The operando analysis reveals that dehydration and related ion-pore interactions govern anion-selective transport. For strongly hydrated ions [(H2O)nF− and (H2O)nCl−], dehydration enhances ion effective charge and thus the electrostatic interactions with membrane, observed as an increase in decomposed energy from electrostatics, leading to more hindered transport. Contrarily, weakly hydrated ions [(H2O)nBr−] have greater permeability as they allow an intact hydration structure during transport due to their smaller size and the most right-skewed hydration distribution. Our work demonstrates that precisely regulating ion dehydration to maximize the difference in ion-pore interactions could enable the development of ideal ion-selective membranes.State-of-the-art ion-selective membranes with ultrahigh precision are of significance for water desalination and energy conservation, but their development is limited by the lack of understanding of the mechanisms of ion transport at the subnanometer scale. Herein, we investigate transport of three typical anions (F The important role of dehydration in anion confined transport was revealed using in situ liquid ToF-SIMS. High-precision ion-selective membranes with subnanometer pores have attracted increasing interest due to their widespread applications in water purification, energy conservation, and resource recovery  with identical charge and minor chemical difference, which are ubiquitous in biological systems and water purification, were selected as model ions. The dehydration behavior of the anions when passing through confined nanochannels in polyamide nanofiltration membranes was investigated using in situ liquid time-of-flight secondary ion mass spectrometry (ToF-SIMS), which enables operando discrimination of hydration states. Coupling operando characterization, TST calculation, and computational simulations, we found that the charge density dictates the ion hydration distribution and hence the confinement-induced dehydration. The quantification of the energy barriers contributed from steric size and electrostatics highlights how dehydration-enhanced ion-pore interactions can appreciably increase anion selectivity. Specifically, the partial dehydration of strongly hydrated anions, i.e., (H2O)nF− and (H2O)nCl−, was found to contribute higher energy barriers from dehydration-enhanced electrostatic interactions, which leads to more hindered transport, while (H2O)nBr− with a softer hydration shell and the most right-skewed hydration distribution exhibits lower energy barriers by maintaining an intact hydrated structure through the polymeric nanochannels. Our findings shed light on a dehydration-driven mechanism dominating ion selectivity in confined transport, which reveals that the precise matching between size effect  and functional groups  is an important guideline for the future development of ion-selective membranes.Collectively, the dehydration mechanism of ion transport and its effect on ion selectivity are still poorly understood. Hence, it is necessary to elucidate the correlation between ionic properties and dehydration by dynamic hydration structure characterization  during transmembrane transport was conducted on an in situ liquid ToF-SIMS microfluidic filtration platform with two polyamide nanofiltration membranes, NF 800 and NF 200 (h−X) of the anions were further calculated by normalizing the ToF-SIMS peak intensities of individual hydrates to the total hydrated ion mass spectrum . In bulk solutions (before filtration), the h−X shows a chi square–like distribution, and the distribution gradually turns to right-skewed as the ionic radii increase. The dominant hydrates of the three anions (representing the hydrated species with highest proportion in h−X) are (H2O)3F−, (H2O)2Cl−, and (H2O) Br−, respectively. The observed dominant hydrates were lower than those measured by molecular dynamics (MD) simulation but were in good agreement with the hydration number obtained from theoretical extractions based on bulk properties. This indicates that h−X determined by ToF-SIMS refers primarily to water molecules that are strongly bound to the ion by its Coulombic field and moved along with the ion in the solution (detailed discussion in note S2). One can see that the charge density dictates an ion’s hydration size as the observed average strongly bound water number (havg) shows the order (H2O)nF− > (H2O)nCl− > (H2O)nBr− nBr− . Given tn) of the larger hydrates and havg even slightly increased (2O)nF− and (H2O)nCl−, as evidenced by the decrease in their havg  notably diminished after the filtration by NF 200 (2O)nF− and (H2O)nCl− must partially lose their solvation shell to reduce their effective size to pass through the tighter membrane. In contrast, (H2O)nBr− has a similar h−Br distribution after being filtered by NF 200 and NF 800 (2O)nBr− even under confinement, which might be attributed to h−Br having the most right-skewed distribution in the bulk (2O)nF− and (H2O)nCl−, most (H2O)nBr− species have a smaller size in the bulk. The smaller size of these hydrated species consequently allows (H2O)nBr− to permeate through membranes more easily. Besides, the lower hydration enthalpy of (H2O)nBr− (table S1) contributes to a smaller and softer hydration shell, which may make the rearrangement of (H2O)nBr− hydration shell more energetically favorable compared to the dehydration for the traverse across nanochannels , no apparent dehydration was observed, as the proportion   > r−H−F (0.352 nm) > r−H−Cl (0.332 nm) > r−H−Br (0.330 nm) > μp,NF200 (0.30 nm) (fig. S1 and table S1), which confirms that dehydration is attributed to the size compatibility between the hydrates and nanochannels. MD simulation was conducted to verify the change in hydration during (H2O)nX− transport through polyamide nanochannels . As shown in fig. S3, the values of h−F and h−Cl markedly decrease after the hydrates enter into the smaller nanochannel with r ≈ 0.3 nm (comparable with μp of NF 200), confirming the confinement-induced partial dehydration of (H2O)nF− and (H2O)nCl−. Contrastingly, no obvious dehydration was observed for any of the anions in the larger nanochannel , evidenced by that the h−X of these ions in the bulk and the 0.5-nm channel being very close (fig. S3). (H2O)nBr− maintains its hydration number even in the 0.3-nm channel , in good agreement with the operando characterization—although the r−H−Br is slightly larger than the pore size. We speculate that the (H2O)nBr− might enter the sterically limited nanochannel by rearrangement of hydration shell rather than dehydration because their hydration layer is smaller and softer than (H2O)nF− and (H2O)nCl− (more detailed discussion is shown in note S3).The pore sizes of the two nanofiltration membranes and the estimated hydrodynamic radii of hydrates (2O)nX− were further obtained by ab initio density functional theory (DFT) (fig. S4). For (H2O)nCl− and (H2O)nBr−, Cl− and Br− are located on the surface of the bound water clusters, thus favoring a surface structure (2O)nF− favors a semisurface structure due to the stronger F−-water interaction (2O)nF− are relatively more sensitive to confinement in comparison with the lopsided surface structures of (H2O)nCl− and (H2O)nBr− where the water molecules are concentrated on one side of the anion . Despite the similar hydrodynamic radii and hydration shapes of (H2O)nCl− and (H2O)nBr−, their dehydration behavior is quite different. Because of the more right-skewed h−Br distribution in the bulk and the softer hydration shell, (H2O)nBr− is thus more likely to maintain an integrated hydration shell. These simulation results coincide well with the h−X distribution obtained by in situ liquid ToF-SIMS. Overall, the results indicate that (i) (H2O)nF− and (H2O)nCl− are partially dehydrated during transport through the sterically limited NF 200 and (ii) no dehydration occurs in the nonconfined NF 800 membrane for the three hydrates.The structures of various (HEpartition) and diffuse  by using the hindered transport theory in combination with TST. As is shown in Epartition is much higher than the Ediffusion, showing that partitioning into the nanochannels contributes higher resistance for the permeation of solvated anions through polyamide nanochannels. We then calculated the potential of mean force (PMF) profile of monovalent anion transport across polymeric nanochannels using an MD simulation platform (Z ≈ 2 nm) , which is in good agreement with the observation by TST. A quartz crystal microbalance (QCM) was then used to quantify the apparent partition energy of sodium-based salts  . The dehydration and electrostatic repulsion at the solution-membrane interface further result in relatively higher Epartition of the anions.Ion transport through nanochannels occurs by two sequential steps: partitioning into the nanochannels and intrapore diffusion. To examine the rate-limiting transport step, we determined the apparent energies for the three anions to partition  . A saddlEa) and h−X solvated size, i.e., Ea(F−) > Ea(Cl−) > Ea(Br−) (Ea for (H2O)nF− and (H2O)nCl− in NF 200 (‡H) and entropic (−T∆S) components  to highlight the molecular features of ion transport. Mechanisms in membrane permeation related to the enthalpic effect, such as dehydration and electrostatic repulsion, can contribute to ∆H, while −T∆S is associated with steric effects  > ∆H(Cl−) > ∆H(Br−), providing further support for the supposition that dehydration plays an important role in the transmembrane hinderance. Note that the ∆H for (H2O)nBr− appears to be independent of the pore size (fig. S7), meaning that soft hydrates could maintain their hydrated structure during transport.The energy contribution during ion transport was further studied using TST. The strong correlation between the overall apparent transmembrane energy barriers ( Ea(Br−) , coincidn NF 200  indicateT∆S) with the order of −T∆S(F−) < −T∆S(Cl−) < −T∆S(Br−) (fig. S8), which mirrors well with the trend of the energy decline observed in the simulated PMF after entering nanochannels , while the dehydration thus takes the reverse (S > 0). Anions with more negative −T∆S  experience relatively higher enthalpic resistance from dehydration. Overall, the results highlight the dominant role of partitioning in anion transport across polymeric nanochannels, which contributes the energy barriers for hydrated anions from enthalpy-related dehydration and charge repulsion to govern ion transport.Another important evidence of the critical role of dehydration during ion partitioning into nanochannels is the entropic compensation mechanism. The three anions showed negative entropic components , and (iii) anion-functional group electrostatic repulsion (Eele). On the basis of the data from in situ liquid ToF-SIMS and TST, the contribution of three aspects was then quantified. Unexpectedly, Eele is the dominant contributor rather than dehydration (2O)nF− and (H2O)nCl− nBr− shows similar Eele in both the membranes due to the intact hydrated structure during transport. The lower Eele in our study could be attributed to the flexible structures with negative carboxyl of polyamide membrane (h−X and PMF of the (H2O)nF− (summarized in the 2O)nF−, ion dehydration dominates from 2 to 3 nm in the polyamide model, whereas the ion-pore interactions dominate from 3 to 4 nm. The corresponding contribution is about 3 and 5 kcal mol−1. This is consistent with our experimental results, i.e., ion-wall interaction plays a more substantial contribution in the studied polyamide membranes. The simulated energy contribution from ion-pore interactions of (H2O)nF− and (H2O)nCl− in the 0.3-nm nanochannel was higher than that in the 0.5-nm nanochannel, which is consistent with our experiment results from in situ liquid ToF-SIMS and TST.The main hindrance of anions during transport in polyamide nanofiltration membrane is from size and charge effect according to the well-accepted anion exclusion mechanisms (ydration . Althoug2O)nX− with DFT calculations to investigate the mechanisms of the dehydration-enhanced ion-pore interactions . The effective charges of the anions increase notably with the decrease in the number of bound water molecules (r0) between hydrates and the negative carboxyl functional groups on the surface of polyamide nanochannels (fig. S9). Since electrostatic repulsion is correlated to effective charges and 2O)nF− thus are more strongly repulsed, resulting in higher energy barriers. The traverse speed of the three anions was simulated, which follows the sequence (H2O)nF− < (H2O)nCl− < (H2O)nBr− (fig. S10), supporting the proposed mechanisms.We further analyzed the effective charges of nF−; 2O)nBr−; fig. S11].The results suggest that anion transport in polyamide membranes is dominated by ∆p−i,X), i.e., p−i,F < p−i,Cl< p−i,Br as expected. The size effects play an important role in the selectivity as a higher selectivity ratio (SR−/F−X) was found in the sterically limited NF 200 nF− make it more hindered compared to (H2O)nCl− and (H2O)nBr− nF− would be more pronounced with the enhancement of the membrane charge due to its stronger dehydration. When pH was then increased to 10.5, the fully ionized carboxyl groups gave both membranes more negatively charged