Membrane Proteins in Action Monitored by pH-Responsive Liquid Crystal Biosensors.

Liquid crystal (LC) biosensors have received significant attention for their potential applications for point-of-care devices due to their sensitivity, low cost, and easy read-out. They have been employed to detect a wide range of important biological molecules. However, detecting the function of membrane proteins has been extremely challenging due to the difficulty of integrating membrane proteins, lipid membranes, and LCs into one system. In this study, we addressed this challenge by monitoring the proton-pumping function of bacteriorhodopsin (bR) using a pH-sensitive LC thin film biosensor. To achieve this, we deposited purple membranes (PMs) containing a 2D crystal form of bRs onto an LC-aqueous interface. Under light, the PM patches changed the local pH at the LC-aqueous interface, causing a color change in the LC thin film that is observable through a polarizing microscope with crossed polarizers. These findings open up new opportunities to study the biofunctions of membrane proteins and their induced local environmental changes in a solution using LC biosensors.

Uniaxial Symmetry Breaking in Bacteriorhodopsin at the Thermal Phase Transition of Lipids of Purple Membranes.

The article correlates between symmetry breaking and phase transition. An analogy, extending from physics to biology, is known to exist between these two topics. Bacteriorhodopsin (bR) as a paradigm of membrane proteins has been used as a case study in the present work. The bR, as the sole protein embedded in what is called a purple membrane (PM), has attracted widespread interest in bionanotechnological applications. The lipids of PM have a crucial role in maintaining the crystal lattice of bR inside PM. For this reason, the present work has been concerned with elucidating the thermal phase transition properties of the PM lipids in orthogonal directions. The results indicated that the axial symmetry of bR exhibits considerable changes occurring at the thermal phase transition of lipids. These changes are brought by an anomaly observed in the time course of orthogonal electric responses during the application of thermal fields on PM. The observed anomaly may bear on symmetry breaking in bR occurring at the phase transition of lipids based on such analogy found between symmetry breaking and phase transition. Lipid-protein interactions may underlie the broken axial symmetry of bR at such lipid thermal transition of PM. Accordingly, thermally perturbed axial symmetry of bR may be of biological relevance relying on the essence of the crystal lattice of bR. Most importantly, a question has to be raised in the present study: Can bR, as a helical protein with broken axial symmetry, affect the symmetry breaking of helical light? This may be of potential technical applications based on a recent discovery that bR breaks the symmetry of helical light.

Detection of Lipid-Bound Bacteriorhodopsin Trimer Complex Directly from Purple Membrane by Native Mass Spectrometry.

Native mass spectrometry (MS) was used to detect the membrane protein, bacteriorhodopsin (bR), in its 27 kDa monomeric form and trimeric assemblies directly from lipid-containing purple membranes (PMs) from the halophilic archaeon, Halobacterium salinarum. Trimer bR ion populations bound to lipid molecules were detected with n-octyl ß-d-glucopyranoside as the solubilizing detergent; the use of octyl tetraethylene glycol monooctyl ether or n-dodecyl-ß-d-maltopyranoside resulted in only detection of monomeric bR. The archaeal lipids phosphotidylglycerolphosphate methyl ester and 3-HSO3-Galp-ß1,6-Manp-α1,2-Glcp-α1,1-sn-2,3-diphytanylglycerol were the only lipids in the PMs found to bind to bR, consistent with previous high-resolution structural studies. Removal of the lipids from the sample resulted in the detection of only the bR monomer, highlighting the importance of specific lipids for stabilizing the bR trimer. To the best of our knowledge, this is the first report of the detection of the bR trimer with resolved lipid-bound species by MS.

Detection of bacteriorhodopsin trimeric rotation at thermal phase transitions of purple membrane in suspension.

Bacteriorhodopsin (bR) of purple membrane (PM) is a retinal protein that forms aggregates in the form of trimers constituting, together with archaeal lipids, the crystalline structure of PM. The rotary motion of bR inside PM may be pertinent in understanding the essence of the crystalline lattice. An attempt has been made to determine the rotation of bR trimers which has been found to be detected solely at thermal phase transitions of PM, namely lipid, crystalline lattice and protein melting phase transitions. The temperature dependences of dielectric versus electronic absorption spectra of bR have been determined. The results suggest that the rotation of bR trimers, together with concomitant bending of PM, are most likely brought by structural changes in bR which might be driven by retinal isomerization and mediated by lipid. The rupturing of the lipid-protein contact might consequently lead to rotation of trimers associated with bending, curling or vesicle formation of PM. So the retinal reorientation may underlie the concomitant rotation of trimers. Most importantly, rotation of trimers might play a role, in terms of the essence of the crystalline lattice, in the functional activity of bR and may serve physiological relevance.

