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Ions surround nucleic acids in what is referred to as an ion atmosphere. As a result, the folding and dynamics of RNA and DNA and their complexes with proteins and with each other cannot be understood without a reasonably sophisticated appreciation of these ions' electrostatic interactions. However, the underlying behavior of the ion atmosphere follows physical rules that are distinct from the rules of site binding that biochemists are most familiar and comfortable with. The main goal of this review is to familiarize nucleic acid experimentalists with the physical concepts that underlie nucleic acid-ion interactions. Throughout, we provide practical strategies for interpreting and analyzing nucleic acid experiments that avoid pitfalls from oversimplified or incorrect models. We briefly review the status of theories that predict or simulate nucleic acid-ion interactions and experiments that test these theories. Finally, we describe opportunities for going beyond phenomenological fits to a next-generation, truly predictive understanding of nucleic acid-ion interactions.
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Íons/química , Ácidos Nucleicos/química , Algoritmos , Sítios de Ligação , Cátions , Cristalografia por Raios X , DNA/química , Magnésio/química , Metais/química , Modelos Teóricos , Conformação de Ácido Nucleico , Distribuição de Poisson , RNA/química , Software , Eletricidade Estática , TermodinâmicaRESUMO
Understanding natural protein evolution and designing novel proteins are motivating interest in development of high-throughput methods to explore large sequence spaces. In this work, we demonstrate the application of multisite λ dynamics (MSλD), a rigorous free energy simulation method, and chemical denaturation experiments to quantify evolutionary selection pressure from sequence-stability relationships and to address questions of design. This study examines a mesophilic phylogenetic clade of ribonuclease H (RNase H), furthering its extensive characterization in earlier studies, focusing on E. coli RNase H (ecRNH) and a more stable consensus sequence (AncCcons) differing at 15 positions. The stabilities of 32,768 chimeras between these two sequences were computed using the MSλD framework. The most stable and least stable chimeras were predicted and tested along with several other sequences, revealing a designed chimera with approximately the same stability increase as AncCcons, but requiring only half the mutations. Comparing the computed stabilities with experiment for 12 sequences reveals a Pearson correlation of 0.86 and root mean squared error of 1.18 kcal/mol, an unprecedented level of accuracy well beyond less rigorous computational design methods. We then quantified selection pressure using a simple evolutionary model in which sequences are selected according to the Boltzmann factor of their stability. Selection temperatures from 110 to 168 K are estimated in three ways by comparing experimental and computational results to evolutionary models. These estimates indicate selection pressure is high, which has implications for evolutionary dynamics and for the accuracy required for design, and suggests accurate high-throughput computational methods like MSλD may enable more effective protein design.
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Escherichia coli , Ribonuclease H , Escherichia coli/genética , Filogenia , Simulação por Computador , Sequência Consenso , Ribonuclease H/genéticaRESUMO
Homomeric dimerization of metabotropic glutamate receptors (mGlus) is essential for the modulation of their functions and represents a promising avenue for the development of novel therapeutic approaches to address central nervous system diseases. Yet, the scarcity of detailed molecular and energetic data on mGlu2 impedes our in-depth comprehension of their activation process. Here, we employ computational simulation methods to elucidate the activation process and key events associated with the mGlu2, including a detailed analysis of its conformational transitions, the binding of agonists, Gi protein coupling, and the guanosine diphosphate (GDP) release. Our results demonstrate that the activation of mGlu2 is a stepwise process and several energy barriers need to be overcome. Moreover, we also identify the rate-determining step of the mGlu2's transition from the agonist-bound state to its active state. From the perspective of free-energy analysis, we find that the conformational dynamics of mGlu2's subunit follow coupled rather than discrete, independent actions. Asymmetric dimerization is critical for receptor activation. Our calculation results are consistent with the observation of cross-linking and fluorescent-labeled blot experiments, thus illustrating the reliability of our calculations. Besides, we also identify potential key residues in the Gi protein binding position on mGlu2, mGlu2 dimer's TM6-TM6 interface, and Gi α5 helix by the change of energy barriers after mutation. The implications of our findings could lead to a more comprehensive grasp of class C G protein-coupled receptor activation.