surface . In other words, electrostatic interactions can substantially improve the ion selectivity when driven by dehydration.The sensitivity to a subnanometer environment is different for the three anions, which is determined by their hydration characteristics . The strH2O)nBr− . The hign NF 200 , left suto 19.22 , left. Fn NF 800 , right. SR−/F−Br > SR−/F−Cl > SR−/F−F; fig. S15). The improvement of ion selectivity by dehydration-enhanced electrostatic repulsion still exists in diffusion and electromigration, as SR−/F−X was improved in NF 200 at higher pH  and electric field . A consistent apparent energy barrier dependence of ion selectivity was observed after excluding the influence of convective flow and concentration polarization  , ethylene glycol , diethylene glycol , polyethylene glycol , nitric acid , hydrochloric acid , and silver nitrate  were purchased from Sinopharm Chemical Regent Co. Ltd., China; 0.1 M NaOH and HCl was used to adjust the solution pH in experiments. The silicon nitride (SiNx) film window was obtained from Norcada Inc. . The QCM Au sensor was purchased from Biolin Scientific. Two types of commercial polyamide flatsheet nanofiltration membranes  were used for all experiments.Deionized (DI) water (>18.2 megaohms·cm) produced from a Milli-Q ultrapure water purification system (Millipore Milli-Q) was used for preparing electrolyte solutions. Sodium fluoride , sodium chloride , sodium bromide , sodium hydroxide , x film (100 nm in thickness) supported on a silicon frame  was used as the detection window. The membrane coupon (3.5 mm by 3.5 mm) was carefully immobilized beneath the SiNx film with epoxy resin glue. The active layer of the membrane faced the vacuum side to avoid the rehydration of ions. The SiNx film with the membrane coupon was then sealed on top of a 6.0 mm by 5.2 mm by 1.0 mm (length by width by depth) liquid tank, which was previously manufactured on a poly ether ether ketone (PEEK) block with epoxy resin glue. Two PEEK tubes were also sealed with epoxy resin glue on the left and right sides of the device, with the thick tube (1/16 inch) serving as the outlet and the thin tube (1/32 inch) as the inlet. The 10 mM NaX  solution was injected through the tube into the liquid tank, which was then sealed with a valve.The high vacuum–compatible microfluidic filtration device was fabricated according to a previously reported method with minor modification (h−X) of (H2O)nX−  before and after filtration by two polyamide membranes with nominal MWCOs of 200 and 800 Da  were assessed. The feed solutions  were first sealed in the microfluidic filtration device (x film. The polyamide membrane was fixed between the feed solution and the SiNx film. The microfluidic filtration device was subsequently loaded into the load lock vacuum chamber (<3 × 10−6 mbar) and main chamber (1 × 10−6 to 2 × 10−6 mbar) of the ToF-SIMS V instrument  to perform in situ liquid SIMS measurements in negative ion mode to obtain the hydration distribution. The conditions of in situ liquid SIMS measurements were modified on the basis of the previously reported work  of the studied anions by the electric field–driven method (fig. S12C), as shown in an Arrhenius-type equation  through the polyamide nanofiltration membrane. The t− is the transport number for the studied anions, which determines the contribution of anion to overall ion conductance and is related to the membrane charge. A is the preexponential factor. Accordingly, the energy barriers calculated by the Arrhenius-type equation are the apparent representations , which reflect contributions from all acting mechanisms during the specific transmembrane process including the influence of transport distance.According to previous work (equation ln(Gt−T)=I-V) curves using the linear sweep voltammetry (LSV) technique  at different temperatures . For each measurement, a membrane coupon with an area of 2.01 cm2 was assembled between the two chambers of the custom-made electro-driven apparatus (fig. S12C). An Ag/AgCl reference electrode was inserted in each chamber of the apparatus to apply an electric potential across the polyamide membrane. The two chambers were filled with sodium salt solution at the same concentration . During LSV measurements, the transmembrane potential between the two reference electrodes was scanned from −100 to 100 mV at a scan rate of 2 mV s−1 (fig. S18A). The G was calculated from the slope of the I-V curves. Notably, all I-V curves showed a very good linear relationship (fig. S18A), which indicates that the G was constant throughout the measurement. We thus can conclude that from the beginning of the electro-driven process to the end of the test, there was no influence of concentration polarization on the ionic flux. Therefore, the concentration polarization can be ignored in the measurement of transmembrane energy barriers by the electro-driven method.The overall ion conductance was measured by current-voltage relation (t−) at the corresponding temperature  was also analyzed by measuring the membrane potential (ΔΦmbr) based on Eq. 2F is the Faraday constant . Since polyamide membranes are negatively charged under the experimental pH in our study (pH ≥ 6.0), cations are preferentially transported over anions with t−<0.5. To determine the membrane potential (ΔΦmbr) at the corresponding temperature, we maintained the electrolyte concentration in one chamber of the electro-driven apparatus to 10 mM (Ch) while gradually reducing the concentration in the other chamber from 10 to 5 and 1 mM (Cl), and the concentration ratios between the two chambers, i.e., I-V curve at different concentration ratios represents the ΔΦmbr. The t− was then calculated using The transport number  can be obtained by substituting the temperature-dependent intrapore diffusion coefficients  into the linearized Arrhenius-type equation . According to the hindered transport theory, which operates under the assumption of rigid solutes transporting in cylindrical pores, the intrapore diffusion coefficients  were given as Eq. 4rs) to pore radius (rp). rs is the effective solute radius being calculated from the Stokes-Einstein relationship . DW denotes the diffusion coefficients of anions in the bulk solution (table S3), f∞ is the Stokes friction coefficient for the solute outside the pore, and f is the friction coefficient for a solute whose center is at a radial position β and translating parallel to the cylinder axis. E is the interaction potential between the solute and the charged pore wall, k is Boltzmann’s constant, and T is the temperature. Using the centerline approximation, i.e., β = 0, the E between the solute and charged pore wall can be calculated byF is the Faraday constant, R is the ideal gas constant, and V is the dimensionless energy factor. For the solid sphere model with constant charge, V can be given asS0 is the integral factor, I1(τ) is the modified Bessel function of the first kind, and h(τλ) is a function about τ and λ. They can be calculated byzi and Ci are the valence and the molar concentration of the electrolyte species i.The apparent energy of ion partitioning and intrapore diffusion was determined by using the hindered transport theory (equation lnDi=lnDipi is the intrinsic permeability (m s−1), iK is the partitioning coefficient, and δ is the thickness of active layer of the membrane measured by QCM. The intrinsic permeability in an electromigration process can be described asmA is the effective membrane area (2.01 cm2). Combining iK can be obtained, and the apparent energy of ion partitioning can thus be calculated by using eq. S8.On the basis of the solution-diffusion model, the relationship between partitioning and diffusion can be described asDW), and the activated jump of hydrates can be described as  versus DW at different temperatures are given in table S3.The apparent energy of anion diffusion in water can be calculated by the relation between diffusion coefficients of ion diffusion in water , the energy of dehydration (Hhyd[(H2O)mX−] and ∆Hhyd[(H2O)nX−] are the hydration enthalpy of hydrates after and before dehydration. Since the proportion difference of each hydrate after and before the dehydration follows the h−X distribution measured by in situ liquid ToF-SIMS, i = 1–6) in h−X distribution after and before filtration by polyamide membrane (Hhyd[(H2O)iX−] is the hydration enthalpy of corresponding hydrate. ∆Hhyd[(H2O)iX−] was calculated by DFT as shown in fig. S19.According to the definition of reaction enthalpy change and hydration enthalpy (∆membrane  measuredEa) of anion during transport are mainly from three aspects: (i) dehydration (Ew), and (iii) electrostatic repulsion (Eele); Eele is given asLast, the energy from electrostatic repulsion was calculated on the basis of the assumption that the apparent transmembrane energy barriers  ensemble was performed to equilibrate the polymer matrix at the temperature of 600 K. Polymer holes with radii of 3 and 5 Å were generated through packing the equilibrated polymer matrix around the carbon nanotubes (CNTs). All systems with CNT contained 252 chains of polymer and were first equilibrated for 20 ns at 600 K to pack the polymer chains close to the CNT forming holes of exact sizes. Then, the system was annealed within 10 ns to the target temperature of 298 K followed by further equilibration of 10 ns. After removal of the CNT, a ~6.5-nm-long hole of the exact radius was obtained in the polymer matrix. Using such relatively straight pores for simulation may underestimate the contribution of pore tortuosity to energy compared to the real nanofiltration system. However, a previous study indicated that the electrostatic repulsion between the anions and the negatively charged pore wall with ionized carboxyl groups leads anions to move away from the pore wall . Each of the 55 replicas was sampled for 3 to 5 ns while taking the last 2 ns for analysis of the free energy using the g_wham program (Atomistic MD simulations were performed in the GROMACS (2O)nX− were investigated by ab initio DFT. The M06-2X is one of the most suitable functions for the study of noncovalent interactions (2O)nX−  were optimized at the M06-2X/def2-TZVP level using the density functional method (2O)nX− were searched by using the Boltzmann distribution law (jE) from previous studies (j configuration (jP) can be given asjn is the molecule number of hydrates with j configuration, R is the gas constant, T is the absolute temperature, Qj(Relat) is the distribution function of hydrates with j configuration, and the subscript “Relat” represents that the Qj(Relat) was calculated from relative binding energies. The jP of each configuration of (H2O)nX− is shown in table S4.The structures of various  to obtain a 4 mM feed solution to start the experiments. Unless otherwise indicated, the water temperature was maintained at a constant temperature of 20°C, and the cross-flow velocity was 19.8 cm s−1. On the basis of the solution diffusion model  was calculated from the measured flux and concentration difference across the membraneiJ is the ion flux (mol m−2 s−1) and C0 and Cp are the concentration of the feed and permeate solution (mM), respectively. C0 and Cp were analyzed by ion chromatography . The selectivity ratio (SR−/F−X) was defined as the ratio of the intrinsic permeability between X−  and F−.A custom-made filtration system with a flat sheet nanofiltration membrane cell driven by pressure, i.e., nanofiltration, was used for ion transport and selectivity tests (fig. S12A). The nanofiltration system was operated in cross-flow mode. The effective area of the membrane sheet was 20.6 cm2). The left-side chamber was filled with 20 ml of concentrated salt solution (C0 = 0.1 M), while the other side was filled with isopycnic DI water as the receiver. All diffusion experiments were constantly stirred with a magnetic stirrer to avoid concentration polarization. Samples from the receiving chamber were collected after 3 hours of diffusion. The concentration of anions in the receiving solution (Cp) was determined by ion chromatography  to calculate the intrinsic permeabilities of the different ions . Two diffusion chambers were separated by a membrane coupon . Ionic conductance (G) was measured using the same two-chamber apparatus as mentioned in the diffusion experiment (fig. S12C). An Ag/AgCl reference electrode was inserted in each chamber to apply an electric potential across the polyamide membrane. The two chambers were filled with sodium salt solution at the same concentration . The transmembrane potential between the two reference electrodes was scanned from −100 to 100 mV at a scan rate of 2 mV·s−1. The intrinsic permeability in an electromigration process can be described as , F is the Faraday constant, C is the electrolyte molar concentration in the bulk solution, t− is the transport number, T is the absolute temperature, and α is a temperature-independent parameter. The δ can be determined by QCM .Ion transport in an electro-driven process, i.e., electromigration, was studied by The pH of the electrolyte solutions was adjusted using 0.1 M NaOH and HCl solutions. Each test was repeated at least three times to obtain the average values under different conditions.


