approach based on computing the gradients of the microscopic pressure tensor does not reproduce the direct non-equilibrium results.Item Open Access Accepted version Peer-reviewed Professor Steven V Ley CBE FRS FMedSci(Elsevier BV, 2018-06-21) Ley, Steven V; Ley, Steven [0000-0002-7816-0042]Professor Steven Ley is currently Professor of Chemistry and Director of Research at at the University of Cambridge. He is also a Fellow of Trinity College and was BP 1702 Professor of Chemistry for 21 years. Steve obtained his PhD from Loughborough University with Professor Harry Heaney and afterwards carried out postdoctoral research with Professor Leo Paquette (Ohio State University) and then Professor Derek Barton (Imperial College). He was appointed as a lecturer at Imperial College in 1975, promoted to Professor in 1983, and became Head of Department there in 1989. In 1990 he was elected to the Royal Society (London) and was President of The Royal Society of Chemistry from 2000-2002. Steve’s research interests are varied and span many disciplines including new synthetic methodologies, the total synthesis of natural products and the development of enabling technologies for chemical synthesis - especially in the area of flow chemistry technologies. Four spin-out companies have emerged from these research interests. Steve has published over 860 papers and has been honoured with 50 major awards including recently (since 2009): the Tetrahedron Prize for Creativity in Organic Chemistry (Elsevier); Heinrich Wieland Prize (Boehringer Ingelheim, Germany); The Paracelsus Prize (Swiss Chemical Society); The Royal Medal (The Royal Society, London); The Longstaff Prize (The Royal Society of Chemistry); the Franco-Britannique Prize (Société Chimique de France); and the IUPAC-Thales Nano Prize in Flow Chemistry. Professor Ley is also recipient of the 2018 Arthur C. Cope Award.Item Open Access Accepted version Peer-reviewed Engineering chemistry for the future of organic synthesis(Elsevier, 2018-06-21) Ley, SV; Ley, Steven [0000-0002-7816-0042]Societal and commercial pressures are impacting more than ever on the methods and techniques by which we assemble today's functional molecules. A holistic appreciation of this complex eco-system necessitates the invention of new tools and stimulates innovative thinking. In particular, the labour intensive and unsustainable practices of the past are being replaced by a more machine-based approach. This engineering of chemistry goes beyond the design of simple, enabling mechanical contrivances to encompass a full range of artificial intelligence (AI) methods, machine learning algorithms, advanced robotics and reaction profiling techniques. Integration of these systems with data collection and evaluation are the new drivers for success. Access to wider process windows, improved mixing and mass and heat transfer methods are providing early kinetic data that aids discovery. Mechanochem, photo-redox and electrochemical devices are further adding to the repertoire of the synthetic chemist. Flow chemistry and continuous processing methods are similarly breaking new ground as delineated by many of authors in this Symposium in Print. Indeed, flow chemistry has proven to be very amenable to automation over several telescoped reaction steps leading to complex natural products and active pharmaceutical ingredients (API's) in particular. The modular nature and flexibility of these systems assists in designing reactor configurations that can accommodate in-line purification, which are increasingly being used in downstream product processing.Item Open Access Published version Peer-reviewed A fluorescence anisotropy assay to discover and characterize ligands targeting the maytansine site of tubulin.(Springer Science and Business Media LLC, 2018-05-29) Menchon, Grégory; Prota, Andrea E; Lucena-Agell, Daniel; Bucher, Pascal; Jansen, Rolf; Irschik, Herbert; Müller, Rolf; Paterson, Ian; Díaz, J Fernando; Altmann, Karl-Heinz; Steinmetz, Michel O; Díaz, J Fernando [0000-0003-2743-3319]; Steinmetz, Michel O [0000-0001-6157-3687]Microtubule-targeting agents (MTAs) like taxol and vinblastine are among the most successful chemotherapeutic drugs against cancer. Here, we describe a fluorescence anisotropy-based assay that specifically probes for ligands targeting the recently discovered maytansine site of tubulin. Using this assay, we have determined the dissociation constants of known maytansine site ligands, including the pharmacologically active degradation product of the clinical