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Receptores de Glutamato Metabotrópico , Receptores de Glutamato Metabotrópico/metabolismo , Receptores de Glutamato Metabotrópico/química , Humanos , Multimerização Proteica , Simulação de Dinâmica Molecular , Conformação Proteica , Ligação ProteicaRESUMO
Solving the mechanism of a chemical reaction requires determining the structures of all the ground states on the pathway and the elusive transition states linking them. 2024 is the centenary of Brønsted's landmark paper that introduced the ß-value and structure-activity studies as the only experimental means to infer the structures of transition states. It involves making systematic small changes in the covalent structure of the reactants and analysing changes in activation and equilibrium-free energies. Protein engineering was introduced for an analogous procedure, Φ-value analysis, to analyse the noncovalent interactions in proteins central to biological chemistry. The methodology was developed first by analysing noncovalent interactions in transition states in enzyme catalysis. The mature procedure was then applied to study transition states in the pathway of protein folding - 'part (b) of the protein folding problem'. This review describes the development of Φ-value analysis of transition states and compares and contrasts the interpretation of ß- and Φ-values and their limitations. Φ-analysis afforded the first description of transition states in protein folding at the level of individual residues. It revealed the nucleation-condensation folding mechanism of protein domains with the transition state as an expanded, distorted native structure, containing little fully formed secondary structure but many weak tertiary interactions. A spectrum of transition states with various degrees of structural polarisation was then uncovered that spanned from nucleation-condensation to the framework mechanism of fully formed secondary structure. Φ-analysis revealed how movement of the expanded transition state on an energy landscape accommodates the transition from framework to nucleation-condensation mechanisms with a malleability of structure as a unifying feature of folding mechanisms. Such movement follows the rubric of analysis of classical covalent chemical mechanisms that began with Brønsted. Φ-values are used to benchmark computer simulation, and Φ and simulation combine to describe folding pathways at atomic resolution.
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Dobramento de Proteína , Proteínas , Simulação por Computador , Proteínas/química , Engenharia de Proteínas , Biologia , Cinética , TermodinâmicaRESUMO
Microtubules (MTs) are large cytoskeletal polymers, composed of αß-tubulin heterodimers, capable of stochastically converting from polymerizing to depolymerizing states and vice versa. Depolymerization is coupled with hydrolysis of guanosine triphosphate (GTP) within ß-tubulin. Hydrolysis is favored in the MT lattice compared to a free heterodimer with an experimentally observed rate increase of 500- to 700-fold, corresponding to an energetic barrier lowering of 3.8 to 4.0 kcal/mol. Mutagenesis studies have implicated α-tubulin residues, α:E254 and α:D251, as catalytic residues completing the ß-tubulin active site of the lower heterodimer in the MT lattice. The mechanism for GTP hydrolysis in the free heterodimer, however, is not understood. Additionally, there has been debate concerning whether the GTP-state lattice is expanded or compacted relative to the GDP state and whether a "compacted" GDP-state lattice is required for hydrolysis. In this work, extensive quantum mechanics/molecular mechanics simulations with transition-tempered metadynamics free-energy sampling of compacted and expanded interdimer complexes, as well as a free heterodimer, have been carried out to provide clear insight into the GTP hydrolysis mechanism. α:E254 was found to be the catalytic residue in a compacted lattice, while in the expanded lattice, disruption of a key salt bridge interaction renders α:E254 less effective. The simulations reveal a barrier decrease of 3.8 ± 0.5 kcal/mol for the compacted lattice compared to a free heterodimer, in good agreement with experimental kinetic measurements. Additionally, the expanded lattice barrier was found to be 6.3 ± 0.5 kcal/mol higher than compacted, demonstrating that GTP hydrolysis is variable with lattice state and slower at the MT tip.