QTamm = 237)is obtained for 11 nm of gold on a dielectric mirror with low porositycorresponding to the resonant spectral position of λTamm of ∼698 nm. Our analysis indicates that Tamm resonances inas-produced Au-coated NAA–GIFs are weak due to the constrainedrange of wavelengths (narrow bands) at which these photonic crystalstructures reflect light. However, after broadening of their photonicstopband upon pore widening, Tamm resonances become better resolved,with higher intensity. It is also observed that the quality of lightconfinement worsens progressively with the thickness of the porousgold coating layer after a critical value. In contrast to conventionalsurface plasmon resonance systems, this hybrid Tamm porous systemdoes not require complex coupling systems and provides a nanoporousstructure that can be readily tailored for a range of photonic technologiessuch as sensing and lasing.Gold-coated gradient-index filters based on nanoporousanodic alumina(Au-coated NAA–GIFs) were used as model platforms to elucidatehow Tamm plasmons can be tailored by engineering the geometric featuresof the plasmonic and photonic components of these hybrid structures.NAA–GIFs with well-resolved, intense photonic stopbands attwo positions of the visible spectrum were fabricated through sinusoidalpulse anodization. These model photonic crystals were used to assesshow the quality of Tamm plasmon resonances can be enhanced by tuningthe features of the dielectric mirror and the thickness of the porousgold coating layer. It is found that the highest value of the qualityfactor of Tamm resonance ( As such, the resonance band of theTamm plasmon system undergoes a spectral shift, which is proportionalto the change of the refractive index. This property in turn can bereadily harnessed as the core principle to develop highly sensitivesensing systems.7One ofthe most interesting aspects of Tamm plasmons is that resonantphotons confined at and traveling along the plasmonic–photonicinterface are highly susceptible to changes in the refractive indexof the surrounding medium.QTamm)—thefigure of merit defined as the ratio of the wavelength of the resonanceband (λTamm) to its full width at half-maximum (FWHMTamm). However, surface plasmon resonances are typically characterizedby broad resonance bands due to the intrinsically high optical lossesassociated with the imaginary part of the dielectric constant of metals,which is associated with the energy losses experienced by photonswhen these interact with the atoms of the metal.9 Thisproperty can be beneficial for a range of photonic applications suchas infrared imaging,11 solar energy conversion,12 and photocatalytic processes.14 However, other applications require a precise control over the spectralposition and linewidth of surface plasmon resonances such as quantumoptics,15 filtering,16 lensing,17 lasing,18 tweezing,19 and sensing.20The sensitivity of Tamm plasmon systems depends on how stronglylight is confined by the thin metallic coating layer–dielectricmirror composite, which can be quantified by the quality factor ofthe Tamm structure structures are particularly suitable platforms for developing opticalsensing systems that harness Tamm plasmons. This class of PCs providesa nanoporous matrix to increase available functional sites for maximizingbinding interactions with targeted analyte molecules. Recently, nanoporousanodic alumina photonic crystals (NAA–PCs) produced by pulse-likeanodization of aluminum27 have been demonstrated as suitableplatforms to develop Tamm plasmon sensors.27To date, a range of materials and structures have been engineeredand integrated into Tamm plasmon systems. These include semiconductors,28 However, these PC structures are characterizedby a broad photonic stopband, which in turn limits the quality ofthe resultant Tamm plasmon resonances.29 In contrast to DBRs, gradient-index filters (GIFs) feature a smooth,sinusoidal variation of optical thickness between high and low values,which is translated into a characteristically narrow photonic stopband(PSB) with suppressed side-lobe reflections around the central PSB.32Conventionally, the photonic element of Tammplasmon systems isbased on a 1D distributed Bragg reflector (DBR) mirror, which is aPC structure featuring a periodic variation of optical thickness  betweenhigh and low values in depth, along the mirror thickness.38 of the dielectric mirror component of this hybrid plasmonic–photonicsystem. To this end, we engineer the structure of NAA–GIFsby sinusoidal pulse anodization38 1a. These38 1b. Upon 38 1c. We us22.13)2CO), ethanol (C2H5OH), perchloric acid (HClO4), oxalic acid (H2C2O4),hydrochloric acid (HCl), and copper chloride (CuCl2) wereprovided by Sigma-Aldrich (Spain). Double deionized water with a conductivityof 18 MΩ cm obtained by a dispensing system with an LC134 0.2μm cutoff filter (ELGA LabWater) was used to prepare all aqueoussolutions used in this study and to wash samples at the differentstages of the fabrication process.High-purity aluminum (Al)sheets  were acquired fromGoodfellow Cambridge Ltd. (UK). Acetone ((CH2.2J(t) is the applied current density (in mA cm–2) at time t (in s), Joffset is the offset of the current density during the anodization process, Jmax is the maximum current density in absolutevalue with respect to its average, T is the anodizationperiod of the sinusoidal profile (in s), which represents the timedifference between consecutive pulses, and N is thenumber of sinusoidal pulses in the anodization profile.Aluminumsheets were cut into squared chips with a side of 2 cm. The surfaceof as-received Al chips was cleaned sequentially with acetone, water,and ethanol to remove impurities before starting the fabrication process.The surface of cleaned Al chips was smoothened by electropolishingin a mixture electrolyte solution of 4:1 v/v ethanol–perchloricacid at 20 V and 5 °C for 8 min. During this process, the directionof stirring was alternated every 60 s. After electropolishing, Alchips were anodized by sinusoidal pulse anodization in a 0.3 M oxalicacid electrolyte at 5 °C. Current density sinusoidal anodizationprofiles were generated in a LabView customized application, following Joffset, Jmax, and N were fixed to 2 mA cm–2, 1 mA cm–2, and 120 pulses, respectively, whereasthe input anodization period was set to two different values  to produce NAA–GIFswith PSBs located at two specific positions of the visible regionof the electromagnetic spectrum.Thevalues of 2.339 After fabrication,NAA–GIFs were coated, and a porous gold coating layer was obtainedthrough a sputtering technique in a Quorum Q 150T Plus turbomolecularpumped coater in the Q 150T S Plus configuration at a vacuum pressureof 5 × 10–5 mbar. These conditions make itpossible to obtain a low grain size of the metal coating layer tominimize undesired scattering, which is a suitable characteristicto study the optical properties of plasmonic–photonic interactionsat the interface of metal/NAA–GIFs. The average thickness ofthe resultant porous gold coating layer was estimated using a KLA-TencorAlpha-Step D-300 stylus profiler. A porous gold coating layer generatedin this study had an average thickness from 6 ± 1 to 23 ±1 nm. Quantification of porous gold coating layer thickness by thistechnique was calibrated by partially masking the surface of referencesamples during the coating process. Then, the thickness of the resultantporous gold coating layer was determined by scanning the surface ofthe sample with the stylus profiler across the transition betweenmasked and unmasked regions. The height of the step corresponds tothe average thickness of the porous gold coating layer.The structure of NAA–GIFs was characterized by a field-emissiongun scanning electron microscope  operating at an accelerating voltage of 5 kV. FEG–SEMimages were analyzed by ImageJ software to quantify the average geometricfeatures of NAA–GIFs.2.42·2H2O 0.16 M dissolved in a 1:4 v/v mixture of HCl and H2Oat room temperature, using a circular mask to create a transparentwindow for optical characterization purposes.32 The absolute reflectance spectra (expressed in %R) of NAA–GIFs were acquired in a PerkinElmer UV–visible–NIRLambda 950 spectrophotometer within the visible range , measured with a 1 nm resolution at an 8° incidence angle.The aluminum substrate remaining after anodization was removedfrom the bottom side of the NAA–GIFs by selective chemicaletching in a saturated solution of CuCl33.1Figure S1a). These regions in turn correspondto periodic variations of low and high levels of the effective refractiveindex, respectively. From magnified views of the anodization profile,it is apparent that there is a delay of 40 ± 20 s between thecurrent density input and the voltage output profile .Periodic sinusoidal variation of the anodizing current densityinput enables a precise means of modulating the effective medium ofNAA by generating regions of higher and lower porosity along the nanopores(Vmax–Vmin)/2)with the anodization time. This process results in the modulationof the nanopore diameter from top to bottom of the anodic film bythe variation of input current density in the form of pulses witha smooth transition from high to low values.40 This in turn generates alternating zones of low and high effectiverefractive index.41This is attributed to therestructuring of the barrier oxide layer at the bottom of the nanopores when the input current density changesfrom high to low values. It is worth noting that this anodizationprocess is entirely performed under mild conditions and that, as such,there is a slight decrement in the average voltage ,which is characterized by a well-resolved, narrow photonic stopband(PSB) in the reflection spectrum.T = 220s. This structure is characterized by a random distribution of nanoporesacross the photonic crystal film surface, the average diameter (dp) and the interpore distance (dint) of which are estimated to be 23 ± 4 and 93 ±21 nm, respectively.32L) of ∼23 μm.A magnified-view image of the cross section reveals periodic modulationsof the diameter along the nanopores, which go from the top to thebottom of the anodic film (dic film 2c.LTp) or distance between nanopore modulations estimatedby FEG–SEM image analysis was determined to be ∼194± 17 nm. Similar results are obtained for sample NAA–GIF–B,manufactured with an anodization period of T = 240s, which translates into an overall thickness (L)of ∼26 μm with the same average diameter (dp) and interpore distance (dint), but the distance between nanopore modulations estimated by FEGSEMimage analysis was determined to be ∼202 ± 11 nm.It is apparent that the sinusoidal modulation ofcurrent densityinput in the anodization profile is precisely translated into sinusoidalvariations of the nanopore diameter. The period length . Of all these, NAA–GIFsare characterized by a smooth periodic variation of the dielectricconstant along the nanopore length. This structural feature is translatedinto a characteristically narrow PSB in the reflection spectrum ofthese PC structures, which indicates a highly selective inhibitionof the flow of photons within a highly constrained range of energiesor wavelengths. Furthermore, since NAA–PCs are a porous material,the macroscopic optical properties of these structures can be mechanisticallydescribed by effective medium