Roles of functional lipids in bacteriorhodopsin photocycle in various delipidated purple membranes.

Purple membrane (PM) is composed of several native lipids and the transmembrane protein bacteriorhodopsin (bR) in trimeric configuration. The delipidated PM (dPM) samples can be prepared by treating PM with CHAPS (3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonate) to partially remove native lipids while maintaining bR in the trimeric configuration. By correlating the photocycle kinetics of bR and the exact lipid compositions of the various dPM samples, one can reveal the roles of native PM lipids. However, it is challenging to compare the lipid compositions of the various dPM samples quantitatively. Here, we utilize the absorbances of extracted retinal at 382 nm to normalize the concentrations of the remaining lipids in each dPM sample, which were then quantified by mass spectrometry, allowing us to compare the lipid compositions of different samples in a quantitative manner. The corresponding photocycle kinetics of bR were probed by transient difference absorption spectroscopy. We found that the removal rate of the polar lipids follows the order of BPG ≈ GlyC < S-TGD-1 ≈ PG < PGP-Me ≈ PGS. Since BPG and GlyC have more nonpolar phytanyl groups than other lipids at the hydrophobic tail, causing a higher affinity with the hydrophobic surface of bR, the corresponding removal rates are slowest. In addition, as the reaction period of PM and CHAPS increases, the residual amounts of PGS and PGP-Me significantly decrease, in concomitance with the decelerated rates of the recovery of ground state and the decay of intermediate M, and the reduced transient population of intermediate O. PGS and PGP-Me are the lipids with the highest correlation to the photocycle activity among the six polar lipids of PM. From a practical viewpoint, combining optical spectroscopy and mass spectrometry appears a promising approach to simultaneously track the functions and the concomitant active components in a given biological system.

Structured Water Molecules on Membrane Proteins Resolved by Atomic Force Microscopy.

Water structuring on the outer surface of protein molecules called the hydration shell is essential as well as the internal water structures for higher-order structuring of protein molecules and their biological activities in vivo. We now show the molecular-scale hydration structure measurements of native purple membrane patches composed of proton pump proteins by a noninvasive three-dimensional force mapping technique based on frequency modulation atomic force microscopy. We successfully resolved the ordered water molecules localized near the proton uptake channels on the cytoplasmic side of the individual bacteriorhodopsin proteins in the purple membrane. We demonstrate that the three-dimensional force mapping can be widely applicable for molecular-scale investigations of the solid-liquid interfaces of various soft nanomaterials.

Effect of the fluorination degree of partially fluorinated octyl-phosphocholine surfactants on their interfacial properties and interactions with purple membrane as a membrane protein model.

Interfacial properties and membrane protein solubilization activity of a series of partially fluorinated octyl-phosphocholine (PC) surfactants were investigated from the viewpoint of the fluorination degree of the hydrophobic chain. The critical micelle concentration (CMC), surface tension lowering activity, molecular occupied area at the CMC and free energy changes of micellization as well as adsorption to the air-water interface for each PC surfactant were estimated from surface tension measurements at 25 °C. The PCs with higher degree of fluorination exhibited low CMC and high surface activity, while the single trifluoromethyl group at the end of the chain appeared to enhance the hydrophilicity of the surfactant molecule. Under conditions where conventional short-chain surfactants, n-octyl-ß-D-glucoside, Triton X-100 and dioctanoylphosphatidylcholine significantly solubilize purple membranes (PM), none of the fluorinated-PCs solubilized PM. This suggests that fluorinated-PCs are low-invasive enough to maintain the structure of lipids/protein assemblies like PM.

Structure retention of silica gel-encapsulated bacteriorhodopsin in purple membrane and in lipid nanodiscs.