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Microtúbulos , Tubulina (Proteína) , Guanosina Trifosfato , Tubulina (Proteína)/química , Hidrólise , Guanosina Difosfato/química , Microtúbulos/químicaRESUMO
The serotonin transporter (SERT) tightly regulates synaptic serotonin levels and has been the primary target of antidepressants. Binding of inhibitors to the allosteric site of human SERT (hSERT) impedes the dissociation of antidepressants bound at the central site and may enhance the efficacy of such antidepressants to potentially reduce their dosage and side effects. Here, we report the identification of a series of high-affinity allosteric inhibitors of hSERT in a unique scaffold, with the lead compound, Lu AF88273 (3-(1-(2-(1H-indol-3-yl)ethyl)piperidin-4-yl)-6-chloro-1H-indole), having 2.1 nM allosteric potency in inhibiting imipramine dissociation. In addition, we find that Lu AF88273 also inhibits serotonin transport in a noncompetitive manner. The binding pose of Lu AF88273 in the allosteric site of hSERT is determined with extensive molecular dynamics simulations and rigorous absolute binding free energy perturbation (FEP) calculations, which show that a part of the compound occupies a dynamically formed small cavity. The predicted binding location and pose are validated by site-directed mutagenesis and can explain much of the structure-activity relationship of these inhibitors using the relative binding FEP calculations. Together, our findings provide a promising lead compound and the structural basis for the development of allosteric drugs targeting hSERT. Further, they demonstrate that the divergent allosteric sites of neurotransmitter transporters can be selectively targeted.
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Citalopram , Proteínas da Membrana Plasmática de Transporte de Serotonina , Humanos , Antidepressivos/farmacologia , Citalopram/química , Citalopram/farmacologia , Inibidores Seletivos de Recaptação de Serotonina , Serotonina/metabolismo , Proteínas da Membrana Plasmática de Transporte de Serotonina/genética , Proteínas da Membrana Plasmática de Transporte de Serotonina/metabolismoRESUMO
Accurate predictions of ligand binding affinities would greatly accelerate the first stages of drug discovery campaigns. However, using highly accurate interatomic potentials based on quantum mechanics (QM) in free energy methods has been so far largely unfeasible due to their prohibitive computational cost. Here, we present an efficient method to compute QM free energies from simulations using cheap reference potentials, such as force fields (FFs). This task has traditionally been out of reach due to the slow convergence of computing the correction from the FF to the QM potential. To overcome this bottleneck, we generalize targeted free energy methods to employ multiple maps-implemented with normalizing flow neural networks (NNs)-that maximize the overlap between the distributions. Critically, the method requires neither a separate expensive training phase for the NNs nor samples from the QM potential. We further propose a one-epoch learning policy to efficiently avoid overfitting, and we combine our approach with enhanced sampling strategies to overcome the pervasive problem of poor convergence due to slow degrees of freedom. On the drug-like molecules in the HiPen dataset, the method accelerates the calculation of the free energy difference of switching from an FF to a DFTB3 potential by three orders of magnitude compared to standard free energy perturbation and by a factor of eight compared to previously published nonequilibrium calculations. Our results suggest that our method, in combination with efficient QM/MM calculations, may be used in lead optimization campaigns in drug discovery and to study protein-ligand molecular recognition processes.
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Proteínas , Teoria Quântica , Termodinâmica , Ligantes , EntropiaRESUMO
We have determined the partial leaflet-leaflet phase diagram of an asymmetric lipid bilayer at ambient temperature using asymmetric giant unilamellar vesicles (aGUVs). Symmetric GUVs with varying amounts of 1,2-dipalmitoyl-sn-glycero-3-phosphocholine and DOPC (1,2-dioleoyl-sn-glycero-3-phosphocholine) were hemifused to a supported lipid bilayer (SLB) composed of DOPC, resulting in lipid exchange between their outer leaflets. The GUVs and SLB contained a red and green lipid fluorophore, respectively, thus enabling the use of confocal fluorescence imaging to determine both the extent of lipid exchange (quantified for individual vesicles by the loss of red intensity and gain of green intensity) and the presence or absence of phase separation in aGUVs. Consistent with previous reports, we found that hemifusion results in large variation in outer leaflet exchange for individual GUVs, which allowed us to interrogate the phase behavior at multiple points within the asymmetric composition space of the binary mixture. When initially symmetric GUVs showed coexisting gel and fluid domains, aGUVs with less than ~50% outer leaflet exchange were also phase-separated. In contrast, aGUVs with greater than 50% outer leaflet exchange were uniform and fluid. In some cases, we also observed three coexisting bilayer-spanning phases: two registered phases and an anti-registered phase. These results suggest that a relatively large unfavorable midplane interaction between ordered and disordered phases in opposing leaflets (i.e., a midplane surface tension) can overwhelm the driving force for lateral phase separation within one of the leaflets, resulting in an asymmetric bilayer with two uniformly mixed leaflets that is poised to phase-separate upon leaflet scrambling.