approximation.48PCs are optical nanostructures with a spatial periodic variationof the dielectric constant in one, two, or three dimensions, whichdetermines the way in which they interact with incident photons. NAAhas emerged as a promising platform material for a range of PC structuresthat enable a versatile control over a range of light–matterinteractions .In this approach, the property of each constituentphase  is averaged according to the spatial distributionof the photonic crystal architecture  as well as the contribution of each phase separately.T = 220 and240 s for A and B, respectively). It is apparent from these spectrathat the position of the PSB of NAA–GIFs red-shift with theanodization period, enabling a precise means of engineering this light–matterinteraction across the broad spectrum through this anodization parameter.The PSBs of NAA–GIF–A and NAA–GIF–B fabricatedwith anodization periods of T = 220 and 240 s havetheir central wavelength (λPSB) at 632 ± 1 and704 ± 1 nm, with full widths at half-maximum (FWHMPSB) of 22 ± 1 and 21 ± 1 nm, respectively.3.3Selective reflection of light in NAA–GIFsis attributed to multiple Bragg scattering interactions across theNAA stacks featuring a sinusoidally modulated nanopore diameter alongthe thickness of the anodic film. The central wavelength of the characteristicPSB of NAA–GIFs indicates the spectral region where the nanoporousPC forbids the flow of incoming photons more efficiently due to constructiveinterference. This light–matter interaction can be controlledby engineering the period length  and the effective refractive index ofthe PC structure. Whereas the former can be precisely controlled bythe period in the anodizing current density input, the latter reliesintrinsically on porosity or the nanopore diameter.tpw) of 0, 5, 10, and 15 min. FEGSEM image analysis determinedaverage nanopore diameters (dp) from thetop surface of the anodic photonic film of 23 ± 4, 34 ±4, 44 ± 5, and 55 ± 5 nm for these values of tpw, respectively with a nanopore enlargement of 2.1 ± 0.1 nm min–1 with tpw. R2 = 0.9878) between the position of the centralwavelength and tpw, in which the latteroptical feature blueshifts at a rate of 3.5 ± 0.3 nm min–1. This result is consistent with previously reportedworks51 and is attributable to the reduction ofthe overall effective refractive index of the photonic film with increasingporosity, where the fraction of air (lower refractive index) increasesover that of alumina (component of the composite structure with ahigher refractive index).The dependence of the average PSB with dp for NAA–GIFs,it reveals a linear correlation(R2 = 0.9849) where the position of thecentral wavelength blueshifts at a rate of 1.7 ± 0.1 nm nm–1 with dp . Therefore, it is possible to control the position ofthe PSB with high precision by adjusting the size of the nanoporein these PC structures, providing an additional degree of freedomto fine-tune the optical features of the PSB. This analysis also indicatesthat the characteristic PSB of NAA–GIFs broadens upon enlargementof the nanopore diameter through pore widening (PSB) with pore widening timereveals a linear broadening of the band (R2 = 0.9826), with values of 21 ± 1, 25 ± 1, 29 ± 1,and 36 ± 1 nm at tpw of 0, 5, 10,and 15 min, respectively .If we correlate the dependence ofλQPSB of the photonic stopband (PSB)based on the relationship betweenthe central wavelength and its FWHM. The behavior of this figure ofmerit when increasing the average pore diameter is also representedin QPSB (R2 = 0.9974), with valuesof 34 ± 1, 28 ± 1, 23 ± 1, and 18 ± 1 at dp of 23 ± 4, 34 ± 4, 44 ± 5,and 55 ± 5 nm, respectively . Table S1 in the Supporting Information summarizes the values of thedifferent optical and geometric parameters at distinct pore wideningtimes.Also, we define in 3.4Figure S2 in the Supporting Information).Tamm plasmons are aclass of light–matter interactions in which incoming photonsare confined between a metallic coating layer and a dielectric mirror.In this system, the geometric and optical features of the metalliccoating layer are critical in determining the capability of this typeof light-confining hybrid plasmonic–photonic structure. Toevaluate the influence of the thickness of the metallic coating layeron the optical features of Tamm plasmons in NAA–GIFs, layersof gold with controlled thicknesses were deposited on the top surfaceof these NAA-based PC structures by a sputtering technique. Four thicknessesof the gold coating layers were deposited on the surface of the NAA–GIF–Aand NAA–GIF–B structures by controlling the sputteringtime . Even after pore widening, there isa quantifiable reduction in the pore diameter with increasing thicknessof gold coating. The results summarized in Table S2 reveal that coating on top of the sample leads to the formationof a 23 ± 1 nm porous gold coating layer that reduces the porediameter size of the sample itself.Preliminary calibration experiments revealed gold coating layerthicknesses of 6 ± 1, 8 ± 1, 11 ± 1, and 23 ±1 nm at 10, 20, 30, and 60 s of deposition time under the conditionsused in our system, respectively. 2 (PSB =632 ± 1 nm)  5a. A quaQTamm is the quality factor of the central wavelength (λTamm) based on the relationship between the central wavelengthand its FWHMTamm.The figure of merit defining how good a Tamm plasmoncavity confineslight within its structure is the quality factor, defined graphicallyin Tamm for porous goldcoating layer thicknesses dAu of 6 and8 nm. However, it becomes better resolved with dAu, and the increase of FWHMTamm becomes clearerfor sample NAA–GIF–A: FWHMTamm broadens withvalues of 10 ± 1, 13 ± 1, 15 ± 1, and 16 ± 1 nmat dAu of 6 ± 1, 8 ± 1, 11 ±1, and 23 ± 1 nm, respectively . For the last two valuesof dAu, 11 ± 1 and23 ± 1 nm, sample NAA–GIF–B is narrower ,and according to the figure of merit defined in QTamm, although the tendency in both samplesis to decrease QTamm with the increasein dAu.At thin thicknesses of gold coating, the Tamm resonanceis poorlyresolved: we cannot calculate FWHMTamm, represented by the dipin reflectance, can be appreciated more clearly within the PSB ofthe PC structure as shown in the reflection spectra depicted in Motivated by this result,we decided to assess the combined effectof a porous gold coating layer thickness and the average nanoporediameter for NAA–GIFs. The pore size of NAA–GIFs wasincreased via pore widening. After 15 min of pore widening, the PSBof NAA–GIF–A and NAA–GIF–B undergoes an∼45 nm blueshift with a concomitant broadening of the averageFWHM, which is estimated to be ∼14 nm. It is apparent thatthe pore widening treatment makes the PC structure evolve from a GIF(narrow band) to a distributed Bragg reflector, which is characterizedby a broad PSB denoting an efficient reflection of light across awider range of wavelengths within the visible spectrum. As a result,the Tamm resonance λTamm) in the reflectionspectrum of NAA–GIFs red-shifts with the porous gold coatinglayer thickness (dAu). These graphs revealthat the intensity of the Tamm resonance increases with the porousgold coating layer thickness, and this effect is more clearly noticeablefor NAA–GIFs with PSBs located at shorter wavelengths .It isapparent from Tamm redshifts its position with increasinggold thickness until reaching a critical point at dAu = 11 nm, from which λTamm blueshiftsits position. In contrast, for the HP range, λTamm redshifts its position asymptotically with the porous gold coatinglayer thickness. A potential reason for this phenomenon is the homogeneityof the porous gold coating layer. As-produced NAA–GIFs havemore available surface to grow a solid, continuous layer of gold asthe thickness of the deposited layer increases. Conversely, afteran extended pore widening treatment, nanopores are larger, and assuch, the available surface on top of the NAA–GIFs that isavailable for coating is substantially reduced.To gain further insights, we extendedthis qualitative analysisby quantifying how the optical features of the Tamm plasmon resonancein these NAA–GIFs structures change with the levels of porosityinduced by the pore widening time  7. It canQTamm for NAA–GIF–A and NAA–GIF–B at tpw = 0 and 15 min .The highest value of the quality of light confinement (QTamm = 237) is obtained at 11 nm of gold thickness foras-produced NAA–GIF–B. For NAA–GIF–A,the average QTamm fluctuates around 49± 10 before pore widening (LP), and it is enhanced by almosttwo-fold to 97 ± 37 after 15 min of pore widening (HP). AlthoughλTamm decreases due to pore widening, the Tamm resonanceis resolved much more for HP than for LP due to a narrower FWHMTamm, and the resulting effect is an increase in QTamm. NAA–GIF–B shows a very similar trendin terms of QTamm, but we can only calculateit for the highest values of dAu due tothe poor resolution of the resonant signal for coatings thinner than11 nm. The average QTamm is estimatedto be 190 ± 67 at LP and 100 ± 13 after a 15 min pore wideningtreatment. In all the cases, QTamm decreasesafter the initial coating. However, QTamm decreases more sharply in the case of NAA–GIF–B forLP and in the case of NAA–GIF–A for HP.QTamm changes with the gold thickness dAu before and after pore widening (QPSB (QPSB = 34 ± 1), without pore widening; see Q values than theaforementioned reference in all cases (Table S2). This result, in principle, justifies the use of the novel hybridstructures based on Au-coated NAA–GIFs for future sensing andlasing experiments. Of all the gold thicknesses studied, the highest QTamm (QTamm = 237± 1) is obtained for 11 nm of gold on a sample of relativelylow porosity (as-produced) corresponding to the resonant signal λTamm of the NAA–GIF–B sample.To compare the Tamm resonances of the hybrid structurewith thephotonic stopband of the GIFs, we analyzed how the quality factor widening 8. The re52 However, after pore widening of the NAA–GIFsand gold coating, Tamm resonances become more resolved, with a higherintensity.Our observationsindicate that Tamm resonances in Au-coated NAA–GIFsare weak due to the constrained range of wavelengths (narrow bands)at which these PC structures reflect light. The selected fabricationparameters (current densities and anodization period) define, in principle,the reflectance levels of the NAA. The photonic stopbands show around50% reflectance, which, despite having sufficient sensitivity (relativelynarrow according to its FWHM) even for applications based on the angularresponse, constitutes a limitation for obtaining strong Tamm plasmons.4In summary, this work demonstratesthat a sinusoidal pulse-likeanodization approach in combination with sputtering makes the generationof Au-coated NAA–GIFs as a model hybrid metal–dielectricplatform with a narrow photonic stopband and Tamm plasmon resonanceswithin specific ranges of the visible electromagnetic spectrum possible.The spectral position of the photonic stopband of model NAA–GIFswas tuned by modifying the anodization period in the input profile.Q factor of each optical signal attwo levels of porosity and at two regions of the visible spectrum.After fabrication, we further engineered the features of the characteristicPSB of NAA–GIFs by pore widening, where this treatment makesit possible to broaden the band and blueshift its position. Then,model NAA–GIFs (dielectric) were combined by a