The integral membrane protein, bacteriorhodopsin (BR) was encapsulated in sol-gel derived porous silica gel monoliths in native purple membrane (BR-PM) and synthetic lipid nanodisc (BR nanodisc) environments. BR nanodiscs were synthesized by solubilizing purple membrane in discoidal phospholipid bilayer stabilized by amphipathic Styrene-Maleic Acid (SMA) copolymer. UV-vis absorbance spectroscopy and dynamic-light scattering indicated the formation of BR monomers solubilized in lipid nanodiscs 10.2 ± 0.7 nm in average diameter. Fluorescence and absorbance spectroscopic techniques were utilized to probe conformational, environmental, and rotational changes associated with the tryptophan residues and the covalently-bound retinal moiety of BR upon entrapment in the silica matrix. We show that the immobilized BR in both membrane environments retained its bound retinal cofactor and the ability of the cofactor to undergo conformational changes upon light illumination necessary for BR's activity as a proton transporter. For purple membrane fragments, the results indicated that the local pH in the pores around BR after encapsulation was important for its stability at temperatures higher than 50 °C. Under the same buffering conditions, retinal was released from silica-encapsulated BR-PM and BR nanodiscs beginning at 80 °C (without a conformational change) and 50 °C (with a conformational change), respectively, reflecting differences in protein-protein (trimeric vs. monomeric) and protein-lipid interactions.

Average Conformation of Branched Chain Lipid PGP-Me That Accounts for the Thermal Stability and High-Salinity Resistance of Archaeal Membranes.

The average conformation of the methyl-branched chains of archaeal lipid phosphatidyl glycerophosphate methyl ester (PGP-Me) was examined in a hydrated bilayer membrane based on the 2H nuclear magnetic resonance (NMR) of enantioselectively 2H-labeled compounds that were totally synthesized for the first time in this study. The NMR results in combination with molecular dynamics simulations revealed that the PGP-Me chain appeared to exhibit behavior different from that of typical membrane lipids such as dimyristoylphosphatidylcholine (DMPC). The C-C bonds of the PGP-Me chain adopt alternative parallel and tilted orientations to the membrane normal as opposed to a DMPC chain where all of the C-C bonds tilt in the same way on average. This characteristic orientation causes the intertwining of PGP-Me chains, which plays an important role in the excellent thermal and high-salinity stabilities of archaeal lipid bilayers and membrane proteins.

Remarkably enhanced photoelectrical efficiency of bacteriorhodopsin in quantum dot - Purple membrane complexes under two-photon excitation.

The photosensitive protein bacteriorhodopsin (bR) has been shown to be a promising material for optoelectronic applications, but it cannot effectively absorb and utilize light energy in the near-infrared (NIR) region of the optical spectrum. Semiconductor quantum dots (QDs) have two-photon absorption cross-sections two orders of magnitude larger than those of bR and can effectively transfer the up-converted energy of two NIR photons to bR via the Förster resonance energy transfer (FRET). In this study, we have engineered a photoelectrochemical cell based on a hybrid material consisting of QDs and bR-containing purple membranes (PMs) of Halobacterium salinarum and demonstrated that this cell can generate an electrical signal under the two-photon laser excitation. We have shown that the efficiency of light conversion by the PM-QD hybrid material under two-photon excitation is up to 4.3 times higher than the efficiency of conversion by PMs alone. The QD integration into the bR-containing PMs significantly improves the bR capacity for utilizing light upon two-photon laser excitation, thus paving the way to the engineering of biologically inspired hybrid NIR nonlinear optoelectronic elements. The nonlinear nature of two-photon excitation may provide considerable advantages, such as a sharp sensitivity threshold and the possibility of precise three-dimensional location of excitation in holography and optical computing.

Tip-Enhanced Infrared Difference-Nanospectroscopy of the Proton Pump Activity of Bacteriorhodopsin in Single Purple Membrane Patches.

