Free Energy Gain Research Articles

Full‐Spectrum Light‐Harvesting Solar Thermal Electrocatalyst Boosts Oxygen Evolution

AbstractEnabling high‐efficiency solar thermal conversion (STC) at catalytic active site is critical but challenging for harnessing solar energy to boost catalytic reactions. Herein, we report the direct integration of full‐spectrum STC and high electrocatalytic oxygen evolution activity by fabricating a hierarchical nanocage architecture composed of graphene‐encapsulated CoNi nanoparticle. This catalyst exhibits a near‐complete 98 % absorptivity of solar spectrum and a high STC efficiency of 97 %, which is superior than previous solar thermal catalytic materials. It delivers a remarkable potential decrease of over 240 mV at various current densities for electrocatalytic oxygen evolution under solar illumination, which is practically unachievable via traditionally heating the system. The high‐efficiency STC is enabled by a synergy between the regulated electronic structure of graphene via CoNi‐carbon interaction and the multiple absorption of lights by the light‐trapping nanocage. Theoretical calculations suggest that high temperature‐induced vibrational free energy gain promotes the potential‐limiting *O to *OOH step, which decreases the overpotential for oxygen evolution.

A van der Waals Model of Solvation Thermodynamics.

Exploiting the van der Waals model of liquids, it is possible to derive analytical formulas for the thermodynamic functions governing solvation, the transfer of a solute molecule from a fixed position in the ideal gas phase to a fixed position in the liquid phase. The solvation Gibbs free energy change consists of two contributions: (a) the high number density of all liquids and the repulsive interactions due to the basic fact that each molecule has its own body leading to the need to spend free energy to produce an appropriate cavity to contain the solute molecule; (b) the ubiquitous intermolecular attractive interactions lead to a gain in free energy for switching-on attractions between the solute molecule and neighboring liquid molecules. Also the solvation entropy change consists of two contributions: (a) there is an entropy loss in all liquids because the cavity presence limits the space accessible to liquid molecules during their continuous translations; (b) there is an entropy gain in all liquids, at room temperature, due to the liquid structural reorganization as a response to the perturbation represented by solute addition. The latter entropy contribution is balanced by a corresponding enthalpy term. The scenario that emerged from the van der Waals model is in qualitative agreement with experimental results.

Competitive Binding of Viral Nuclear Localization Signal Peptide and Inhibitor Ligands to Importin-α Nuclear Transport Protein.

Venezuelan equine encephalitis virus (VEEV) is a highly virulent pathogen whose nuclear localization signal (NLS) sequence from capsid protein binds to the host importin-α transport protein and blocks nuclear import. We studied the molecular mechanisms by which two small ligands, termed I1 and I2, interfere with the binding of VEEV's NLS peptide to importin-α protein. To this end, we performed all-atom replica exchange molecular dynamics simulations probing the competitive binding of the VEEV coreNLS peptide and I1 or I2 ligand to the importin-α major NLS binding site. As a reference, we used our previous simulations, which examined noncompetitive binding of the coreNLS peptide or the inhibitors to importin-α. We found that both inhibitors completely abrogate the native binding of the coreNLS peptide, forcing it to adopt a manifold of nonnative loosely bound poses within the importin-α major NLS binding site. Both inhibitors primarily destabilize the native coreNLS binding by masking its amino acids rather than competing with it for binding to importin-α. Because I2, in contrast to I1, binds off-site localizing on the edge of the major NLS binding site, it inhibits fewer coreNLS native binding interactions than I1. Structural analysis is supported by computations of the free energies of the coreNLS peptide binding to importin-α with or without competition from the inhibitors. Specifically, both inhibitors reduce the free energy gain from coreNLS binding, with I1 causing significantly larger loss than I2. To test our simulations, we performed AlphaScreen experiments measuring IC50 values for both inhibitors. Consistent with in silico results, the IC50 value for I1 was found to be lower than that for I2. We hypothesize that the inhibitory action of I1 and I2 ligands might be specific to the NLS from VEEV's capsid protein.

Role of Shape in Particle-Lipid Membrane Interactions: From Surfing to Full Engulfment.

