Surface-induced dissociation of peptides and protein complexes in a quadrupole/time-of-flight mass spectrometer

Ion Mobility Mass Spectrometry (IM-MS) for Structural Biology: Insights Gained by Measuring Mass, Charge, and Collision Cross Section

The investigation of macromolecular biomolecules with ion mobility mass spectrometry (IM-MS) techniques has provided substantial insights into the field of structural biology over the past two decades. An IM-MS workflow applied to a given target analyte provides mass, charge, and conformation, and all three of these can be used to discern structural information. While mass and charge are determined in mass spectrometry (MS), it is the addition of ion mobility that enables the separation of isomeric and isobaric ions and the direct elucidation of conformation, which has reaped huge benefits for structural biology. In this review, where we focus on the analysis of proteins and their complexes, we outline the typical features of an IM-MS experiment from the preparation of samples, the creation of ions, and their separation in different mobility and mass spectrometers. We describe the interpretation of ion mobility data in terms of protein conformation and how the data can be compared with data from other sources with the use of computational tools. The benefit of coupling mobility analysis to activation via collisions with gas or surfaces or photons photoactivation is detailed with reference to recent examples. And finally, we focus on insights afforded by IM-MS experiments when applied to the study of conformationally dynamic and intrinsically disordered proteins.

Surface-induced Dissociation Mass Spectrometry as a Structural Biology Tool

Native mass spectrometry (nMS) is evolving into a workhorse for structural biology. The plethora of online and offline preparation, separation, and purification methods as well as numerous ionization techniques combined with powerful new hybrid ion mobility and mass spectrometry systems has illustrated the great potential of nMS for structural biology. Fundamental to the progression of nMS has been the development of novel activation methods for dissociating proteins and protein complexes to deduce primary, secondary, tertiary, and quaternary structure through the combined use of multiple MS/MS technologies. This review highlights the key features and advantages of surface collisions (surface-induced dissociation, SID) for probing the connectivity of subunits within protein and nucleoprotein complexes and, in particular, for solving protein structure in conjunction with complementary techniques such as cryo-EM and computational modeling. Several case studies highlight the significant role SID, and more generally nMS, will play in structural elucidation of biological assemblies in the future as the technology becomes more widely adopted. Cases are presented where SID agrees with solved crystal or cryoEM structures or provides connectivity maps that are otherwise inaccessible by "gold standard" structural biology techniques.

Surface-Induced Dissociation for Protein Complex Characterization

Native mass spectrometry (nMS) enables intact non-covalent complexes to be studied in the gas phase. nMS can provide information on composition, stoichiometry, topology, and, when coupled with surface-induced dissociation (SID), subunit connectivity. Here we describe the characterization of protein complexes by nMS and SID. Substructural information obtained using this method is consistent with the solved complex structure, when a structure exists. This provides confidence that the method can also be used to obtain substructural information for unknowns, providing insight into subunit connectivity and arrangements. High-energy SID can also provide information on proteoforms present. Previously SID has been limited to a few in-house modified instruments and here we focus on SID implemented within an in-house-modified Q Exactive UHMR. However, SID is currently commercially available within the Waters Select Series Cyclic IMS instrument. Projects are underway that involve the NIH-funded native MS resource (nativems.osu.edu), instrument vendors, and third-party vendors, with the hope of bringing the technology to more platforms and labs in the near future. Currently, nMS resource staff can perform SID experiments for interested research groups.

Surface-induced dissociation of protein complexes on a cyclic ion mobility spectrometer