sputtering techniqueto generate a porous gold coating layer on the top surface of thesePCs. Upon coating, Tamm plasmon resonances were observed in the reflectancespectra of these structures. We then studied the effect of the goldcoating on the Q factoris obtained for 11 nm of gold on a sample of relatively low porosity(as-produced) corresponding to the resonant signal λTamm of the NAA–GIF–B sample (at a relatively longer wavelengthin the visible range of the electromagnetic spectrum) although a decreasein the Q factor can be expected as the amount ofgold deposited increases.As-produced NAA-based GIFs feature Tamm resonances after coatingtheir top surface with noncontinuous gold layers. However, the qualityof light confinement worsens progressively with the porous gold coatinglayer thickness after a critical value. This constraint can be addressedby widening the nanoporous structure and broadening its characteristicphotonic stopband. The highest value of the 37 Although Tamm plasmon modes were predicted years ago, empiricaldemonstrations of this phenomenon are recent, and it is still an areaof development. The main advantage of Tamm plasmon systems is that,in contrast to conventional SPR systems that require the couplingwith a prism and complex optics, these are simple since they do notneed any specific arrangement or complex optics. Also, they have theadvantage that they can be used with white light illumination andcan be engineered to work across the spectrum.Very few theoretical investigationshave focused on the use ofmetal in contact with GIFs at the contact interface.Our advancesprovide new opportunities to develop novel nanostructuresin the development of new sensing or biosensing platforms. The opticalproperties of the combined material, the propagation of the electromagneticfield through the physical interface of separation, and its sensingcapacity, among other issues, continue to be challenges for nanoplasmonicsthat is in full development.


We provide direct evidence that local rotations govern relaxation for twisted homobilayers, while local dilations are prominent in heterobilayers possessing a sufficiently large lattice mismatch. Encapsulation of the moiré layers in hBN further localizes and enhances these in-plane reconstruction pathways by suppressing out-of-plane corrugation. We also find that extrinsic uniaxial heterostrain, which introduces a lattice constant difference in twisted homobilayers, leads to accumulation and redistribution of reconstruction strain, demonstrating another route to modify the moiré potential.Lattice reconstruction and corresponding strain accumulation plays a key role in defining the electronic structure of two-dimensional moiré superlattices, including those of transition metal dichalcogenides (TMDs). Imaging of TMD moirés has so far provided a qualitative understanding of this relaxation process in terms of interlayer stacking energy, while models of the underlying deformation mechanisms have relied on simulations. Here, we use interferometric four-dimensional scanning transmission electron microscopy to quantitatively map the mechanical deformations through which reconstruction occurs in small-angle twisted bilayer MoS Lattice reconstruction crucially influences the electronic properties of twisted van der Waals structures. Here, the authors report a quantitative characterization of the mechanical deformations occurring in small-angle twisted bilayers and heterobilayers of 2D semiconductors via interferometric 4D scanning transmission electron microscopy. Moiré architectures comprised of semiconducting transition metal dichalcogenides (TMDs) are of considerable fundamental and technological interest because they exhibit distinctively tunable optoelectronic features, such as inter- and intralayer moiré excitons and trions14, as well as relatively robust correlated electronic phases21. While the electronic band structures of moiré superlattices can be intentionally modified by changing the extent of crystallographic misalignment between constituent layers, intrinsic lattice reconstruction also plays an underlying yet substantial role in controlling the emergent behavior in these systems27. Reconstruction of the superlattice and the development of intralayer shear strain subsequently lead to reconstruction of the electronic band structure, affecting features such as the depth of the moiré potential28, the ‘flatness’ of low-energy bands30, and the real-space localization of charge carriers33.Moiré superlattices, formed by vertically stacking van der Waals layers with a small rotational offset and/or lattice mismatch, are a versatile platform for modulating the physicochemical behavior of two-dimensional solids∘) or anti-parallel  orientation between layers. Scanning probe28 and electron microscopy23 techniques have provided a qualitative picture of reconstruction in TMD moiré homo- and heterobilayers, understood in terms of the variation in interlayer stacking energy throughout the superlattice. However, the physical mechanisms by which reconstruction occurs have thus far only been simulated. Here we use Bragg interferometry34, an imaging methodology based on four-dimensional scanning transmission electron microscopy35 (4D-STEM), to directly map the intralayer mechanical deformations driving reconstruction in TMD moiré systems. We identify distinct reconstruction mechanisms for moiré homobilayers versus heterobilayers and examine their twist angle dependence, distinguishing the relative importance of local lattice rotations and dilations in both systems as well as the critical role that encapsulation layers play in affecting the balance between these in-plane deformations and out-of-plane corrugations. We also measure reconstruction-induced strain fields and demonstrate how application of an external mechanical force, e.g. heterostrain, can be leveraged to manipulate strain distributions.Group VI (Mo- and W-based) H-phase TMDs, which are non-centrosymmetric in the monolayer limit, have two distinct reconstructed forms with unique band structures depending on whether there is a parallel  hexagonal boron nitride (hBN). Twisted homobilayers were fabricated using the tear-and-stack method36 to introduce a desired interlayer moiré twist angle (θm). Heterobilayers were made by stacking two separate TMD monolayers with straight flake edges aligned, and the stacking orientation (P or AP) was confirmed using second harmonic generation spectroscopy (see sample fabrication details in Supplementary Note 1)37.We prepared MoSθm) for homobilayers  for heterobilayers , the local displacement vector that describes the interlayer offset between the TMD lattices , which provides insight into the reconstruction mechanisms in these systems.While 4D-STEM-based strain mapping has typically been performed by tracking changes in Bragg disk positions throughout a data set2 moiré homobilayers. The intralayer reconstruction rotation (θR), shown in Fig. θm) and the measured total fixed-body rotation (θT) in each TMD layer: θR = θT − (θm/2). For the P orientation  , thus θR > 0∘, while XMMX regions have the lowest stacking energy and θR < 0∘ . Figure To determine whether other deformation mechanisms contribute to the reconstruction process, we also calculated dilations from the measured local strain tensors. Dilation, also referred to as dilatation or an in-plane volumetric strain45. These inhomogeneous, intrinsic, intralayer strain fields are thought to be particularly important in AP moiré homobilayers, where they are implicated in the tight confinement of charge carriers in XX and MM sites and subsequent formation of ultraflat electronic bands32. In the case of rotation-driven reconstruction, shear is the predominant type of strain present and has been theoretically predicted to occur at the boundaries between stacking domains29. To visualize and measure the reconstruction strain fields, we calculated the engineering shear strain  at each point in the moiré superlattice. This γmax value indicates the maximum amount of intralayer shear strain present in any direction42. Indeed, we measure a concentration of shear strain in the saddle point (SP) areas  between regions with the same sign of θR  around 1.25–1.5∘ . As a result, at larger θm ( > θc) we observe a slightly negative θR in the MM regions, allowing some local domain expansion  to accommodate rapid expansion of XMMX into large hexagonal domains 43, fewer stacking sequences in the AP case correspond to the energy extremes. While reconstruction in a P moiré bilayer is driven by a preference for both MX and XM stacking over MMXX, reconstruction in AP moiré bilayers is driven predominantly by a preference for XMMX over XX stacking with relatively little preference for size of MM regions. This produces a stronger driving force for reconstruction in the P moiré bilayer.Comparing how reconstruction evolves with twist angle in the P and AP moiré homobilayers, it appears that the P orientation is more strongly reconstructed overall. When 2 and MoS2. In these systems, the lattice constant difference between the two dissimilar TMD layers, rather than (or in addition to) global interlayer rotation, generates the moiré pattern. Based on the displacement fields shown in Fig. We next turn our attention to the moiré heterobilayers, composed of WSeReal-space local dilation maps and corresponding average dilations as a function of displacement vector are provided for both AP Fig. d, e and θm = 0.13∘), these rotations strengthen in the AP heterobilayer with a larger interlayer twist  and their distribution resembles that of the AP twisted homobilayer . This could be due to a couple of factors. First, the twist angle in the sample measured might be below the threshold for substantial contributions from rotational relaxation. A second possibility is that out-of-plane corrugations in the layers have weakened and delocalized the rotational reconstruction, as we will discuss next. Simulated dilation and rotation fields for P and AP heterobilayers are provided in Supplementary Figs. Next we consider the effects of introducing an interlayer twist angle on heterobilayer reconstruction mechanisms. While the average local reconstruction rotations are relatively weak and independent of stacking order for the AP heterobilayer with a near zero-degree twist angle , partially encapsulated (hBN on top), and suspended (no hBN). Example convergent beam electron diffraction patterns from the three regions with varying extents of encapsulation are provided in Fig. ∘. Figure ∘ sample and a similar sample with θm ≈ 0.1–0.2∘. In these 2D plots, it is evident that hBN encapsulation layers affect the magnitude and extent of localization of the reconstruction rotation and dilation fields for both twist angle ranges  between both the suspended and encapsulated (no hBN − hBNT/B) and suspended and partially encapsulated (nohBN − hBNT) regions as a function of stacking parameter, as shown in Fig. Dil profile for the encapsulated versus suspended case displays clear similarities to that for the theoretical corrugated structure, indicating that the suspended heterobilayer has undergone a combination of in-plane and out-of-plane reconstruction while the fully encapsulated structure is reconstructed almost entirely in-plane. The residual differences between