Understanding and manipulating the interactions between foreign bodies and cell membranes during endo- and phagocytosis is of paramount importance, not only for the fate of living cells but also for numerous biomedical applications. This study aims to elucidate the role of variables such as anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength in this essential process using a minimal experimental biomimetic system comprising giant unilamellar vesicles and rod-like particles with different curvatures and aspect ratios. We find that the particle wrapping process is dictated by the balance between the elastic free energy penalty and adhesion free energy gain, leading to two distinct engulfment pathways, tip-first and side-first, emphasizing the significance of the particle orientation in determining the pathway. Moreover, our experimental results are consistent with theoretical predictions in a state diagram, showcasing how to control the wrapping pathway from surfing to partial to complete wrapping by the interplay between membrane tension and adhesive strength. At moderate particle concentrations, we observed the formation of rod clusters, which exhibited cooperative and sequential wrapping. Our study contributes to a comprehensive understanding of the mechanistic intricacies of endocytosis by highlighting how the interplay between the anisotropic particle shape, curvature, orientation, membrane tension, and adhesive strength can influence the engulfment pathway.

Complex chemistry of carbon nanotubes toward efficient and stable p-type doping

Developing efficient and stable carbon nanotube (CNT) doping techniques and elucidating their chemistry is essential for their further implementation in electronic and energy devices. Here, protonic acids and lithium salts are employed as p-type inducers and stabilizers of the doped state, respectively. Leveraging the electron-withdrawing capability of protons, protonic acids can easily induce heavily p-doped states in CNTs. Anionic species from the acids attach to the positively charged CNTs to achieve charge compensation. Introducing lithium salts with bulky, charge-delocalized anions to the p-doped CNTs results in an anion replacement driven by the free energy gain. The newly formed complexes demonstrate outstanding thermal stability in air, enduring a temperature of 100 °C for over a year. The chemical hardness of the applied anion effectively explains the difference in stability of the doped CNTs, indicating that the doping process and its stabilization can be understood and controlled through complex chemistry.

Two-photon excited-state dynamics of mEGFP-linker-mScarlet-I crowding biosensor in controlled environments.

Macromolecular crowding affects many cellular processes such as diffusion, biochemical reaction kinetics, protein-protein interactions, and protein folding. Mapping the heterogeneous, dynamic crowding in living cells or tissues requires genetically encoded, site-specific, crowding sensors that are compatible with quantitative, noninvasive fluorescence micro-spectroscopy. Here, we carried out time-resolved 2P-fluorescence measurements of a new mEGFP-linker-mScarlet-I macromolecular crowding construct (GE2.3) to characterize its environmental sensitivity in biomimetic crowded solutions (Ficoll-70, 0-300 g L-1) via Förster resonance energy transfer (FRET) analysis. The 2P-fluorescence lifetime of the donor (mEGFP) was measured under magic-angle polarization, in the presence (intact) and absence (enzymatically cleaved) of the acceptor (mScarlet-I), as a function of the Ficoll-70 concentration. The FRET efficiency was used to quantify the sensitivity of GE2.3 to macromolecular crowding and to determine the environmental dependence of the mEGFP-mScarlet-I distance. We also carried out time-resolved 2P-fluorescence depolarization anisotropy to examine both macromolecular crowding and linker flexibility effects on GE2.3 rotational dynamics within the context of the Stokes-Einstein model as compared with theoretical predictions based on its molecular weight. These time-resolved 2P-fluorescence depolarization measurements and conformational population analyses of GE2.3 were also used to estimate the free energy gain upon the structural collapse in crowded environment. Our results further the development of a rational engineering design for bioenvironmental sensors without the interference of cellular autofluorescence. Additionally, these results in well-defined environments will inform our future in vivo studies of genetically encoded GE2.3 towards the mapping of the crowded intracellular environment under different physiological conditions.

Thermodynamic prediction of complex hydration processes and verification by experiments for the Ca-Al-C (CA, calcite, water) and Ca-Al-S (ye'elimite, gypsum, water) systems

The solubility of relevant phases in the calcium aluminate cements with limestone and in calcium sulfoaluminate cements with gypsum indicate several potential phase assemblages which might be formed during hydration. Thermodynamic calculations and pore solution data indicate that initially the solution is oversaturated with respect to several phases and thermodynamically metastable phase combinations may form. Some initially formed metastable phase assemblages contain more phases than predicted by the Gibbs phase rule and gain less Gibbs free energy than the stable phase assemblage. Solubility curves are used to define potential phase assemblages, the associated potential Gibbs free energy gain, to plot possible kinetic paths and to evaluate their respective probability. If different kinetic paths are conceivable, the reaction occurs along the solubility of the initially formed stable phases, namely monocarbonate in the calcium aluminate and ettringite in calcium sulfoaluminate system.