We describe the implementation of a simple three-electrode surface-induced dissociation (SID) cell on a cyclic ion mobility spectrometer (cIMS) and demonstrate the utility of multipass mobility separations for resolving multiple conformations of protein complexes generated during collision-induced and surface-induced unfolding (CIU & SIU) experiments. In addition to CIU and SIU, SID of protein complexes is readily accomplished within the native instrument software and with no additional external power supplies by entering a single SID collision energy, a simplification in user experience compared to prior implementations. A set of cyclic homomeric protein complexes and a heterohexamer with known CID and SID behavior were analyzed to investigate mass and mobility resolution improvements, the latter of which improved by 20-50% (median: 33%) compared to a linear travelling wave device. Multiple passes of intact complexes, or their SID fragments, increased the mobility resolution by an average of 15% per pass, with the racetrack effect being observed after ∼3 or 4 passes, depending on the drift time spread of the analytes. Even with modest improvements to apparent mobility resolving power, multipass experiments were particularly useful for separating conformations produced from CIU and SIU experiments. We illustrate several examples where either (1) multipass experiments revealed multiple overlapping conformations previously unobserved or obscured due to limited mobility resolution, or (2) CIU or SIU conformations that appeared 'native' in a single pass experiment were actually slightly compacted or expanded, with the change only being measurable through multipass experiments. The work conducted here, the first utilization of multipass cyclic ion mobility for CIU, SIU, and SID of protein assemblies and a demonstration of a wholly integrated SIU/SID workflow, paves the way for widespread adoption of SID technology for native mass spectrometry and also improves our understanding of gas-phase protein complex CIU and SIU conformationomes.

Integration of Mass Spectrometry Data for Structural Biology

Mass spectrometry (MS) is increasingly being used to probe the structure and dynamics of proteins and the complexes they form with other macromolecules. There are now several specialized MS methods, each with unique sample preparation, data acquisition, and data processing protocols. Collectively, these methods are referred to as structural MS and include cross-linking, hydrogen-deuterium exchange, hydroxyl radical footprinting, native, ion mobility, and top-down MS. Each of these provides a unique type of structural information, ranging from composition and stoichiometry through to residue level proximity and solvent accessibility. Structural MS has proved particularly beneficial in studying protein classes for which analysis by classic structural biology techniques proves challenging such as glycosylated or intrinsically disordered proteins. To capture the structural details for a particular system, especially larger multiprotein complexes, more than one structural MS method with other structural and biophysical techniques is often required. Key to integrating these diverse data are computational strategies and software solutions to facilitate this process. We provide a background to the structural MS methods and briefly summarize other structural methods and how these are combined with MS. We then describe current state of the art approaches for the integration of structural MS data for structural biology. We quantify how often these methods are used together and provide examples where such combinations have been fruitful. To illustrate the power of integrative approaches, we discuss progress in solving the structures of the proteasome and the nuclear pore complex. We also discuss how information from structural MS, particularly pertaining to protein dynamics, is not currently utilized in integrative workflows and how such information can provide a more accurate picture of the systems studied. We conclude by discussing new developments in the MS and computational fields that will further enable in-cell structural studies.

Protein-Small Molecule Interactions in Native Mass Spectrometry

Small molecule drug discovery has been propelled by the continual development of novel scientific methodologies to occasion therapeutic advances. Although established biophysical methods can be used to obtain information regarding the molecular mechanisms underlying drug action, these approaches are often inefficient, low throughput, and ineffective in the analysis of heterogeneous systems including dynamic oligomeric assemblies and proteins that have undergone extensive post-translational modification. Native mass spectrometry can be used to probe protein-small molecule interactions with unprecedented speed and sensitivity, providing unique insights into polydisperse biomolecular systems that are commonly encountered during the drug discovery process. In this review, we describe potential and proven applications of native MS in the study of interactions between small, drug-like molecules and proteins, including large multiprotein complexes and membrane proteins. Approaches to quantify the thermodynamic and kinetic properties of ligand binding are discussed, alongside a summary of gas-phase ion activation techniques that have been used to interrogate the structure of protein-small molecule complexes. We additionally highlight some of the key areas in modern drug design for which native mass spectrometry has elicited significant advances. Future developments and applications of native mass spectrometry in drug discovery workflows are identified, including potential pathways toward studying protein-small molecule interactions on a whole-proteome scale.