antibody-drug conjugate trastuzumab emtansine. In addition, we discovered that the two natural products spongistatin-1 and disorazole Z with established cellular potency bind to the maytansine site on β-tubulin. The high-resolution crystal structures of spongistatin-1 and disorazole Z in complex with tubulin allowed the definition of an additional sub-site adjacent to the pocket shared by all maytansine-site ligands, which could be exploitable as a distinct, separate target site for small molecules. Our study provides a basis for the discovery and development of next-generation MTAs for the treatment of cancer.Item Open Access Accepted version Peer-reviewed The Engineering of Chemical Synthesis: Humans and Machines Working in Harmony(Wiley, 2018-05-04) Ley, Steven V; Ley, Steven [0000-0002-7816-0042]Words and phrases such as Artificial Intelligence, Machine Learning, Neural Networks, Robotics, the Cloud, Big Data and the Internet of Things are typically associated with many modern technological and scientific developments. Until recently, however, they have not been applied systematically to the chemical assembly of society’s functional molecules. Indeed, due to the lack of suitable tools, chemical synthesis in the past has tended to rely heavily on robust labour intensive batch processes that were often developed decades ago. This situation is changing rapidly owing to many reasons and, in particular, to the continuing need to discover new reactivity and new reactions, especially more sustainable processes. Smart, self-optimising platforms for continuous compound production along with a vast range of new analytical, monitoring and control devices for improved management of research experimentation and for accelerating the synthesis process are now available.Item Open Access Published version Peer-reviewed Backbone conformation affects duplex initiation and duplex propagation in hybridisation of synthetic H-bonding oligomers.(Royal Society of Chemistry (RSC), 2018-06-06) Iadevaia, Giulia; Núñez-Villanueva, Diego; Stross, Alexander E; Hunter, Christopher A; Iadevaia, Giulia [0000-0002-1182-0341]; Hunter, Christopher [0000-0002-5182-1859]Synthetic oligomers equipped with complementary H-bond donor and acceptor side chains form multiply H-bonded duplexes in organic solvents. Comparison of the duplex forming properties of four families of oligomers with different backbones shows that formation of an extended duplex with three or four inter-strand H-bonds is more challenging than formation of complexes that make only two H-bonds. The stabilities of 1 : 1 complexes formed between length complementary homo-oligomers equipped with either phosphine oxide or phenol recognition modules were measured in toluene. When the backbone is very flexible (pentane-1,5-diyl thioether), the stability increases uniformly by an order of magnitude for each additional base-pair added to the duplex: the effective molarities for formation of the first intramolecular H-bond (duplex initiation) and subsequent intramolecular H-bonds (duplex propagation) are similar. This flexible system is compared with three more rigid backbones that are isomeric combinations of an aromatic ring and methylene groups. One of the rigid systems behaves in exactly the same way as the flexible backbone, but the other two do not. For these systems, the effective molarity for formation of the first intramolecular H-bond is the same as that found for the other two backbones, but additional H-bonds are not formed between the longer oligomers. The effective molarities are too low for duplex propagation in these systems, because the oligomer backbones cannot adopt conformations compatible with formation of an extended duplex.Item Open Access Accepted version Peer-reviewed Cycling non-aqueous lithium-air batteries with dimethyl sulfoxide and sulfolane co-solvent(Johnson Matthey, 2018) Kim, G; Liu, T; Temprano, I; Petrucco, EA; Barrow, N; Grey, CP; Kim, Gunwoo [0000-0001-9153-3141]; Grey, Clare [0000-0001-5572-192X]Despite considerable research efforts, finding a chemically stable electrolyte mixture in the presence of reduced oxygen species remains a great challenge. Previously, dimethyl sulfoxide (DMSO) and sulfolane (tetramethylene sulfone (TMS))-based electrolytes were reported to be stable for lithium air (Li-O2) battery applications. Recently lithium hydroxide (LiOH) based chemistries have been demonstrated to involve supressed side reactions in water-added ether- and DMSO-based electrolytes. Herein, we investigate the