Lipid modulation of membrane protein conformational equilibria does not require lipid immobilization in long-lasting protein-lipid complexes.

Lipid regulation of membrane proteins is widely rationalized as a process whereby lipid molecules become immobilized in a complex with the protein, supposedly due to strong, specific interactions. While this conventional paradigm might apply to some regulatory processes, we posit that it is not a universal mechanism. As a counterexample, we examine the mechanism by which lipids modulate the dimerization reaction of the bacterial CL−/H+ antiporter CLC-ec1. Using molecular simulations, we have shown that monomeric CLC-ec1 induces a pronounced defect in the morphology of the surrounding membrane, including thinning of the hydrophobic core due to drastic lipid tilting and entanglement of the two bilayer leaflets. Upon dimerization, this interface becomes buried, and the morphological defect in the membrane is completely eliminated. Using advanced simulation methods, we have shown that the free-energy gain resulting from the elimination of this defect accounts for much of the free-energy of CLC-ec1 association measured experimentally. These experiments, based on single-molecule microscopy, also demonstrate that introduction of short-chain lipids drastically destabilize dimerization, but the concentration dependence of this inhibitory effect is incoherent with a conventional competitive ligand-binding process. To examine the microscopic mechanism underlying these intriguing observations, we calculate a continuous 40-microsecond molecular dynamics trajectory of all-atom monomeric CLC-ec1 embedded in a 70:30 mixture of POPC and DLPC lipids. This simulation shows that DLPC molecules become enriched within the thinned-membrane defect, alleviating its energetic cost and hence inhibits dimerization. However, we find that this enrichment does not stem from the immobilization of these lipids in a long-lasting protein-lipid complex, but from subtle yet statistically significant differences in the residence times and exchange frequency of PO and DL lipids within the first solvation shells.

Rigorous formalism for unconventional symmetry breaking in Fermi liquid theory and its application to nematicity in FeSe

Unconventional symmetry breaking due to nonlocal order parameters has attracted considerable attention in many strongly correlated metals. Famous examples are the nematic order in Fe-based superconductors and the star-of-David charge density order in kagome metals. Such exotic symmetry breaking in metals is a central issue of modern condensed matter physics, while its theoretical foundation is still unclear in comparison with the well-established theory of superconductivity. To overcome this difficulty, here we introduce the "form factor" that generalizes the nonlocal order parameter into the Luttinger-Ward (LW) Fermi liquid theory. We then construct a rigorous formalism of the "density-wave equation" that gives the thermodynamically stable form factor, similarly to the superconducting-gap equation. In addition, a rigorous expression of the Ginzburg-Landau free-energy for the unconventional order is presented to calculate various thermodynamic properties. In the next stage, we apply the derived formalism to a typical Fe-based superconductor FeSe, by using the one-loop LW function that represents the free-energy gain due to the interference among paramagnons. The following key experiments are naturally explained: (i) Lifshitz transition (=disappearance of an electron-pocket) due to the bond+orbital order below $T_c$. (ii) Curie-Weiss behavior of the nematic susceptibility at higher T, and the deviation from the Curie-Weiss behavior at lower T near the nematic quantum-critical-point. (iii) Scaling relation of the specific heat jump at $T_c$, $\Delta C/T_c \propto T_c^b$ with $b \sim 3$. (Note that b=0 in the BCS theory.) These results lead to a conclusion that the nematicity in FeSe is the bond+orbital order due to the "paramagnon interference mechanism". The present theory paves the way for solving various unconventional phase transition systems.

Benzoate group attachment to TEMPO provides enhanced discrimination of liposomes fabricated using human lung normal and carcinoma cells

It is widely accepted that the lipid compositions of the plasma membranes of healthy and cancer cells significantly differ from each other. During the cancer progression, cancer cells change the lipid constituent of the membranes resulting in the loss of lipid asymmetry between the membrane leaflets. Consequently, physicochemical properties of the cell membranes are also changed in response to altered lipid organization. Partitioning of the spin probe 2,2,6,6-tetramethylpiperidine-1-oxyl (TEMPO) into the membranes of the cells has broadly been applied to characterize membrane properties of various cells in health and disease conditions. In this work, we used liposomes fabricated using lipids extracted from normal and carcinoma cells. This system permits the determination of the properties of the healthy and cancer cell membranes provided exclusively by its lipid components. Application of TEMPO-benzoate, in which the benzoate group is attached to the TEMPO, indicates significantly enhanced discrimination of liposomes between cancer and normal cells. Partitioning experiments with TEMPO-benzoate revealed relatively enhanced incorporation efficiency for liposomes of cancer cells. On the contrary, TEMPO incorporation efficiency in the same liposomes of cancer cells was not much different compared to healthy cells. Data indicate that TEMPO-benzoate as a probe is more suitable than TEMPO to discriminate cancer cells from healthy cells. Free energy gain observed for TEMPO-benzoate resulted mainly from the hydrophobic effect of the benzoate group.