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Bicamadas Lipídicas , Lipossomas Unilamelares , Corantes Fluorescentes , FosfatidilcolinasRESUMO
Mechanosensitive PIEZO channels constitute potential pharmacological targets for multiple clinical conditions, spurring the search for potent chemical PIEZO modulators. Among them is Yoda1, a widely used synthetic small molecule PIEZO1 activator discovered through cell-based high-throughput screening. Yoda1 is thought to bind to PIEZO1's mechanosensory arm domain, sandwiched between two transmembrane regions near the channel pore. However, how the binding of Yoda1 to this region promotes channel activation remains elusive. Here, we first demonstrate that cross-linking PIEZO1 repeats A and B with disulfide bridges reduces the effects of Yoda1 in a redox-dependent manner, suggesting that Yoda1 acts by perturbing the contact between these repeats. Using molecular dynamics-based absolute binding free energy simulations, we next show that Yoda1 preferentially occupies a deeper, amphipathic binding site with higher affinity in PIEZO1 open state. Using Yoda1's binding poses in open and closed states, relative binding free energy simulations were conducted in the membrane environment, recapitulating structure-activity relationships of known Yoda1 analogs. Through virtual screening of an 8 million-compound library using computed fragment maps of the Yoda1 binding site, we subsequently identified two chemical scaffolds with agonist activity toward PIEZO1. This study supports a pharmacological model in which Yoda1 activates PIEZO1 by wedging repeats A and B, providing a structural and thermodynamic framework for the rational design of PIEZO1 modulators. Beyond PIEZO channels, the three orthogonal computational approaches employed here represent a promising path toward drug discovery in highly heterogeneous membrane protein systems.
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Ensaios de Triagem em Larga Escala , Canais Iônicos , Canais Iônicos/metabolismo , Descoberta de Drogas , Sítios de Ligação , Termodinâmica , Mecanotransdução Celular/fisiologiaRESUMO
A previously reported autoreactive antigen, termed the X-idiotype, isolated from a unique cell population in Type 1 diabetes (T1D) patients, was found to stimulate their CD4+ T cells. This antigen was previously determined to bind more favorably than insulin and its mimic (insulin superagonist) to HLA-DQ8, supporting its strong role in CD4+ T cell activation. In this work, we probed HLA-X-idiotype-TCR binding and designed enhanced-reactive pHLA-TCR antigens using an in silico mutagenesis approach which we functionally validated by cell proliferation assays and flow cytometry. From a combination of single, double, and swap mutations, we identified antigen-binding sites p4 and p6 as potential mutation sites for HLA binding affinity enhancement. Site p6 is revealed to favor smaller but more hydrophobic residues than the native tyrosine, such as valine (Y6V) and isoleucine (Y6I), indicating a steric mechanism in binding affinity improvement. Meanwhile, site p4 methionine mutation to hydrophobic residues isoleucine (M4I) or leucine (M4L) modestly increases HLA binding affinity. Select p6 mutations to cysteine (Y6C) or isoleucine (Y6I) exhibit favorable TCR binding affinities, while a swap p5-p6 tyrosine-valine double mutant (V5Y_Y6V) and a p6-p7 glutamine-glutamine double mutant (Y6Q_Y7Q) exhibit enhanced HLA binding affinity but weakened TCR affinity. This work holds relevance to potential T1D antigen-based vaccine design and optimization.