impact of DMSO-based electrolyte and sulfolane co-solvent on cell chemistry in the presence of water. We found that DMSO-based electrolyte leads to formation of a peroxide-hydroxide mixture as discharge products and the removal of both LiOH and lithium peroxide (Li2O2) on charging from 3.2–3.6 V (vs. Li+/Li) is observed. In the presence of sulfolane as co-solvent, a mixture of Li2O2 and LiOH is formed as major discharge products with slightly more LiOH formation than in the absence of sulfolane. The presence of sulfolane has also significant effects on the charging behaviour, exhibiting a clearer 3 e−/O2 oxygen evolution reaction profile during the entire charging process. This work provides insights into understanding the effects of the primary solvent on promoting LiOH formation and decomposition in lithium iodide (LiI) mediated non-aqueous Li-O2 batteries.Item Open Access Published version Peer-reviewed Advances in the Synthesis and Long-Term Protection of Zero-Valent Iron Nanoparticles(Wiley, 2018) Mehta, JP; Knappett, BR; Divitini, G; Ringe, E; Midgley, PA; Fairen-Jimenez, D; Wheatley, AEH; Wheatley, AEH [0000-0002-2624-6063]AbstractCore@shell Fe@Fe3O4 nanoparticles (NPs) are synthesized via the thermal decomposition of iron pentacarbonyl (Fe(CO)5) in the presence either of oleylamine (OAm) or a mixture of OAm and oleic acid (OA). The heterostructured nanocomposites formed do so by a postsynthetic modification of isolated Fe seeds. This proves the versatility of the coating procedure and represents a significant advantage over previous work with Co seeds owing to the higher magnetic susceptibility, reduced toxicity, and excellent biocompatibility of Fe. Furthermore, the latter system allows the synthetic methodology to be developed from a two‐pot scenario where seeds are isolated then coated, to an easier and more efficient direct one‐pot scenario. The two‐pot method yields proportionately larger cores. However, in both cases, the monodisperse product reveals a carbonaceous interface between the Fe core and oxide shell. Meanwhile for the one‐pot synthesis, the OA:OAm ratio influences both the morphology and dispersity of the product. This is interpreted in terms of competing interactions of the ligands with the iron precursor. Superparamagnetism (SPM) is observed, and microscopic studies reveal oxidative stability of the Fe(0) cores achieved by either method for >6 months. It is proposed that the carbonaceous interface is critical to this sustained oxidative stability.Item Open Access Published version Peer-reviewed Optical fibre-tip probes for SERS: numerical study for design considerations.(Optica Publishing Group, 2018-06-11) Hutter, Tanya; Elliott, Stephen R; Mahajan, Sumeet; Hutter, Tanya [0000-0001-8106-1830]Enhancement of sub-wavelength optical fields using sub-micron plasmonic probes has found many applications in chemical, material, biological and medical sciences. The enhancement is via localised surface-plasmon resonance (LSPR) which enables the highly sensitive vibrational-spectroscopy technique of surface-enhanced Raman scattering (SERS). Combining SERS with optical fibres can allow the monitoring of biochemical reactions in situ with high resolution. Here, we study the electromagnetic-field enhancement of a tapered optical fibre-tip coated with gold nanoparticles (AuNPs) using finite-element simulations. We investigate the electric-field enhancement associated with metallic NPs and study the effect of parameters such as tip-aperture radius, cone angle, nanoparticle size and gaps between them. Our study provides an understanding of the design and application of metal-nanoparticle-coated optical-fibre-tip probes for SERS. The approach of using fibre-coupled delivery adds flexibility and simplifies the system requirements in SERS, making it suitable for cellular imaging and mapping bio-interfaces.Item Open Access Accepted version Peer-reviewed Unprecedented stability of raspberry-like colloids(Springer Nature) Vignolini, S; Vignolini, Silvia [0000-0003-0664-1418]Aqueous colloidal suspensions, both man-made and natural, are part of our everyday life. The applicability of colloidal suspensions, however, is highly limited by the range of conditions over which they are stable. Here, we report a novel type of highly monodisperse ‘raspberry’ colloids, which are prepared in a single-step synthesis that relies on simultaneous dispersion and emulsion polymerisation. The resulting raspberry colloids behave almost like hard spheres. In aqueous solutions such prepared