In silico analysis of the predicted protein-protein interaction of syntaxin-18, a putative receptor of Peregrinus maidis Ashmead (Hemiptera: Delphacidae) with Maize mosaic virus glycoprotein

The corn planthopper, Peregrinus maidis Ashmead (Hemiptera:Delphacidae), is a widely distributed insect pest which serves as a vector of two phytopathogenic viruses, Maize mosaic virus (MMV) and Maize stripe virus (MStV). It transmits the viruses in a persistent and propagative manner. MMV is an alphanucleorhabdovirus with a negative-sense, single-stranded RNA unsegmented genome. One identified insect vector protein that may serve as receptor to MMV is Syntaxin-18 (PmStx18) which belongs to the SNAREs (soluble N-ethylmaleimide-sensitive factor attachment protein receptors) proteins. SNAREs play major roles in the final stage of docking and subsequent fusion of diverse vesicle-mediated transport events. In this work, in silico analysis of the interaction of MMV glycoprotein (MMV G) and PmStx18 was performed. Various freely available protein-protein docking web servers were used to predict the 3 D complex of MMV G and PmStx18. Analysis and protein-protein interaction (PPI) count showed that the complex predicted by the ZDOCK server has the highest number of interaction and highest affinity, as suggested by the calculated solvation free energy gain upon formation of the interface (ΔiG = −31 kcal/mol). Molecular dynamics simulation of the complex revealed important interactions at the interface over the course of 25 ns. This is the first in silico analysis performed for the interaction on a putative receptor of P. maidis and MMV G. The results of the PPI prediction provide novel information for studying the role of Stx18 in the transport, docking and fusion events involved in virus particle transport in the insect vector cells and its release. Communicated by Ramaswamy H. Sarma

Determinants of Lipid Domain Size.

Lipid domains less than 200 nm in size may form a scaffold, enabling the concerted function of plasma membrane proteins. The size-regulating mechanism is under debate. We tested the hypotheses that large values of spontaneous monolayer curvature are incompatible with micrometer-sized domains. Here, we used the transition of photoswitchable lipids from their cylindrical conformation to a conical conformation to increase the negative curvature of a bilayer-forming lipid mixture. In contrast to the hypothesis, pre-existing micrometer-sized domains did not dissipate in our planar bilayers, as indicated by fluorescence images and domain mobility measurements. Elasticity theory supports the observation by predicting the zero free energy gain for splitting large domains into smaller ones. It also indicates an alternative size-determining mechanism: The cone-shaped photolipids reduce the line tension associated with lipid deformations at the phase boundary and thus slow down the kinetics of domain fusion. The competing influence of two approaching domains on the deformation of the intervening lipids is responsible for the kinetic fusion trap. Our experiments indicate that the resulting local energy barrier may restrict the domain size in a dynamic system.

A simple model of protein cold denaturation

Cold denaturation is a general feature of the conformational stability of globular proteins. Its modelization is still an important goal of biophysics. We present a modified version of the Schellman-Brandts model that is able to reproduce the occurrence of two conformational transitions, cold and hot denaturations. The model suggests that: (a) globular protein cooperativity can be obtained by distinguishing an inner core, buried from water contact, in a spherical globule; (b) the latter is stabilized by the hydrophobic effect that can be modelled by the Gibbs free energy gain associated with the burial of nonpolar side chains in the inner core; (c) cold denaturation comes from the decrease in the stabilization provided by the hydrophobic effect at low temperature.