Photosensitive proteins embedded in the cell membrane (about 5 nm thickness) act as photoactivated proton pumps, ion gates, enzymes, or more generally, as initiators of stimuli for the cell activity. They are composed of a protein backbone and a covalently bound cofactor (e.g. the retinal chromophore in bacteriorhodopsin (BR), channelrhodopsin, and other opsins). The light-induced conformational changes of both the cofactor and the protein are at the basis of the physiological functions of photosensitive proteins. Despite the dramatic development of microscopy techniques, investigating conformational changes of proteins at the membrane monolayer level is still a big challenge. Techniques based on atomic force microscopy (AFM) can detect electric currents through protein monolayers and even molecular binding forces in single-protein molecules but not the conformational changes. For the latter, Fourier-transform infrared spectroscopy (FTIR) using difference-spectroscopy mode is typically employed, but it is performed on macroscopic liquid suspensions or thick films containing large amounts of purified photosensitive proteins. In this work, we develop AFM-assisted, tip-enhanced infrared difference-nanospectroscopy to investigate light-induced conformational changes of the bacteriorhodopsin mutant D96N in single submicrometric native purple membrane patches. We obtain a significant improvement compared with the signal-to-noise ratio of standard IR nanospectroscopy techniques by exploiting the field enhancement in the plasmonic nanogap that forms between a gold-coated AFM probe tip and an ultraflat gold surface, as further supported by electromagnetic and thermal simulations. IR difference-spectra in the 1450-1800 cm-1 range are recorded from individual patches as thin as 10 nm, with a diameter of less than 500 nm, well beyond the diffraction limit for FTIR microspectroscopy. We find clear spectroscopic evidence of a branching of the photocycle for BR molecules in direct contact with the gold surfaces, with equal amounts of proteins either following the standard proton-pump photocycle or being trapped in an intermediate state not directly contributing to light-induced proton transport. Our results are particularly relevant for BR-based optoelectronic and energy-harvesting devices, where BR molecular monolayers are put in contact with metal surfaces, and, more generally, for AFM-based IR spectroscopy studies of conformational changes of proteins embedded in intrinsically heterogeneous native cell membranes.

A concise method for quantitative analysis of interactions between lipids and membrane proteins.

Although interactions between lipids and membrane proteins (MPs) have been considered crucially important for understanding the functions of lipids, lack of useful and convincing experimental methods has hampered the analysis of the interactions. Here, we developed a surface plasmon resonance (SPR)-based concise method for quantitative analysis of lipid-MP interactions, coating the sensor chip surface with self-assembled monolayer (SAM) with C6-chain. To develop this method, we used bacteriorhodopsin (bR) as an MP, and examined its interaction with various types of lipids. The merits of using C6-SAM-modified sensor chip are as follows: (1) alkyl-chains of SAM confer a better immobilization of MPs because of the efficient preconcentration due to hydrophobic contacts; (2) SAM provides immobilized MPs with a partial membranous environment, which is important for the stabilization of MPs; and (3) a thinner C6-SAM layer (1 nm) compared with MP size forces the MP to bulge outward from the SAM surface, allowing extraneously injected lipids to be accessible to the hydrophobic transmembrane regions. Actually, the amount of bR immobilized on C6-SAM is 10 times higher than that on a hydrophilic CM5 sensor chip, and AFM observations confirmed that bR molecules are exposed on the SAM surface. Of the lipids tested, S-TGA-1, a halobacterium-derived glycolipid, had the highest specificity to bR with a nanomolar dissociation constant. This is consistent with the reported co-crystal structure that indicates the formation of several intermolecular hydrogen bonds. Therefore, we not only reproduced the specific lipid-bR recognition, but also succeeded in its quantitative evaluation, demonstrating the validity and utility of this method.

Fast and high-resolution mapping of elastic properties of biomolecules and polymers with bimodal AFM.

Fast, high-resolution mapping of heterogeneous interfaces with a wide elastic modulus range is a major goal of atomic force microscopy (AFM). This goal becomes more challenging when the nanomechanical mapping involves biomolecules in their native environment. Over the years, several AFM-based methods have been developed to address this goal. However, none of these methods combine sub-nanometer spatial resolution, quantitative accuracy, fast data acquisition speed, wide elastic modulus range and operation in physiological solutions. Here, we present detailed procedures for generating high-resolution maps of the elastic properties of biomolecules and polymers using bimodal AFM. This requires the simultaneous excitation of the first two eigenmodes of the cantilever. An amplitude modulation (AM) feedback acting on the first mode controls the tip-sample distance, and a frequency modulation (FM) feedback acts on the second mode. The method is fast because the elastic modulus, deformation and topography images are obtained simultaneously. The method is efficient because only a single data point per pixel is needed to generate the aforementioned images. The main stages of the bimodal imaging are sample preparation, calibration of the instrument, tuning of the microscope and generation of the nanomechanical maps. In addition, with knowledge of the deformation, bimodal AFM enables reconstruction of the true topography of the surface. It takes ~9 h to complete the whole procedure.