raspberries show unprecedented stability against aggregation over large variations of added salt concentrations without addition of surfactants or other stabilisers. We present simple DLVO-calculations performed on raspberries and smooth colloids showing that this stability results from our raspberries’ unique morphology preventing salt-induced colloidal aggregation, which extends our understanding of colloidal stability against salting. Our calculations are supported by salting experiments using a variety of salts and differently sized colloids with varying ‘roughness’. Further, the raspberies’ stability facilitates the formation of superspheres and thin films in which the raspberry colloids self-assemble into hexagonally close-packed photonic crystals with exquisite reproducibility. Introduction The ability to disperse charged colloids in water is generally determined by the interplay between attractive van der Waals andItem Open Access Accepted version Peer-reviewed Origin of radiation tolerance in amorphous Ge2Sb2Te5 phase-change random-access memory material.(Proceedings of the National Academy of Sciences, 2018-05-22) Konstantinou, Konstantinos; Lee, Tae Hoon; Mocanu, Felix C; Elliott, Stephen R; Konstantinou, Konstantinos [0000-0003-1291-817X]The radiation hardness of amorphous Ge2Sb2Te5 phase-change random-access memory material has been elucidated by ab initio molecular-dynamics simulations. Ionizing radiation events have been modeled to investigate their effect on the atomic and electronic structure of the glass. Investigation of the short- and medium-range order highlights a structural recovery of the amorphous network after exposure to the high-energy events modeled in this study. Analysis of the modeled glasses reveals specific structural rearrangements in the local atomic geometry of the glass, as well as an increase in the formation of large shortest-path rings. The electronic structure of the modeled system is not significantly affected by the ionizing radiation events, since negligible differences have been observed before and after irradiation. These results provide a detailed insight into the atomistic structure of amorphous Ge2Sb2Te5 after irradiation and demonstrate the radiation hardness of the glass matrix.Item Open Access Published version Peer-reviewed Stapled peptides as a new technology to investigate protein-protein interactions in human platelets.(Royal Society of Chemistry (RSC), 2018-05-28) Iegre, Jessica; Ahmed, Niaz S; Gaynord, Josephine S; Wu, Yuteng; Herlihy, Kara M; Tan, Yaw Sing; Lopes-Pires, Maria E; Jha, Rupam; Lau, Yu Heng; Sore, Hannah F; Verma, Chandra; O' Donovan, Daniel H; Pugh, Nicholas; Spring, David R; Iegre, Jessica [0000-0002-9074-653X]; Gaynord, Josephine S [0000-0002-4091-8030]; Tan, Yaw Sing [0000-0002-2522-9421]; O' Donovan, Daniel H [0000-0002-8400-2198]; Pugh, Nicholas [0000-0002-6916-4199]; Spring, David R [0000-0001-7355-2824]Platelets are blood cells with numerous crucial pathophysiological roles in hemostasis, cardiovascular thrombotic events and cancer metastasis. Platelet activation requires the engagement of intracellular signalling pathways that involve protein-protein interactions (PPIs). A better understanding of these pathways is therefore crucial for the development of selective anti-platelet drugs. New strategies for studying PPIs in human platelets are required to overcome limitations associated with conventional platelet research methods. For example, small molecule inhibitors can lack selectivity and are often difficult to design and synthesise. Additionally, development of transgenic animal models is costly and time-consuming and conventional recombinant techniques are ineffective due to the lack of a nucleus in platelets. Herein, we describe the generation of a library of novel, functionalised stapled peptides and their first application in the investigation of platelet PPIs. Moreover, the use of platelet-permeable stapled Bim BH3 peptides confirms the part of Bim in phosphatidyl-serine (PS) exposure and reveals a role for the Bim protein in platelet activatory processes. Our work demonstrates that functionalised stapled peptides are a complementary alternative to conventional platelet research methods, and could make a significant contribution to the understanding of platelet signalling pathways and hence to the development of anti-platelet drugs.Item Open Access Accepted version Peer-reviewed Parapred: antibody paratope prediction using convolutional and recurrent neural networks.