the experimental and theoretical curves suggest that some out-of-plane corrugation may remain in the encapsulated structure since the thin hBN is not perfectly rigid; however, overall the corrugations have been largely suppressed by the presence of hBN on both sides. Meanwhile, the ΔDil profile for the partially encapsulated versus suspended case differs more substantially from that of the corrugated model due to further mixing of in-plane and out-of-plane reconstruction when only one side of the heterobilayer is encapsulated.We then quantitatively compare the dilations in the three regions of the sample with 28. As a further point, we note that full encapsulation of the moiré layers dramatically increases the homogeneity of the reconstructed superlattice, as demonstrated by comparing the real-space dilation maps for the 0.1–0.2∘ sample /2, where δ is the lattice mismatch, ϵ is the percent heterostrain, and ρ is the Poisson ratio (0.234 for MoS2) (see Supplementary Note ϵ = 1.4%), nearly an order of magnitude smaller than that of the WSe2/MoS2 system discussed in Figs. 2/MoSe2, δ = 0.3%).Moiré heterobilayers are prepared using two dissimilar TMD materials. However, introduction of a heterostrain, wherein one TMD layer is stretched relative to the other, also creates a lattice constant difference in moiré homobilayers, making them heterobilayer-like. This raises the question of how rotational and dilational reconstruction compete in heterostrained moiré homobilayers. To investigate these relaxation dynamics, we performed Bragg interferometry on P and AP moiré homobilayers with varying amounts of uniaxial heterostrain. Figure γmax for P and AP moiré homobilayers with the heterostrain axis stretching versus contracting the moiré unit cell. Each of these scenarios yields a distinct strain field, including stripe  and even magnetic 2D moiré superlattices consisting of CrI3 bilayers48. As a diffraction-based imaging technique, Bragg interferometry is also distinctively compatible with both freely suspended and encapsulated moiré structures. Leveraging this capability, we found that hBN capping layers suppress out-of-plane relaxation modes and subsequently promote in-plane deformations, implicating critical connections between sample design, substrate effects, and emergent properties in moiré systems. The versatility of this methodology could also enable extension to more complex, multi-component vertical heterostructures, such as those containing gate electrodes, opening avenues for direct correlative measurements between lattice reconstruction and electrically controllable emergent (opto)electronic phenomena.In summary, here we have introduced the Bragg interferometry methodology for imaging non-centrosymmetric and heterobilayer systems, enabling us to directly probe intralayer mechanical deformations in TMD moiré bilayers. We demonstrate that it is variations in the symmetry of fixed-body rotation fields that are responsible for the morphological differences that have previously been observed in relaxed P and AP moiré homobilayers. The presence of an extrinsic heterostrain preserves these rotation fields and can be used to redistribute intralayer shear strain that is localized in domain boundaries, yielding a diversity of strain patterns. Since intralayer strain affects the positions of the conduction and valence band edges throughout the moiré unit cellElectron microscopy was performed at the National Center for Electron Microscopy in the Molecular Foundry at Lawrence Berkeley National Laboratory. Four-dimensional STEM datasets were acquired using a Gatan K3 direct detection camera located at the end of a Gatan Continuum imaging filter on a TEAM I microscope (aberration-corrected Thermo Fisher Scientific Titan 80–300). The microscope was operated in energy-filtered STEM mode at 80 kV with a 10 eV energy filter centred around the zero-loss peak, an indicated convergence angle of 1.71 mrad, and a typical beam current of 45–65 pA depending on the sample. These conditions yield an effective probe size of 1.25 nm . Diffraction patterns were collected using a step size of either 0.5 nm or 1 nm with 50 x 50 to 300 x 300 beam positions, covering an area ranging from 25 nm x 25 nm to 300 nm x 300 nm. The K3 camera was used in full-frame electron counting mode with a binning of 4 × 4 pixels and an energy-filtered STEM camera length of 800 mm. Each diffraction pattern had an exposure time of 13 ms, which is the sum of multiple counted frames.u, shown in Fig. 25. To summarize, for each diffraction pattern  the average diffuse scattering was first fit to a Lorentzian profile and removed. The average intensities in each of the twelve regions of Bragg disk overlap  such that u + na1 + ma2 is continuously oriented, followed by use of a mixed-integer program to refine zone boundaries.We note that adding integer multiples of u is smoothed with a Gaussian filter (σ = 2 pixels per a0 where a0 is the average lattice constant for the two layers) and differentiated numerically using a centered 3-pt finite difference stencil. We then divide the interlayer displacement vector by two to obtain the single intralayer displacement utop. Our analysis therefore assumes that the measured displacements can be equally partitioned between the two layers such that utop = (rtop − rbottom)/2 and the two single layer displacements are equal and opposite. This is enforced by symmetry in the homobilayers and, while it may not in principle hold true for generic heterobilayers, calculations suggest that the relaxation magnitudes in MoS2 and WSe2 differ by only 13% . The following analysis therefore assumes a large moiré pattern λ ≫ a0 and that the local variation of utop in reconstructed materials preserves ∣∣ ∇ utop∣∣∞ ≪ 1. Under these assumptions, we can decompose the displacement gradient ∇ utop as the sum of a symmetric infinitesimal strain tensor utop as We then rely on the small displacement theory approximation  in which the displacement gradient is assumed small enough to motivate a linearization of the strain tensorsγmax, is the difference between the maximum and minimum eigenvalues of 42.The eigenvalues and eigenvectors of ∘ from comparison of an ADF image and corresponding unscattered beam in the diffraction pattern using a defocused STEM probe. The second rotational offset is one of convenience that arises because we rotated the y-axis to align with the 25.To obtain the strain tensor, we needed to account for the rotational offset between the displacement vector coordinate system and the 4D-STEM scan axes. This rotational offset is controlled by two factors. The first is a rotation between the diffraction pattern and the scan direction inherent to the instrument, which we measured as 191u into stacking order categories as described in Supplementary Note a0/25 by a0/25 bins where a0 is the average lattice constant for the two layers. All statistical analyses and stacking order partitioning were performed after smoothing the interlayer displacements with a Gaussian filter, for which we used a σ = 2 pixels per a0 for all data included in Figs Stacking area percents Figs. a–c were 53. All other code was custom-written by the authors. Density functional theory calculations were performed using the Vienna ab initio software package (VASP)54 with further calculation parameters given in Supplementary Note All processing and analyses of 4D-STEM data were performed using Python on a personal computer, using published modules for Bragg disk detection, image processing and optimizationSupplementary InformationPeer Review File


A single variant (rs12949158), in SPNS2, achieved genome-wide significance (p = 4.29 × 10−8) implicating sphingosine-1-phosphate signalling in outcome after aSAH. A large multicentre international effort to recruit samples for validation is required and ongoing. Validation of these findings will provide significant insight into the pathophysiology of outcomes after aSAH with potential implications for treatment.Candidate gene studies have identified genetic variants associated with clinical outcomes following aneurysmal subarachnoid haemorrhage (aSAH), but no genome-wide association studies have been performed to date. Here we report the results of the discovery phase of a two-stage genome-wide meta-analysis of outcome after aSAH. We identified 157 independent loci harbouring 756 genetic variants associated with outcome after aSAH (The online version contains supplementary material available at 10.1007/s12975-022-01095-4. Aneurysmal subarachnoid haemorrhage (aSAH) is a devastating form of stroke with the worst outcomes and highest socioeconomic burden of any stroke type . The patThe best outcome prediction model after aSAH, utilising clinical, demographic and imaging characteristics only explains up to 31% of the variation in outcome following aSAH . ConsequIn 2018, the HATCH consortium highlighted the need to better understand the pathophysiological mechanisms underlying outcome and proposed a large multicentre genetic analysis of outcome following aSAH .The aim of this manuscript is to (1) report the completion of the discovery stage of the study including preliminary results and (2) raise awareness of the study to recruit further samples for the validation stage.This is a two-stage  GWA meta-analysis of outcome following aSAH. The results of the discovery analysis are reported in this manuscript. All analyses were performed according to the published protocol . The stuFor the discovery analysis, individuals were identified from (1) six studies from the HATCH consortium network and (2) the UK Biobank, a major biomedical database with extensive genetic and clinical data, previously described in detail  , 12 or GR2 > 0.2) and within 250 kb of each other. Index SNPs with suggestive significance (p < 1 × 10−4) were selected for validation. The threshold for genome-wide significance was p ≤ 5 × 10−8 and all analyses were performed using PLINK, STATA , wANNOVAR  .Including all seven datasets (−4) Fig.  and B. A9)] Fig. . Arrays Including both analyses, a total of 157 independent loci were identified from 756 unique SNPs and these will be taken forward for validation.p < 1 × 10−4) for validation. We also report that the rs12949158 alternate A allele, located within the SPNS2 gene, was associated with an increased risk of poor outcome after aSAH (OR 2.15 95% CI 1.63–2.82) with genome-wide significance (p = 4.29 × 10−8). Although one possible alternative explanation is that rs12949158 associates with psychomotor reaction time independent of aSAH, this association was not observed in control individuals in the UK Biobank.In this discovery genome-wide meta-analysis, we identified 157 independent loci from 756 unique SNPs associated with outcome following aSAH (n = 833). Secondly, the finding is primarily driven by the UK Biobank, which uses an outcome measure that is different from the other datasets (psychomotor reaction time). In the second stage, a customised genotyping array will be used to directly capture all variants targeted for validation including rs12949158.The genome-wide significant rs12949158 finding is not conclusive and requires validation. Firstly, the rs12949158 genotype was only typed in a subset of the discovery cohort Below is the link to the electronic supplementary material.