Development of a focused high-energy macromolecular ion beam

In this work, we report the development of a focused macromolecular ion beam with kinetic energy of up to 110 keV. The system consists of a quadrupole ion trap (QIT), einzel lens and linear accelerator (LINAC). Based on the combination of matrix-assisted laser desorption ionization (MALDI) and quadrupole ion trapping (QIT), ions were desorbed from the surface and trapped with an ion trap to form biomolecular ion packets. Positive- and negative-pulsed voltages were applied on each end-cap electrode of the QIT to extract the ion packets and form an ion beam that was subsequently focused via an einzel lens and accelerated by stepwise pulsed voltages. The tabletop instrument was designed and successfully demonstrated via measurements of molecular ions of insulin, cytochrome c and bovine serum albumin (BSA) with mass-to-charge ratios (m/z) ranging from ∼5.8 to 66.5 k. This is the first report of both a focused and high-kinetic-energy protein ion beam. In addition, both secondary ions and electrons were observed from the surface by hypervelocity ion beam bombardment. This focused macromolecular ion beam has demonstrated its potential in the study of interactions between large molecular ions with other molecules either in the gas phase or upon a surface.

Tandem surface-induced dissociation of protein complexes on an ultrahigh resolution platform

We describe instrumentation for conducting tandem surface-induced dissociation (tSID) of native protein complexes on an ultrahigh resolution Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer. The two stages of SID are accomplished with split lenses replacing the entrance lenses of the quadrupole mass filter (stage 1, referred to herein as SID-Q) and the collision cell (stage 2, Q-SID). After SID-Q, the scattered projectile ions and subcomplexes formed in transit traverse the 20 mm pre-filter prior to the mass-selecting quadrupole, providing preliminary insights into the SID fragmentation kinetics of noncovalent protein complexes. The isolated SID fragments (subcomplexes) are then fragmented by SID in the collision cell entrance lens (Q-SID), generating subcomplexes of subcomplexes. We show that the ultrahigh resolution of the FT-ICR can be used for deconvolving species overlapping in m/z, which are particularly prominent in tandem SID spectra due to the combination of symmetric charge partitioning and narrow product ion charge state distributions. Various protein complex topologies are explored, including homotetramers, homopentamers, a homohexamer, and a heterohexamer.

Higher-order structural characterisation of native proteins and complexes by top-down mass spectrometry

In biology, it can be argued that if the genome contains the script for a cell's life cycle, then the proteome constitutes an ensemble cast of actors that brings these instructions to life. Their interactions with each other, co-factors, ligands, substrates, and so on, are key to understanding nearly any biological process. Mass spectrometry is well established as the method of choice to determine protein primary structure and location of post-translational modifications. In recent years, top-down fragmentation of intact proteins has been increasingly combined with ionisation of noncovalent assemblies under non-denaturing conditions, i.e., native mass spectrometry. Sequence, post-translational modifications, ligand/metal binding, protein folding, and complex stoichiometry can thus all be probed directly. Here, we review recent developments in this new and exciting field of research. While this work is written primarily from a mass spectrometry perspective, it is targeted to all bioanalytical scientists who are interested in applying these methods to their own biochemistry and chemical biology research.

Simple and Minimally Invasive SID Devices for Native Mass Spectrometry

We describe a set of simple devices for surface-induced dissociation of proteins and protein complexes on three instrument platforms. All of the devices use a novel yet simple split lens geometry that is minimally invasive (requiring a few millimeters along the ion path axis) and is easier to operate than prior generations of devices. The split lens is designed to be small enough to replace the entrance lens of a Bruker FT-ICR collision cell, the dynamic range enhancement (DRE) lens of a Waters Q-IM-TOF, or the exit lens of a transfer multipole of a Thermo Scientific Extended Mass Range (EMR) Orbitrap. Despite the decrease in size and reduction in number of electrodes to 3 (from 10 to 12 in Gen 1 and ∼6 in Gen 2), we show sensitivity improvement in a variety of cases across all platforms while also maintaining SID capabilities across a wide mass and energy range. The coupling of SID, high resolution, and ion mobility is demonstrated for a variety of protein complexes of varying topologies.