(Oxford University Press (OUP), 2018-09-01) Liberis, Edgar; Velickovic, Petar; Sormanni, Pietro; Vendruscolo, Michele; Liò, Pietro; Sormanni, Pietro [0000-0002-6228-2221]; Vendruscolo, Michele [0000-0002-3616-1610]; Lio, Pietro [0000-0002-0540-5053]MOTIVATION: Antibodies play essential roles in the immune system of vertebrates and are powerful tools in research and diagnostics. While hypervariable regions of antibodies, which are responsible for binding, can be readily identified from their amino acid sequence, it remains challenging to accurately pinpoint which amino acids will be in contact with the antigen (the paratope). RESULTS: In this work, we present a sequence-based probabilistic machine learning algorithm for paratope prediction, named Parapred. Parapred uses a deep-learning architecture to leverage features from both local residue neighbourhoods and across the entire sequence. The method significantly improves on the current state-of-the-art methodology, and only requires a stretch of amino acid sequence corresponding to a hypervariable region as an input, without any information about the antigen. We further show that our predictions can be used to improve both speed and accuracy of a rigid docking algorithm. AVAILABILITY AND IMPLEMENTATION: The Parapred method is freely available as a webserver at http://www-mvsoftware.ch.cam.ac.uk/and for download at https://github.com/eliberis/parapred. SUPPLEMENTARY INFORMATION: Supplementary information is available at Bioinformatics online.Item Open Access Published version Peer-reviewed Using Peptidomimetics and Constrained Peptides as Valuable Tools for Inhibiting Protein⁻Protein Interactions.(MDPI AG, 2018-04-19) Robertson, Naomi S; Spring, David R; Robertson, Naomi S [0000-0001-5519-9158]; Spring, David R [0000-0001-7355-2824]Protein⁻protein interactions (PPIs) are tremendously important for the function of many biological processes. However, because of the structure of many protein⁻protein interfaces (flat, featureless and relatively large), they have largely been overlooked as potential drug targets. In this review, we highlight the current tools used to study the molecular recognition of PPIs through the use of different peptidomimetics, from small molecules and scaffolds to peptides. Then, we focus on constrained peptides, and in particular, ways to constrain α-helices through stapling using both one- and two-component techniques.Item Open Access Accepted version Peer-reviewed Designing the Macrocyclic Dimension in Main Group Chemistry(Wiley-Blackwell, 2018-03-02) Wright, DS; Niu, H-C; Plajer, Alex J; Garcia-Rodriguez, Raul; Singh, Sanjay; Wright, Dominic [0000-0002-9952-3877]; Niu, Hao-Che [0000-0001-6660-4841]Outside the confines and well-established domain of organic chemistry, the systematic building of large macromolecular arrangements based on non-carbon elements represents a significant and exciting challenge. Our aim in the past two decades has been to develop robust synthetic methods to construct new types of main group architectures in a methodical way, principles of design that parallel those used in the organic arena. This concept article addresses the fundamental thermodynamic and kinetic problems involved in the design and synthesis of main group macrocycles and looks to future developments of macromolecules in this area, as well as new applications in coordination chemistry.Item Open Access Published version Peer-reviewed Exfoliation of Layered Na-Ion Anode Material Na2Ti3O7for Enhanced Capacity and Cyclability(ACS, 2018-03-13) Tsiamtsouri, MA; Allan, PK; Pell, AJ; Stratford, JM; Kim, G; Kerber, RN; Magusin, PCMM; Jefferson, DA; Grey, CP; Stratford, Joshua [0000-0002-6867-4226]; Kim, Gunwoo [0000-0001-9153-3141]; Magusin, Petrus [0000-0003-1167-3764]; Grey, Clare [0000-0001-5572-192X]We report the exfoliation of layered Na2Ti3O7, a promising anode material for Na-ion batteries, and restacking using HNO3and NaOH to form H-[Ti3O7] and Na(x)-[Ti3O7] compositions, respectively. The materials were characterized by a range of techniques (SEM, TEM, solid-state NMR, XRD, PDF). Although the formation of aggregated nanoparticles is favored under acidic restacking conditions, the use of basic conditions can lead to control over the adherence between the exfoliated layers. Pair distribution function (PDF) analysis confirms that the local TiO6connectivity of the pristine material is maintained. The lowest sodium-containing phase Na(1)-[Ti3O7], which is the stable product upon Na+leaching after consecutive washing steps, displays the best performance among the compositions studied, affording a stable reversible capacity of about 200 mAh·g-1for 20 cycles at a C/20 rate. Washing removes the excess of "free/reactive" Na+, which otherwise forms inactive Na2CO3in the insufficiently washed compositions.Item Open Access Optimal Design of Experiments by Combining Coarse and Fine Measurements.