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Diabetes Mellitus Tipo 1 , Vacinas , Humanos , Autoantígenos , Glutamina , Isoleucina , Insulina , Receptores de Antígenos de Linfócitos T , MutagêneseRESUMO
Most cancer cells exhibit high glycolysis rates under conditions of abundant oxygen. Maintaining a stable glycolytic rate is critical for cancer cell growth as it ensures sufficient conversion of glucose carbons to energy, biosynthesis, and redox balance. Here we deciphered the interaction between PKM2 and the thermodynamic properties of the glycolytic pathway. Knocking down or knocking out PKM2 induced a thermodynamic equilibration in the glycolytic pathway, characterized by the reciprocal changes of the Gibbs free energy (ΔG) of the reactions catalyzed by PFK1 and PK, leading to a less exergonic PFK1-catalyzed reaction and a more exergonic PK-catalyzed reaction. The changes of the ΔGs of the two reactions causes the accumulation of intermediates, including the substrate PEP (the substrate of PK), in the segment between PFK1 and PK. The increased concentration of PEP in turn increased PK activity in the glycolytic pathway. Thus, the interaction between PKM2 and the thermodynamic properties of the glycolytic pathway maintains the reciprocal relationship between PK concentration and its substrate PEP concentration, by which, PK activity in the glycolytic pathway can be stabilized and effectively counteracts the effect of PKM2 KD or KO on glycolytic rate. In line with our previous reports, this study further validates the roles of the thermodynamics of the glycolytic pathway in stabilizing glycolysis in cancer cells. Deciphering the interaction between glycolytic enzymes and the thermodynamics of the glycolytic pathway will promote a better understanding of the flux control of glycolysis in cancer cells.
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The gastric proton pump (H+,K+-ATPase) transports a proton into the stomach lumen for every K+ ion exchanged in the opposite direction. In the lumen-facing state of the pump (E2), the pump selectively binds K+ despite the presence of a 10-fold higher concentration of Na+. The molecular basis for the ion selectivity of the pump is unknown. Using molecular dynamics simulations, free energy calculations, and Na+ and K+-dependent ATPase activity assays, we demonstrate that the K+ selectivity of the pump depends upon the simultaneous protonation of the acidic residues E343 and E795 in the ion-binding site. We also show that when E936 is protonated, the pump becomes Na+ sensitive. The protonation-mimetic mutant E936Q exhibits weak Na+-activated ATPase activity. A 2.5-Å resolution cryo-EM structure of the E936Q mutant in the K+-occluded E2-Pi form shows, however, no significant structural difference compared with wildtype except less-than-ideal coordination of K+ in the mutant. The selectivity toward a specific ion correlates with a more rigid and less fluctuating ion-binding site. Despite being exposed to a pH of 1, the fundamental principle driving the K+ ion selectivity of H+,K+-ATPase is similar to that of Na+,K+-ATPase: the ionization states of the acidic residues in the ion-binding sites determine ion selectivity. Unlike the Na+,K+-ATPase, however, protonation of an ion-binding glutamate residue (E936) confers Na+ sensitivity.