Crystal structures of apo- and FAD-bound human peroxisomal acyl-CoA oxidase provide mechanistic basis explaining clinical observations

Peroxisomal acyl-CoA oxidase 1a (ACOX1a) catalyzes the first and rate-limiting step of fatty acid oxidation, the conversion of acyl-CoAs to 2-trans-enoyl-CoAs. The dysfunction of human ACOX1a (hACOX1a) leads to deterioration of the nervous system manifesting in myeloneuropathy, hypotonia and convulsions. Crystal structures of hACOX1a in apo- and cofactor (FAD)-bound forms were solved at 2.00 and 2.09 Å resolution, respectively. hACOX1a exists as a homo-dimer with solvation free energy gain (ΔGo) of −44.7 kcal mol−1. Two FAD molecules bind at the interface of protein monomers completing the active sites. The substrate binding cleft of hACOX1a is wider compared to human mitochondrial very-long chain specific acyl-CoA dehydrogenase. Mutations (p.G178C, p.M278V and p.N237S) reported to cause dysfunctionality of hACOX1a are analyzed on its 3D-structure to understand structure-function related perturbations and explain the associated phenotypes.

Contribution of Different Molecules and Moieties to the Surface Tension in Aqueous Surfactant Solutions. II: Role of the Size and Charge Sign of the Counterions.

Understanding the role of the counterion species in surfactant solutions is a complicated task, made harder by the fact that, experimentally, it is not possible to vary independently bulk and surface quantities. Here, we perform molecular dynamics simulations at constant surface coverage of the liquid/vapor interface of lithium, sodium, potassium, rubidium, and cesium dodecyl sulfate aqueous solutions. We investigate the effect of counterion type and charge sign on the surface tension of the solution, analyzing the contribution of different species and moieties to the lateral pressure profile. The observed trends are qualitatively compatible with the Hofmeister series, with the notable exception of sodium. We point out a possible shortcoming of what is at the moment, in our experience, the most realistic nonpolarizable force field (CHARMM36) that includes the parametrization for the whole series of alkali counterions. In the artificial system where the counterion and surfactant charges are inverted in sign, the counterions become considerably harder. This charge inversion changes considerably the surface tension contributions of the counterions, surfactant headgroups, and water molecules, stressing the key role of the hardness of the counterions in this respect. However, the hydration free energy gain of the counterions, occurring upon charge inversion, is compensated by the concomitant free energy loss of the headgroups and water molecules, leading to a negligible change in the surface tension of the entire system.

Distinct sequence and structural feature of trypanosoma malate dehydrogenase

Glycosomal malate dehydrogenase from Trypanosoma cruzi (tcgMDH) catalyzes the oxidation/reduction of malate/oxaloacetate, a crucial step of the glycolytic process occurring in the glycosome of the human parasite. Inhibition of tcgMDH is considered a druggable trait for the development of trypanocidal drugs. Sequence comparison of MDHs from different organisms revealed a distinct insertion of a prolin rich 9-mer (62-KLPPVPRDP-70) in tcgMDH as compared to other eukaryotic MDHs. Crystal structure of tcgMDH is solved here at 2.6 Å resolution with Rwork/Rfree values of 0.206/0.216. The tcgMDH forms homo-dimer with the solvation free energy (ΔGo) gain of −9.77 kcal/mol. The dimeric form is also confirmed in solution by biochemical assays, chemical-crosslinking and dynamic light scattering. The inserted 9-mer adopts a structure of a solvent accessible loop in the vicinity of NAD+ binding site. The distinct sequence and structural feature of tcgMDH, revealed in the present report, provides an anchor point for the development of inhibitors specific for tcgMDH, possible trypanocidal agents of the future.

Effect of Met/Leu substitutions on the stability of NAD+-dependent formate dehydrogenases from Gossypium hirsutum.

NAD+-dependent formate dehydrogenases (FDHs) are extensively used in the regeneration of NAD(P)H and the reduction of CO2 to formate. In addition to their industrial importance, FDHs also play a crucial role in the maintenance of a reducing environment to combat oxidative stress in plants. Therefore, it is important to investigate the response of NAD+-dependent FDH against both temperature and H2O2, to understand the defense mechanisms, and to increase its stability under oxidative stress conditions. In the present study, we characterized the oxidative and thermal stability of NAD+-dependent FDH isolated from cotton, Gossypium hirsutum (GhFDH), by investigating the effect of Met/Leu substitutions in the positions of 225, 234, and 243. Results showed that the single mutant, M234L (0.72 s-1 mM-1), and the triple mutant, M225L/M234L/M243L (0.55 s-1 mM-1), have higher catalytic efficiency than the native enzyme. Substitution of methionine by leucine on the position of 243 increased the free energy gain by 670 J mol-1. The most remarkable results in chemical stability were seen for double and triple mutants, cumulatively. Double and triple substitution of Met to Leu (M225L/M243L and M225L/M243L/M234L) reduce the kefin by a factor of 2 (12.3×10-5 and 12.8×10-5 s-1, respectively.Key points• The closer the residue to NAD+, in which we substituted methionine to leucine, the lower the stability against H2O2 we observed.• The significant gain in the Tm value for the M243L mutant was observed as +5°C.• Residue 234 occupies a critical position for oxidation defense mechanisms. Graphical abstract (a) Methionine amino acids on the protein surface are susceptible to oxidative stress and can be converted to methionine sulfoxide by reactive oxygen derivatives (such as hydrogen peroxide). Therefore, they are critical regions in the change of protein conformation and loss of activity. (b) Replacing the amino acid methionine, which is susceptible to oxidation due to the sulfur group, with the oxidation-resistant leucine amino acid is an important strategy in increasing oxidative stability.