Native IM-Orbitrap MS: Resolving What Was Hidden

Native ion mobility-mass spectrometry (IM-MS) is an emerging biophysical approach to probe the intricate details of protein structure and function. The instrument design enables measurements of accurate first-principle determinations of rotationally-averaged ion-neutral collision cross sections coupled with high-mass, high-resolution mass measurement capabilities of Orbitrap MS. The inherent duty-cycle mismatch between drift tube IM and Orbitrap MS is alleviated by operating the drift tube in a frequency modulated mode while continuously acquiring mass spectra with the Orbitrap MS. Fourier transform of the resulting time-domain signal, i.e., ion abundances as a function of the modulation frequency, yields a frequency domain spectrum that is then converted (s-1 to s) to IM drift time. This multiplexed approach allows for a duty-cycle of 25% compared to <1% for traditional "pulse-and-wait" IM-ToF-MS. Improvements in mobility and mass resolution of the IM-Orbitrap allows for accurate analysis of intact protein complexes and the possibility of capturing protein dynamics.

A Tilted Surface and Ion Carpet Array for SID

The development of native mass spectrometry (MS) has provided structural biologists an additional tool to probe the structures of large macromolecular systems. Surface-induced dissociation (SID) is one activation method used within tandem MS experiments that has proven useful in interrogating the connectivity and topology of biologically-relevant protein complexes. We present here the use of a tilted surface and ion carpet array within a new SID device design, enabling decreased dimensions along the ion path and fewer lenses to tune. This device works well in fragmenting ions of both low (peptides) and high (protein complexes) m/z. Results show that the ion carpet array, while enabling simplification of the back-end of the device, has deficiencies in product collection and subsequently signal at higher SID energies when fragmenting protein complexes. However, the use of the tilted surface is advantageous as an effective way to shorten the device and reduce the number of independent voltages.

Further insights from structural mass spectrometry into endocytosis adaptor protein assemblies

As a fundament in many biologically relevant processes, endocytosis in its different guises has been arousing interest for decades and still does so. This is true for the actual transport and its initiation alike. In clathrin-mediated endocytosis, a comparatively well understood endocytic pathway, a set of adaptor proteins bind specific lipids in the plasma membrane, subsequently assemble and thus form a crucial bridge from clathrin to actin for the ongoing process. These adaptor proteins are highly interesting themselves and the subject of this manuscript. Using many of the instruments that are available now in the mass spectrometry toolbox, we added some facets to the picture of how these minimal assemblies may look, how they form, and what influences the structure. Especially, lipids in the adaptor protein complexes result in reduced charging of a normal sized complex due to their specific binding position. The results further support our structural model of a double ring structure with interfacial lipids.

Design and Performance of a Second-Generation Surface-Induced Dissociation Cell for Fourier Transform Ion Cyclotron Resonance Mass Spectrometry of Native Protein Complexes

A second-generation ("Gen 2") device capable of surface-induced dissociation (SID) and collision-induced dissociation (CID) for Fourier transform ion cyclotron resonance mass spectrometry of protein complexes has been designed, simulated, fabricated, and experimentally compared to a first-generation device ("Gen 1"). The primary goals of the redesign were to (1) simplify SID by reducing the number of electrodes, (2) increase CID and SID sensitivity by lengthening the collision cell, and (3) increase the mass range of the device for analysis of larger multimeric proteins, all while maintaining the normal instrument configuration and operation. Compared to Gen 1, Gen 2 exhibits an approximately 10× increase in sensitivity in flythrough mode, 7× increase in CID sensitivity for protonated leucine enkephalin (m/z 556), and 14× increase of CID sensitivity of 53 kDa streptavidin tetramer. It also approximately doubles the useful mass range (from m/z 8000 to m/z 15 000) using a rectilinear ion trap with a smaller inscribed radius or triples it (to m/z 22 000) using a hexapole collision cell and yields a 3-10× increase in SID sensitivity. We demonstrate the increased mass range and sensitivity on a variety of model molecules spanning nearly 3 orders of magnitude in absolute mass and present examples where the high resolution of the FT-ICR is advantageous for deconvoluting overlapping SID fragments.