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Simulação de Dinâmica Molecular , Potássio , Potássio/metabolismo , Estômago , Sítios de Ligação , Sódio/metabolismo , Adenosina Trifosfatases/metabolismo , ATPase Trocadora de Sódio-Potássio/metabolismo , ATPase Trocadora de Hidrogênio-Potássio/genética , ATPase Trocadora de Hidrogênio-Potássio/metabolismoRESUMO
Binding free energy calculation of a ligand to a protein receptor is a fundamental objective in drug discovery. Molecular mechanics/Generalized-Born (Poisson-Boltzmann) surface area (MM/GB(PB)SA) is one of the most popular methods for binding free energy calculations. It is more accurate than most scoring functions and more computationally efficient than alchemical free energy methods. Several open-source tools for performing MM/GB(PB)SA calculations have been developed, but they have limitations and high entry barriers to users. Here, we introduce Uni-GBSA, a user-friendly automatic workflow to perform MM/GB(PB)SA calculations, which can perform topology preparation, structure optimization, binding free energy calculation and parameter scanning for MM/GB(PB)SA calculations. It also offers a batch mode that evaluates thousands of molecules against one protein target in parallel for efficient application in virtual screening. The default parameters are selected after systematic testing on the PDBBind-2011 refined dataset. In our case studies, Uni-GBSA produced a satisfactory correlation with the experimental binding affinities and outperformed AutoDock Vina in molecular enrichment. Uni-GBSA is available as an open-source package at https://github.com/dptech-corp/Uni-GBSA. It can also be accessed for virtual screening from the Hermite web platform at https://hermite.dp.tech. A free Uni-GBSA web server of a lab version is available at https://labs.dp.tech/projects/uni-gbsa/. This increases user-friendliness because the web server frees users from package installations and provides users with validated workflows for input data and parameter settings, cloud computing resources for efficient job completions, a user-friendly interface and professional support and maintenance.
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Descoberta de Drogas , Simulação de Dinâmica Molecular , Fluxo de Trabalho , Entropia , Ligantes , Internet , Ligação ProteicaRESUMO
Understanding drug selectivity mechanism is a long-standing issue for helping design drugs with high specificity. Designing drugs targeting cyclin-dependent kinases (CDKs) with high selectivity is challenging because of their highly conserved binding pockets. To reveal the underlying general selectivity mechanism, we carried out comprehensive analyses from both the thermodynamics and kinetics points of view on a representative CDK12 inhibitor. To fully capture the binding features of the drug-target recognition process, we proposed to use kinetic residue energy analysis (KREA) in conjunction with the community network analysis (CNA) to reveal the underlying cooperation effect between individual residues/protein motifs to the binding/dissociating process of the ligand. The general mechanism of drug selectivity in CDKs can be summarized as that the difference of structural cooperation between the ligand and the protein motifs leads to the difference of the energetic contribution of the key residues to the ligand. The proposed mechanisms may be prevalent in drug selectivity issues, and the insights may help design new strategies to overcome/attenuate the drug selectivity associated problems.
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Quinases Ciclina-Dependentes , Simulação de Dinâmica Molecular , Quinases Ciclina-Dependentes/metabolismo , Ligantes , Ligação Proteica , TermodinâmicaRESUMO
SignificanceMonte Carlo methods, tools for sampling data from probability distributions, are widely used in the physical sciences, applied mathematics, and Bayesian statistics. Nevertheless, there are many situations in which it is computationally prohibitive to use Monte Carlo due to slow "mixing" between modes of a distribution unless hand-tuned algorithms are used to accelerate the scheme. Machine learning techniques based on generative models offer a compelling alternative to the challenge of designing efficient schemes for a specific system. Here, we formalize Monte Carlo augmented with normalizing flows and show that, with limited prior data and a physically inspired algorithm, we can substantially accelerate sampling with generative models.
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Antibodies and T cell receptors (TCRs) are the fundamental building blocks of adaptive immunity. Repertoire-scale functionality derives from their epitope-binding properties, just as macroscopic properties like temperature derive from microscopic molecular properties. However, most approaches to repertoire-scale measurement, including sequence diversity and entropy, are not based on antibody or TCR function in this way. Thus, they potentially overlook key features of immunological function. Here we present a framework that describes repertoires in terms of the epitope-binding properties of their constituent antibodies and TCRs, based on analysis of thousands of antibody-antigen and TCR-peptide-major-histocompatibility-complex binding interactions and over 400 high-throughput repertoires. We show that repertoires consist of loose overlapping classes of antibodies and TCRs with similar binding properties. We demonstrate the potential of this framework to distinguish specific responses vs. bystander activation in influenza vaccinees, stratify cytomegalovirus (CMV)-infected cohorts, and identify potential immunological "super-agers." Classes add a valuable dimension to the assessment of immune function.