(American Physical Society (APS), 2017-11-17) Lee, Alpha A; Brenner, Michael P; Colwell, Lucy J; Colwell, Lucy [0000-0003-3148-0337]In many contexts, it is extremely costly to perform enough high-quality experimental measurements to accurately parametrize a predictive quantitative model. However, it is often much easier to carry out large numbers of experiments that indicate whether each sample is above or below a given threshold. Can many such categorical or "coarse" measurements be combined with a much smaller number of high-resolution or "fine" measurements to yield accurate models? Here, we demonstrate an intuitive strategy, inspired by statistical physics, wherein the coarse measurements are used to identify the salient features of the data, while the fine measurements determine the relative importance of these features. A linear model is inferred from the fine measurements, augmented by a quadratic term that captures the correlation structure of the coarse data. We illustrate our strategy by considering the problems of predicting the antimalarial potency and aqueous solubility of small organic molecules from their 2D molecular structure.Item Open Access Published version Peer-reviewed Solvatomorphism of Reichardt's dye(Royal Society of Chemistry (RSC), 2018) Pike, SJ; Bond, AD; Hunter, CA; Bond, Andrew [0000-0002-1744-0489]; Hunter, Christopher [0000-0002-5182-1859]Six different crystal structures are obtained depending on the crystallization solvent.
Item Open Access Published version Peer-reviewed The Impact of Stratospheric Ozone Feedbacks on Climate Sensitivity Estimates(American Geophysical Union (AGU), 2018) Nowack, PJ; Abraham, NL; Braesicke, P; Pyle, JA; Nowack, PJ [0000-0003-4588-7832]; Abraham, NL [0000-0003-3750-3544]; Braesicke, P [0000-0003-1423-0619]; Pyle, JA [0000-0003-3629-9916]AbstractA number of climate modeling studies have shown that differences between typical choices for representing ozone can affect climate change projections. Here we investigate potential climate impacts of a specific ozone representation used in simulations of the Hadley Centre Global Environment Model for the Coupled Model Intercomparison Project Phase 5. The method considers ozone changes only in the troposphere and lower stratosphere and prescribes stratospheric ozone elsewhere. For a standard climate sensitivity simulation, we find that this method leads to significantly increased global warming and specific patterns of regional surface warming compared with a fully interactive atmospheric chemistry setup. We explain this mainly by the suppressed part of the stratospheric ozone changes and the associated alteration of the stratospheric water vapor feedback. This combined effect is modulated by simultaneous cirrus cloud changes. We underline the need to understand better how representations of ozone can affect climate modeling results and, in particular, global and regional climate sensitivity estimates.Item Open Access Accepted version Peer-reviewed Theoretical prediction of thermal polarisation(American Physical Society, 2018-06-01) Wirnsberger, Peter; Dellago, Christoph; Frenkel, D; Reinhardt, Aleks; Wirnsberger, Peter [0000-0001-5961-5817]; Frenkel, Daan [0000-0002-6362-2021]We present a mean-field theory to explain the thermo-orientation effect in an off-center Stockmayer fluid. This effect is the underlying cause of thermally induced polarization and thermally induced monopoles, which have recently been predicted theoretically. Unlike previous theories that are based either on phenomenological equations or on scaling arguments, our approach does not require any fitting parameters. Given an equation of state and assuming local equilibrium, we construct an effective Hamiltonian for the computation of local Boltzmann averages. This simple theoretical treatment predicts molecular orientations that are in very good agreement with simulation results for the range of dipole strengths investigated. By decomposing the overall alignment into contributions from the temperature and density gradients, we shed further light on how the nonequilibrium result arises from the competition between the two gradients.