Experimental and theoretical investigation of overall energy deposition in surface-induced unfolding of protein ions

Recent advances in native mass spectrometry have enabled its use to probe the structure of and interactions within biomolecular complexes. Surface-induced dissociation, in which inter- and intramolecular interactions are disrupted following an energetic ion-surface collision, is a method that can directly interrogate the topology of protein complexes. However, a quantitative relationship between the ion kinetic energy at the moment of surface collision and the internal energy deposited into the ion has not yet been established for proteins. The factors affecting energy deposition in surface-induced unfolding (SIU) of protein monomers were investigated and a calibration relating laboratory-frame kinetic energy to internal energy developed. Protein monomers were unfolded by SIU and by collision-induced unfolding (CIU). CIU and SIU cause proteins to undergo the same unfolding transitions at different values of laboratory-frame kinetic energy. There is a strong correlation between the SIU and CIU energies, demonstrating that SIU, like CIU, can largely be understood as a thermal process. The change in internal energy in CIU was modeled using a Monte Carlo approach and theory. Computed values of the overall efficiency were found to be approximately 25% and used to rescale the CIU energy axis and relate nominal SIU energies to internal energy. The energy deposition efficiency in SIU increases with mass and kinetic energy from a low of ∼20% to a high of ∼68%, indicating that the effective mass of the surface increases along with the mass of the ion. The effect of ion structure on energy deposition was probed using multiple stages of ion activation. Energy deposition in SIU strongly depends on structure, decreasing as the protein is elongated, due to decreased effective protein-surface collisional cross section and increased transfer to rotational modes.

Surface-Induced Dissociation of Noncovalent Protein Complexes in an Extended Mass Range Orbitrap Mass Spectrometer

Native mass spectrometry continues to develop as a significant complement to traditional structural biology techniques. Within native mass spectrometry (MS), surface-induced dissociation (SID) has been shown to be a powerful activation method for the study of noncovalent complexes of biological significance. High-resolution mass spectrometers have become increasingly adapted to the analysis of high-mass ions and have demonstrated their importance in understanding how small mass changes can affect the overall structure of large biomolecular complexes. Herein we demonstrate the first adaptation of surface-induced dissociation in a modified high-mass-range, high-resolution Orbitrap mass spectrometer. The SID device was designed to be installed in the Q Exactive series of Orbitrap mass spectrometers with minimal disruption of standard functions. The performance of the SID-Orbitrap instrument has been demonstrated with several protein complex and ligand-bound protein complex systems ranging from 53 to 336 kDa. We also address the effect of ion source temperature on native protein-ligand complex ions as assessed by SID. Results are consistent with previous findings on quadrupole time-of-flight instruments and suggest that SID coupled to high-resolution MS is well-suited to provide information on the interface interactions within protein complexes and ligand-bound protein complexes.

Initial Protein Unfolding Events in Ubiquitin, Cytochrome c and Myoglobin Are Revealed with the Use of 213 nm UVPD Coupled to IM-MS

The initial stages of protein unfolding may reflect the stability of the entire fold and can also reveal which parts of a protein can be perturbed, without restructuring the rest. In this work, we couple UVPD with activated ion mobility mass spectrometry to measure how three model proteins start to unfold. Ubiquitin, cytochrome c and myoglobin ions produced via nESI from salty solutions are subjected to UV irradiation pre-mobility separation; experiments are conducted with a range of source conditions which alter the conformation of the precursor ion as shown by the drift time profiles. For all three proteins, the compact structures result in less fragmentation than more extended structures which emerge following progressive in-source activation. Cleavage sites are found to differ between conformational ensembles, for example, for the dominant charge state of cytochrome c [M + 7H]⁷⁺, cleavage at Phe10, Thr19 and Val20 was only observed in activating conditions whilst cleavage at Ala43 is dramatically enhanced. Mapping the photo-cleaved fragments onto crystallographic structures provides insight into the local structural changes that occur as protein unfolding progresses, which is coupled to global restructuring observed in the drift time profiles. Graphical Abstract.