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Imunidade Adaptativa , Epitopos , Receptores de Antígenos de Linfócitos T , Epitopos/metabolismo , Humanos , Imunidade/imunologia , Peptídeos/metabolismoRESUMO
Anaerobic microbial respiration in suboxic and anoxic environments often involves particulate ferric iron (oxyhydr-)oxides as terminal electron acceptors. To ensure efficient respiration, a widespread strategy among iron-reducing microorganisms is the use of extracellular electron shuttles (EES) that transfer two electrons from the microbial cell to the iron oxide surface. Yet, a fundamental understanding of how EES-oxide redox thermodynamics affect rates of iron oxide reduction remains elusive. Attempts to rationalize these rates for different EES, solution pH, and iron oxides on the basis of the underlying reaction free energy of the two-electron transfer were unsuccessful. Here, we demonstrate that broadly varying reduction rates determined in this work for different iron oxides and EES at varying solution chemistry as well as previously published data can be reconciled when these rates are instead related to the free energy of the less exergonic (or even endergonic) first of the two electron transfers from the fully, two-electron reduced EES to ferric iron oxide. We show how free energy relationships aid in identifying controls on microbial iron oxide reduction by EES, thereby advancing a more fundamental understanding of anaerobic respiration using iron oxides.
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Elétrons , Espaço Extracelular/química , Compostos Férricos/química , Bases de Dados como Assunto , Compostos de Ferro/química , Minerais/química , TermodinâmicaRESUMO
Solid-solid phase transformations can affect energy transduction and change material properties (e.g., superelasticity in shape memory alloys and soft elasticity in liquid crystal elastomers). Traditionally, phase-transforming materials are based on atomic- or molecular-level thermodynamic and kinetic mechanisms. Here, we develop elasto-magnetic metamaterials that display phase transformation behaviors due to nonlinear interactions between internal elastic structures and embedded, macroscale magnetic domains. These phase transitions, similar to those in shape memory alloys and liquid crystal elastomers, have beneficial changes in strain state and mechanical properties that can drive actuations and manage overall energy transduction. The constitutive response of the elasto-magnetic metamaterial changes as the phase transitions occur, resulting in a nonmonotonic stress-strain relation that can be harnessed to enhance or mitigate energy storage and release under high-strain-rate events, such as impulsive recoil and impact. Using a Landau free energy-based predictive model, we develop a quantitative phase map that relates the geometry and magnetic interactions to the phase transformation. Our work demonstrates how controllable phase transitions in metamaterials offer performance capabilities in energy management and programmable material properties for high-rate applications.
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SignificanceThe free energy functional is a central component of continuum dynamical models used to describe phase transitions, microstructural evolution, and pattern formation. However, despite the success of these models in many areas of physics, chemistry, and biology, the standard free energy frameworks are frequently characterized by physically opaque parameters and incorporate assumptions that are difficult to assess. Here, we introduce a mathematical formalism that provides a unifying umbrella for constructing free energy functionals. We show that Ginzburg-Landau framework is a special case of this umbrella and derive a generalization of the widely employed Cahn-Hilliard equation. More broadly, we expect the framework will also be useful for generalizing higher-order theories, establishing formal connections to microscopic physics, and coarse graining.
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Primary nucleation is the fundamental event that initiates the conversion of proteins from their normal physiological forms into pathological amyloid aggregates associated with the onset and development of disorders including systemic amyloidosis, as well as the neurodegenerative conditions Alzheimer's and Parkinson's diseases. It has become apparent that the presence of surfaces can dramatically modulate nucleation. However, the underlying physicochemical parameters governing this process have been challenging to elucidate, with interfaces in some cases having been found to accelerate aggregation, while in others they can inhibit the kinetics of this process. Here we show through kinetic analysis that for three different fibril-forming proteins, interfaces affect the aggregation reaction mainly through modulating the primary nucleation step. Moreover, we show through direct measurements of the Gibbs free energy of adsorption, combined with theory and coarse-grained computer simulations, that overall nucleation rates are suppressed at high and at low surface interaction strengths but significantly enhanced at intermediate strengths, and we verify these regimes experimentally. Taken together, these results provide a quantitative description of the fundamental process which triggers amyloid formation and shed light on the key factors that control this process.