Highly Efficient Transfer of 7TM Membrane Protein from Native Membrane to Covalently Circularized Nanodisc.

Incorporating membrane proteins into membrane mimicking systems is an essential process for biophysical studies and structure determination. Monodisperse lipid nanodiscs have been found to be a suitable tool, as they provide a near-native lipid bilayer environment. Recently, a covalently circularized nanodisc (cND) assembled with a membrane scaffold protein (MSP) in circular form, instead of conventional linear form, has emerged. Covalently circularized nanodiscs have been shown to have improved stability, however the optimal strategies for the incorporation of membrane proteins, as well as the physicochemical properties of the membrane protein embedded in the cND, have not been studied. Bacteriorhodopsin (bR) is a seven-transmembrane helix (7TM) membrane protein, and it forms a two dimensional crystal consisting of trimeric bR on the purple membrane of halophilic archea. Here it is reported that the bR trimer in its active form can be directly incorporated into a cND from its native purple membrane. Furthermore, the assembly conditions of the native purple membrane nanodisc (PMND) were optimized to achieve homogeneity and high yield using a high sodium chloride concentration. Additionally, the native PMND was demonstrated to have the ability to assemble over a range of different pHs, suggesting flexibility in the preparation conditions. The native PMND was then found to not only preserve the trimeric structure of bR and most of the native lipids in the PM, but also maintained the photocycle function of bR. This suggests a promising potential for assembling a cND with a 7TM membrane protein, extracted directly from its native membrane environment, while preserving the protein conformation and lipid composition.

Effect of Temperature and Hydration Level on Purple Membrane Dynamics Studied Using Broadband Dielectric Spectroscopy from Sub-GHz to THz Regions.

To investigate the effects of temperature and hydration on the dynamics of purple membrane (PM), we measured the broadband complex dielectric spectra from 0.5 GHz to 2.3 THz using a vector network analyzer and terahertz time-domain spectroscopy from 233 to 293 K. In the lower temperature region down to 83 K, the complex dielectric spectra in the THz region were also obtained. The complex dielectric spectra were analyzed through curve fitting using several model functions. We found that the hydrated states of one relaxational mode, which was assigned as the coupled motion of water molecules with the PM surface, began to overlap with the THz region at approximately 230 K. On the other hand, the relaxational mode was not observed for the dehydrated state. On the basis of this result, we conclude that the protein-dynamical-transition-like behavior in the THz region is due to the onset of the overlap of the relaxational mode with the THz region. Temperature hysteresis was observed in the dielectric spectrum at 263 K when the hydration level was high. It is suggested that the hydration water behaves similarly to supercooled liquid at that temperature. The third hydration layer may be partly formed to observe such a phenomenon. We also found that the relaxation time is slower than that of a globular protein, lysozyme, and the microscopic environment in the vicinity of the PM surface is suggested to be more heterogeneous than lysozyme. It is proposed that the spectral overlap of the relaxational mode and the low-frequency vibrational mode is necessary for the large conformational change of protein.

Heterogeneity of the Transmembrane Protein Conformation in Purple Membranes Identified by Infrared Nanospectroscopy.

Cell membranes are intrinsically heterogeneous, as the local protein and lipid distribution is critical to physiological processes. Even in template systems embedding a single protein type, like purple membranes, there can be a different local response to external stimuli or environmental factors, resulting in heterogeneous conformational changes. Despite the dramatic advances of microspectroscopy techniques, the identification of the conformation heterogeneity is still a challenging task. Tip-enhanced infrared nanospectroscopy is here used to identify conformational changes connected to the hydration state of the transmembrane proteins contained in a 50 nm diameter cell membrane area, without the need for fluorescent labels. In dried purple membrane monolayers, areas with fully hydrated proteins are found among large numbers of molecules with randomly distributed hydration states. Infrared nanospectroscopy results are compared to the spectra obtained with diffraction-limited infrared techniques based on the use of synchrotron radiation, in which the diffraction limit still prevents the observation of nanoscale heterogeneity.

Cell-Free Synthetic Biology Chassis for Nanocatalytic Photon-to-Hydrogen Conversion.