ATRA influences decision-making by embryonic stem (ES) cells for differentiation including lineage fate. From studies of knockout mice, RARα and RARγ regulate haematopoiesis whereby active RARα modulates the frequency of decision-making for myeloid differentiation, but is not essential for myelopoiesis, and active RARγ supports stem cell self-renewal and maintenance. From studies of zebrafish embryo development, active RARγ plays a negative role in stem cell decision-making for differentiation whereby, in the absence of exogenous ATRA, selective agonism of RARγ disrupted stem cell decision-making for differentiation patterning for development. From transactivation studies, 0.24 nM ATRA transactivated RARγ and 19.3 nM (80-fold more) was needed to transactivate RARα. Therefore, the dose of ATRA that cells are exposed to in vivo, from gradients created by cells that synthesize and metabolize, is important to RARγ versus RARα and RARγ activation and balancing of the involvements in modulating stem cell maintenance versus decision-making for differentiation. RARγ activation favours stemness whereas concomitant or temporal activation of RARγ and RARα favours differentiation. Crosstalk with signalling events that are provoked by membrane receptors is also important.All- They, as a heterodimer with retinoid X receptor, bind to target gene retinoic acid response elements (RAREs) to drive transcription when ATRA binds to RARs. When ATRA is absent, DNA-bound RAR/RXR heterodimers are associated with corepressors which with recruited histone deacetylases maintain a condensed chromatin and repress gene expression  cell lines and examined genome-wide transcription following treatment with ATRA for 24 and 48 h . ATRA diet genes  and ATRAet genes . The traet genes .in vitro studies of ES cells and haematopoietic stem cells (HSCs). Regarding HSCs, various findings have challenged a longstanding model for how HSCs ‘choose’ to differentiate towards a mature cell type. Though new principles are still a matter of debate they are highly pertinent to consideration of how RARs influence HSC decision-making. In the conventional model of haematopoiesis, the progeny of HSCs undergoes a series of stepwise commitment decisions that eventually restrict intermediate progenitors to a single cell lineage. But HSCs can affiliate directly to a cell lineage as they are a heterogeneous population of cells as evidenced by the existence of megakaryocyte, erythroid, and macrophage lineage biased/affiliated HSCs [reviewed in This review examines the roles of RARs in stem cell decision-making for cell differentiation from information gained from knockout mice and in vivo. The defects seen for double null mutant mice recapitulated the congenital malformations seen in foetuses from dams fed a vitamin A-deficient diet, and these null mutant mice displayed additional abnormalities  cells are competent regarding the production of all the cell types and ATRA has been used to obtain different cell types from mouse ES cells grown as monolayers or as hanging drops to form embryoid bodies. Cells resembling male germ cells spontaneously arise from embryoid bodies and treatment with 2 μM ATRA, with or without testosterone, significantly increased the expression of male germ cell lineage-associated genes. . The finntiation . Other intiation  and thatntiation . Neural ntiation . A 100 nntiation .trans-retinol and the level of ATRA in the serum of humans and other mammalians is ∼ 4–14 nM (Sox1) was reliant on ATRA produced endogenously  to differentiate ES cells is a concern. The affinities of ATRA for RARα, RARβ, and RARγ are 9 nM, 3 nM, and 10 nM, respectively , and the 4–14 nM . As mentgenously . ATRA wantiation .Rara and Rarg genes (meis homeobox 2(Meis2), left right determination factor 1 (Lefty1), hepatocyte nuclear factor 1 homeobox B (Hnf1b), arginase 1, and the homeobox (Hox) genes Hoxa3, and Hoxa5. RARs are phosphorylated in response to ATRA and the importance of phosphorylation of RARγ2 was investigated by expressing forms of RARγ2 that had been modulated in phospho-acceptor sites. For ATRA-mediated neuronal differentiation, gene expression that was controlled by phosphorylation of RARγ2 included that of Meis2, Lefty1, Hnf1b, and gastrulation brain homeobox 2. The genes targeted by phosphorylated RARγ2 depicted atypical DR7 retinoic acid response elements in addition to canonical DR2 and DR5 elements and the phosphorylated form of RARγ2 was recruited by DR7 and DR5 elements in response to ATRA. RARα1 was phosphorylated in vitro and in vivo by protein kinase A and phosphorylation at the site is involved in dibutyryl cAMP modulation of the differentiation of F9 embryonal carcinoma cells  of ATRA influences decision-making for differentiation including lineage fate. Endogenously produced ATRA plays a key role because vitamin A signalling is, in essence, driven by the intracellular ATRA concentration. In general, evaluation of the effect of treating cells with ATRA is confounded by all-n medium  because 25—50 nM . This isThe RARα gene is expressed in almost all adult tissues, and expression of the major isoform RARa1 is also ubiquitous . During A role for RARα in myeloid differentiation is well established . ATRA prThe influence of ATRA on neutrophil differentiation is particularly well-documented. ATRA and RARα also promote monocyte differentiation as shown from studies of the promyelocytic cell line NB4 and myeloblast blast-like cell line KG-1 . These cin vitro cultures of cells from null mutant mice suggested roles for RARα1 and RARγ in neutrophil maturation  was investigated by using diethylaminobenzaldehyde to inhibit ALDH activity. This impeded HSC differentiation leading to a ninefold expansion of HSCs, as measured by cells that were able to reconstitute lethally irradiated mice   .+ cells are enriched for HSCs and the role of RARα was investigated by treating these cells with antagonists. Cell production peaked at day 20 for control cultures and viable cells then declined rapidly. The pan-RAR antagonist AGN194310 treated cultures were maintained for up to 55 days, with 4-fold more cells by day 40. Both cultures produced mostly neutrophils and monocytes, in equal ratios, with the antagonist treated cultures generating more of the two mature cell types (as to the increased cumulative cell number)  had delayed mouse LSK + cell differentiation (see above). The two cell populations are different regarding their heterogeneity and the culture conditions used were different. Otherwise, the findings point to complex actions for RARα and RARγ. A lack of active RARα (RARα antagonism) had delayed the differentiation of human lineage-, CD133+, CD34+ cells whereas the presence of activated RARγ (ATRA agonism) may have interfered with the differentiation of the mouse LSK + cells .Purified human lineage-, CD133+, CD34 number) . AGN1943 number)  and that number) . CD11b+ versus macrophages generated nor appeared to accelerate the terminal maturation of immature myeloid cells. Instead, active RARα positively modulated the frequency of decision-making for differentiation to favour differentiation. In other words, unliganded interferes with gene expression for differentiation which is promoted when ATRA or a specific RARα agonist is bound  was needed to transactivate RARα  in the blood for transfer into cells which is mediated by binding to Stra6. LRAT converts all-trans retinol into retinyl esters for storage, CRABP2 delivers ATRA to the nucleus and RARs, and CYP26A1 catabolises ATRA to polar metabolites for elimination. RARγ expression by stem cells might autoregulate a low ATRA content by virtue of ATRA activation leading to the diversion of “excess” all-trans retinol into retinyl esters for storage and elevated CYP26A1 expression increasing ATRA breakdown. These controls on ATRA-driven RAR events may be an important “housekeeping” function to stem cell stemness. From the studies of ATRA-regulated genes in the early zebrafish embryo, CYP26A1 was identified as one of the most robust genes regarding ATRA regulation, even when ATRA availability is drastically reduced , lecithin:retinol acyltransferase (LRAT), cellular retinoic acid binding protein 2 (CRABP2), and cytochrome p450 26A1 (CYP26A1) . Retinol reduced , and, as reduced .versus differentiation . Treatment led to the development of viable fish that were substantially abnormal. There were substantial changes to head morphology, associated with loss of cranial bones and tissue, a reduced antero-posterior axis length, due to somite loss, and heart abnormalities that led to oedema. Regarding the loss of cranial bones and anterior line ganglia, the prevalence of Sox-9 neural crest cells was not affected other than a slight decrease in the head region. The agonist prevented caudal and pectoral fin formation and Tbx5a progenitors that form the pectoral fin were present in the bud region. The lack of pectoral outgrowth, provoked by the RARγ agonist at 4 hpf, was reversed by the addition, at 23 h post fertilization, of a RARγ antagonist, to reverse the action of the RARγ agonist, or wash out of the RARγ agonist at 23 h. The experiments were performed in E3 medium (for zebrafish embryos) which is a balanced salt solution. Therefore, and in the absence of exogenous ATRA, agonising RARγ had disrupted stem cell decision-making for differentiation for the patterning of zebrafish development. The option for fin development had been sustained within bud stem cells as to the reversibility of the action of the RARγ agonist  cells were efficiently derived from ES cells by coculture with OP9 bone marrow stromal cells. When isolated cells were cultured on MS-5 stromal cells with the addition of stem cell factor, Flt-3 ligand, interleukin 7 (IL-7), and IL-3 they generated granulocytes, macrophages, B-cell, and natural killer cells  generate the hierarchy of developing cells to sustain a cancer . CSCs apA role for the fusion gene PML-RARα in the pathogenesis of acute promyelocytic leukaemia is well established . For ninvia activation of the Akt/NFκB and Wnt/B-catenin pathways and upregulation of P glycoprotein (via the regulation of cell proliferation (Hoxa and Hoxb gene clusters. It was required for broad epigenomic organisation and necessary for the gene-specific removal of the polycomb repressive mark H3K27me3 during ES cell differentiation. Hox gene cluster reorganisation was triggered by RARγ located at the Hoxa1 3´-RARE and deletion of the RARγ binding site within the Hoxa1 enhancer attenuated epigenomic activation of Hoxa and Hoxb gene structures (From the importance of RARγ to decision-making by stem cells, we might expect RARγ to be an oncogene. RARγ overexpression has been reported for good proportions of patients with cholangiocarcinoma, clear cell renal cell carcinoma, colorectal cancer, ovarian cancer, and pancreatic ductal adenocarcinoma. For cholangiocarcinoma, overexpression was associated with poor differentiation and metastasis to lymph nodes and contributed to multidrug resistance. Findings suggested that the role of RARγ is mediated oprotein . RARγ anoprotein . For coloprotein . High exferation . Overexpferation . For theferation . The panferation . The extferation , agonisiferation , and theferation . Regardiructures .Distinct ATRA gradients and boundaries, from cells that synthesize and metabolize, are important to patterning embryogenesis, but there does not appear to be a linear relationship between dose and phenotype . Gradienvia growth factors and hematopoietic cytokines provide a further input to ES cell and HSC decision-making for cell differentiation, respectively. That stem cell differentiation is a progressive and gradual process presumably requires learning and memory of the events that are provoked by growth factors/cytokines. There is evidence to support integration of ATRA signalling with how cells learn from the events that are provoked by growth factors because CRABP1 delivers ATRA to the CYP26 family members for degradation and such dampens the sensitivity of ES cells to growth factors to affect their learning and memory (The roles of RARα and RARγ are modulatory, rather than obligatory, which raises the question what is nature of the events that are being modulated. Signalling d memory . An intrd memory . As abovPresently, we know how RARs work as heterodimers with RXRs, how they bind to response elements, that they repress gene expression in the absence of ligand and drive expression when ligand is bound, and that the RAR subtypes can regulate sub-sets of genes. However, the more complete picture regarding how all of this modulates the specification of cell lineage and/or the switch from stem cell maintenance to the onset of differentiation is still a complex and unresolved puzzle. Considerations include the extent to which ATRA is synthesized endogenously, which though cryptic is at a physiological level, the provision of ATRA by neighbouring cells including from gradients, which is again physiological, whether RARα and/or RARγ are activated, and crosstalk with other cytokine-provoked signalling cascades including phosphorylation of RARs.