Proteins and Polyampholytes Interacting with Polyelectrolyte Brushes and Microgels: The Charge Reversal Concept Revised.

Weak polyampholytes and globular proteins among them can be efficiently absorbed from solutions by polyelectrolyte brushes or microgels even if the net charge of the polyampholyte is of the same sign as that of the brush/microgel. We use a mean-field approach for calculating the free energy of insertion of a probe polyampholyte molecule into a polyelectrolyte brush/microgel. We anticipate that the insertion of the polyampholyte into similarly charged brush/microgel may be thermodynamically favorable due to the gain in the cumulative re-ionization free energy of the pH-sensitive acidic and basic residues. Importantly, we demonstrate that the polyampholyte (protein) charge sign inversion upon transfer from the bulk of the solution to the brush/microgel does not provide sufficient conditions to assure negative re-ionization free energy balance. Thus (in the absence of other driving or stopping mechanisms), charge sign inversion does not necessarily provoke spontaneous absorption of the polyampholyte into the brush/microgel.

Comparison of Penta and Tetra-pyridyl Cobalt-based Catalysts for Water Reduction: H2 Production Cycle, Solvent Response and Reduction Free Energy.

Understanding water reduction towards H2 generation is crucial to overcome today's renewable energy obstacles. Previous studies have shown the superior H2 production performances of Cobalt based penta-pyridyl (CoaPPy) and tetra-pyridyl (CoaTPy) complexes in solution. We investigate H2 production cycles of CoaPPy and CoaTPy complexes immersed in water solution by means of Ab-initio Molecular Dynamics and Density Functional Theory. We monitor dynamic properties of the systems, solvent response and structural changes occurring in the catalysts, by simulating all intermediate steps of the H2 production cycle. Reduction free energies and reorganization energies are calculated. Our results show that, following the first electron injection, H2 production proceeds with the singlet spin state. Following the first electron insertion, we observe a significant rearrangement of the hydrogen bonding network in the first solvation shell. The cobalt center turns out to be more accessible for the surrounding water molecules in the case of CoaTPy at all the intermediate steps, which explains its higher catalytic performance over CoaPPy. Following the first reduction reaction, a larger gain in reduction free energy is estimated for CoaTPy with respect to CoaPPy, with a difference of 0.14 eV, in line with the experiments. For the second reduction, instead, CoaPPy shows more negative reduction potential, by 0.41 eV.

Breaking time-reversal and translational symmetry at edges of d -wave superconductors: Microscopic theory and comparison with quasiclassical theory

We report results of a microscopic calculation of a second-order phase transition into a state breaking time-reversal and translational invariance along pair-breaking edges of $d$-wave superconductors. By solving a tight-binding model through exact diagonalization with the Bogoliubov-de~Gennes method, we find that such a state with current loops having a diameter of a few coherence lengths is energetically favorable below $T^*$ between 10%-20% of $T_{\mathrm{c}}$ of bulk superconductivity, depending on model parameters. This extends our previous studies of such a phase crystal within the quasiclassical theory of superconductivity, and shows that the instability is not qualitatively different when including a more realistic band structure and the fast oscillations on the scale of the Fermi wavelength. Effects of size quantization and Friedel oscillations are not detrimental. We also report on a comparison with quasiclassical theory with the Fermi surfaces extracted from the tight-binding models used in the microscopic calculation. There are quantitative differences in for instance the value of $T^*$ between the different models, but we can explain the predicted transition temperature within each model as due to the different spectral weights of zero-energy Andreev bound states and the resulting gain in free energy by breaking time-reversal and translational invariance below $T^*$.