We report on an entirely man-made nano-bio architecture fabricated through noncovalent assembly of a cell-free expressed transmembrane proton pump and TiO2 semiconductor nanoparticles as an efficient nanophotocatalyst for H2 evolution. The system produces hydrogen at a turnover of about 240 µmol of H2 (µmol protein)-1 h-1 and 17.74 mmol of H2 (µmol protein)-1 h-1 under monochromatic green and white light, respectively, at ambient conditions, in water at neutral pH and room temperature, with methanol as a sacrificial electron donor. Robustness and flexibility of this approach allow for systemic manipulation at the nanoparticle-bio interface toward directed evolution of energy transformation materials and artificial systems.

Direct, label-free, selective, and sensitive microbial detection using a bacteriorhodopsin-based photoelectric immunosensor.

A photoelectric immunosensor using purple membranes (PM) as the transducer, which contains photoactive bacteriorhodopsin, is here first demonstrated for direct and label-free microbial detection. Biotinylated polyclonal antibodies against Escherichia coli were immobilized on a PM-coated electrode through further surface biotinylation and bridging avidin or NeutrAvidin. The photocurrent generated by the antibody-coated sensor was reduced after incubation with E. coli K-12 cultures, with the reduction level increased with the culture populations. The immunosensor prepared via NeutrAvidin exhibited much better selectivity than the one prepared via avidin, recognizing almost none of the tested Gram-positive bacteria. Cultures with populations ranging from 1 to 107CFU/10mL were detected in a single step without any preprocessing. Both AFM and Raman analysis confirmed the layer-by-layer fabrication of the antibody-coated substrates as well as the binding of microorganisms. By investigating the effect of illumination orientation and simulating the photocurrent responses with an equivalent circuit model containing a chemical capacitance, we suggest that the photocurrent reduction was primarily caused by the light-shielding effect of the captured bacteria. Using the current fabrication technique, versatile bacteriorhodopsin-based photoelectric immunosensors can be readily prepared to detect a wide variety of biological cells.

Native MS Analysis of Bacteriorhodopsin and an Empty Nanodisc by Orthogonal Acceleration Time-of-Flight, Orbitrap and Ion Cyclotron Resonance.

Over the past two decades, orthogonal acceleration time-of-flight has been the de facto analyzer for solution and membrane-soluble protein native mass spectrometry (MS) studies; this however is gradually changing. Three MS instruments are compared, the Q-ToF, Orbitrap, and the FT-ICR, to analyze, under native instrument and buffer conditions, the seven-transmembrane helical protein bacteriorhodopsin-octylglucoside micelle and the empty nanodisc (MSP1D1-Nd) using both MS and tandem-MS modes of operation. Bacteriorhodopsin can be released from the octylglucoside-micelle efficiently on all three instruments (MS-mode), producing a narrow charge state distribution (z = 8+ to 10+) by either increasing the source lens or collision cell (or HCD) voltages. A lower center-of-mass collision energy (0.20-0.41 eV) is required for optimal bacteriorhodopsin liberation on the FT-ICR, in comparison to the Q-ToF and Orbitrap instruments (0.29-2.47 eV). The empty MSP1D1-Nd can be measured with relative ease on all three instruments, resulting in a highly complex spectrum of overlapping, polydisperse charge states. There is a measurable difference in MSP1D1-Nd charge state distribution (z = 15+ to 26+), average molecular weight (141.7 to 169.6 kDa), and phospholipid incorporation number (143 to 184) under low activation conditions. Utilizing tandem-MS, bacteriorhodopsin can be effectively liberated from the octylglucoside-micelle by collisional (Q-ToF and FT-ICR) or continuous IRMPD activation (FT-ICR). MSP1D1-Nd spectral complexity can also be significantly reduced by tandem-MS (Q-ToF and FT-ICR) followed by mild collisional or continuous IRMPD activation, resulting in a spectrum in which the charge state and phospholipid incorporation levels can easily be determined.

Stray light correction in the optical spectroscopy of crystals.

It has long been known in spectroscopy that light not passing through a sample, but reaching the detector (i.e., stray light), results in a distortion of the spectrum known as absorption flattening. In spectroscopy with crystals, one must either include such stray light or take steps to exclude it. In the former case, the derived spectra are not accurate. In the latter case, a significant amount of the crystal must be masked off and excluded. In this paper, we describe a method that allows use of the entire crystal by correcting the distorted spectrum.