Immunoglobulin G (IgG) is the most common type of antibodyfoundin blood and extracellular fluids and plays an essential role in ourimmune response. However, studies of the dynamics and reaction kineticsof IgG–antigen binding under physiological crowding conditionsare scarce. Herein, we develop a coarse-grained model of IgG consistingof only six beads that we find minimal for a coarse representationof IgG’s shape and a decent reproduction of its flexibilityand diffusion properties measured experimentally. Using this modelin Brownian dynamics simulations, we find that macromolecular crowdingaffects only slightly the IgG’s flexibility, as described bythe distribution of angles between the IgG’s arms and stem.Our simulations indicate that, contrary to expectations, crowdersslow down the translational diffusion of an IgG less strongly thanthey do for a smaller Ficoll 70, which we relate to the IgG’sconformational size changes induced by crowding. We also find thatcrowders affect the binding kinetics by decreasing the rate of thefirst binding step and enhancing the second binding step. While antigen-bindingsites come in a wide variety to recognize millions of different antigens,the remaining parts of immunoglobulins are relatively constant andoccur only in a few variants. Among them, immunoglobulin G (IgG) isthe most common type found in blood, representing about 75% of serumantibodies in humans.4Immunoglobulins are large, flexible glycoproteinsand one of themost important molecules in living organisms, playing a critical rolein the immune response system5 Assumingthat the average protein density isabout 1.3 times larger than that of water,6 it translates into about 7% of the occupied volume fraction. Whilethis is much less than typical intracellular crowding,8 the all-atom rigid-model simulations11 of IgG in physiologicallyrelevant crowded environments are nevertheless computationally challengingowing to the immense size of IgG (about 150 kDa) and other macromolecules.Moreover, the high flexibility of IgG, reported by atomic force microscopy12 and cryo-electron tomography,13 would likely make such simulations unphysical.Proteins amountto about 9% of the blood plasma mass.14 introduced12- and 26-bead models of two therapeutic antibodies and studied therole of interactions in their self-association.16 These authors considered only two configurations of rigid antibodiesinstead of accounting for their full flexibility. Galanti et al.17 developed a 96-bead model, finely approximatingthe IgG shape and adjusting the parameters to reproduce the distributionof angles measured experimentally with cryo-electron tomography.13 De Michele et al.18 took a similar route but considered a coarser model consisting ofonly seven beads. However, these authors used ellipsoidal beads tobetter approximate the IgG arms and stem, which is difficult to implementand simulate using the available simulation packages.Severalcoarse-grained models of antibodies have been developedrecently. Chaudhri et al.21 simulations to investigate how physiologically relevant macromolecularcrowding affects IgG’s flexibility, diffusion, and bindingkinetics. We find that the dependence of IgG diffusion on crowdingdiffers qualitatively from the behavior expected for rigid bodies.Our simulations indicate, however, that crowders affect the angledistribution and the binding kinetics relatively weakly.In thisstudy, we propose a six-bead coarse-grained model of IgGthat reproduces the distribution of angles and diffusion coefficientof IgG measured experimentally. We call it a “minimal model”as we find that reproducing the IgG flexibility and shape with fewerbeads is problematic. We use this model in Brownian dynamics (BD)25 . We accounted for hydrodynamic interactions between the beads withinthe Rotne–Prager–Yamakawa (far-field) approximation,28 which is essential to obtain the correct value of the diffusioncoefficient.30 From the BD trajectories, wecomputed a mean square displacement (MSD) and the distributions ofangles between the arms (ψ) and between the arm and the stem(φ). The diffusion coefficient D0 was extracted from the MSD in the usual way as D0 = MSD/6t in the limit of large t. In D0 = 36.80(103) nm2 μs–1 and Dr,0 = 1.110(34) rad2 μs–1. From D0 and using theStokes–Einstein–Sutherland relation, we get for thehydrodynamic radius aH ≈ 5.8 nm,closely matching the measured value ≈6 nm.31To relate themodel parameters to measurable quantities such asthe IgG hydrodynamic radius and angle distributions, we performedBD simulations of a single IgG .We first studied how crowdingaffects the distribution of angles. To this end, we performed BD simulationsof mixtures of IgG and Ficoll 70 3a, which33 also observed that an IgG preserves its high flexibilityin solutions crowded with poly(ethylene glycol) (PEG) (6% weight/volumeconcentration). However, we note that PEGs are soft and can form polymericnetworks at high concentrations,34 providingdifferent crowding environments. Słyk et al.35 have demonstrated that diffusion in soft and hard crowderscan differ substantially, particularly for non-spherical particles.It will be interesting to study in future work how IgG’s flexibilityand diffusion depend on the type of crowders.occ. Although IgG’s hydrodynamic radius (aH ≈ 5.8 nm) is larger than that of Ficoll 70 (5.1nm), its diffusion coefficient is reduced less strongly with increasingϕocc. This is unexpected because crowders typicallyslow down the diffusion of larger macromolecules more strongly.37We next investigated the translational diffusionof IgG. In Rg of IgG in all crowded systems. Rg as a function of ϕocc, andin occ, includinginfinite dilution (ϕocc = 0). These plots show that Rg decreases with ϕocc due tothe suppression of most extended conformations (the increase in thenumber of compact structures is moderate and spans a broader rangeof gyration radii). Thus, the dependence of the diffusion coefficienton ϕocc is an interplay of two competing effects.On the one hand, the IgG diffusion slows down because crowders actas obstacles. On the other hand, they reduce the IgG size, thus enhancingits diffusion. To demonstrate this interplay, we assume D ≈ kBT (1 –αϕocc)/(6πηaH(ϕocc)), where η is the dynamic viscosity.Note that α depends on the size of tracer particles.38 Ignoring this dependence in the lowest order in ϕocc and taking a constant α = αIgGnonflex (diffusion decrease rate assuminga non-flexible IgG of average size at zero crowding), one finds D ≈ D0 (1 – [αIgGnonflex–αg]ϕocc), where we have used aH ≈ aH(ϕocc = 0)(1 – αgϕocc), assuming that the hydrodynamic radius of IgG follows the samedependence on ϕocc as Rg; fitting this equation to the simulation data in g ≈ 0.17. Fitting now D(ϕocc) = 1 – αϕocc to the simulation datain Ficoll ≈ 0.89 for Ficoll and αIgG ≈ 0.71 for IgG, the latter giving αIgGnonflex = αIgG + αg ≈ 0.88. Although αIgGnonflex is onlycomparable to αFicoll , this estimate demonstrates how the crowding-inducedreduction in the IgG size can enhance its diffusion.To understand this result, we calculated the radiusof gyration Dr increasesas an inverse cube and D onlyinversely proportionally to the particle size, the reduced IgG sizeshould affect Dr even more strongly than D. Yet, rotational diffusion per se is less affected bycrowding than translational diffusion,40 making resolving the ϕocc dependencecomputationally more challenging. We extracted Dr through fitting to orientation autocorrelation functions(Section S1.4.2) and found that indeed Dr varies rather weakly with ϕocc. However, the value of Dr was sensitiveto statistics and the time window wherein the fitting was applied, preventing us from drawingdefinite conclusions about the dependence of Dr on ϕocc. We leave such studies to futurework.Since therotational diffusion coefficient 41 implemented in the pyBrownsimulation package.29 Within this approach,the association rate between two molecules is computed from Brownian(or molecular) dynamics simulations of two reacting molecules by startinga simulation at separation l0 betweenthe molecules and counting the number of reacting trajectories. Areaction counts as occurring when a certain reaction criterion  is satisfied and not occurringwhen the particle separation becomes larger than a certain escapedistance lesc. The reaction rate is thengiven by41D is the mutual diffusioncoefficient andl0 and lesc and Ω isthe probability that the molecules at separation lesc get back to separation l0, which for spherical, non-interacting particles is equal to l0/lesc. We notethat both D and Reff dependon crowding.We now turn to the binding kineticsand investigate how the rate of the first binding step depends oncrowding. To this end, we employed the Northrup–Allison–McCammon(NAM) approach,A2 or A2′unit was sufficiently close to an antigen (we chose the surface-to-surfacedistance of 0.1 nm). Consequently, we present only the ratio of thereaction constant to its value at zero crowding. For other parameters,we chose l0 = 30 nm and lesc = 35 nm . For each occupiedvolume fraction ϕocc, we performed at least 1000independent simulation runs.An IgG binds to an antigen by a paratope, a smallantigen binding site located at the tip of each IgG arm. However,using such a binding criterion led to poor simulation statistics,requiring many independent simulation runs. Since we are solely interestedin the effect of crowding on binding, for simplicity of calculationsand to speed up our simulations, we used a criterion in which the k(ϕocc) divided by k(ϕocc = 0) and theinset shows the effective reaction radius Reff computed according to  from eachother and an IgG bound to one antigen with one of its arms antigen .We have introduced a computationally inexpensivecoarse-grainedmodel of IgG, consisting of only six beads connected so as to mimicthe IgG shape 1. We tun13 2 and the37 We relatedthis behavior to the IgG’s flexibility and crowding-inducedconformational changes, which effectively reduce the IgG size as theconcentration of crowders increases (We used our IgG model in BD simulations to investigatehow crowdingaffects the diffusion and binding of IgG to antigens in biologicallyrelevant macromolecularly crowded media. We found that the IgG diffusionslows down less strongly with increasing crowding than the diffusionof Ficoll, even though the IgG is larger and expected to move slowerunder the same crowding conditions.ncreases 4.We found that crowding only weaklyaffects the distribution ofangles between the IgG’s arms and stem 3. As a cWe hope this model and the resultsmotivate further simulationand experimental studies on the behavior of IgG under physiologicallyrelevant crowding conditions. The knowledge acquired with such studieswill help us better understand our immune response system and maybe useful to develop novel biomedical applications.