Surface Induced Dissociation Coupled with High Resolution Mass Spectrometry Unveils Heterogeneity of a 211 kDa Multicopper Oxidase Protein Complex

Manganese oxidation is an important biogeochemical process that is largely regulated by bacteria through enzymatic reactions. However, the detailed mechanism is poorly understood due to challenges in isolating and characterizing these unknown enzymes. A manganese oxidase, Mnx, from Bacillus sp. PL-12 has been successfully overexpressed in active form as a protein complex with a molecular mass of 211 kDa. We have recently used surface induced dissociation (SID) and ion mobility-mass spectrometry (IM-MS) to release and detect folded subcomplexes for determining subunit connectivity and quaternary structure. The data from the native mass spectrometry experiments led to a plausible structural model of this multicopper oxidase, which has been difficult to study by conventional structural biology methods. It was also revealed that each Mnx subunit binds a variable number of copper ions. Becasue of the heterogeneity of the protein and limited mass resolution, ambiguities in assigning some of the observed peaks remained as a barrier to fully understanding the role of metals and potential unknown ligands in Mnx. In this study, we performed SID in a modified Fourier transform-ion cyclotron resonance (FTICR) mass spectrometer. The high mass accuracy and resolution offered by FTICR unveiled unexpected artificial modifications on the protein that had been previously thought to be iron bound species based on lower resolution spectra. Additionally, isotopically resolved spectra of the released subcomplexes revealed the metal binding stoichiometry at different structural levels. This method holds great potential for in-depth characterization of metalloproteins and protein-ligand complexes. Graphical Abstract ᅟ.

193 nm Ultraviolet Photodissociation Mass Spectrometry of Tetrameric Protein Complexes Provides Insight into Quaternary and Secondary Protein Topology

Protein-protein interfaces and architecture are critical to the function of multiprotein complexes. Mass spectrometry-based techniques have emerged as powerful strategies for characterization of protein complexes, particularly for heterogeneous mixtures of structures. In the present study, activation and dissociation of three tetrameric protein complexes (streptavidin, transthyretin, and hemoglobin) in the gas phase was undertaken by 193 nm ultraviolet photodissociation (UVPD) for the characterization of higher order structure. High pulse energy UVPD resulted in the production of dimers and low charged monomers exhibiting symmetrical charge partitioning among the subunits (the so-called symmetrical dissociation pathways), consistent with the subunit organization of the complexes. In addition, UVPD promoted backbone cleavages of the monomeric subunits, the abundances of which corresponded to the more flexible loop regions of the proteins.

Ion Mobility-Mass Spectrometry Analysis of Cross-Linked Intact Multiprotein Complexes: Enhanced Gas-Phase Stabilities and Altered Dissociation Pathways

Analysis of protein complexes by ion mobility-mass spectrometry is a valuable method for the rapid assessment of complex composition, binding stoichiometries, and structures. However, capturing labile, unknown protein assemblies directly from cells remains a challenge for the technology. Furthermore, ion mobility-mass spectrometry measurements of complexes, subcomplexes, and subunits are necessary to build complete models of intact assemblies, and such data can be difficult to acquire in a comprehensive fashion. Here, we present the use of novel mass spectrometry cleavable cross-linkers and tags to stabilize intact protein complexes for ion mobility-mass spectrometry. Our data reveal that tags and linkers bearing permanent charges are superior stabilizers relative to neutral cross-linkers, especially in the context of retaining compact forms of the assembly under a wide array of activating conditions. In addition, when cross-linked protein complexes are collisionally activated in the gas phase, a larger proportion of the product ions produced are often more compact and reflect native protein subcomplexes when compared with unmodified complexes activated in the same fashion, greatly enabling applications in structural biology.

A dimer interface mutation in glyceraldehyde-3-phosphate dehydrogenase regulates its binding to AU-rich RNA

Glyceraldehyde-3-phosphate dehydrogenase (GAPDH) is an enzyme best known for its role in glycolysis. However, extra-glycolytic functions of GAPDH have been described, including regulation of protein expression via RNA binding. GAPDH binds to numerous adenine-uridine rich elements (AREs) from various mRNA 3'-untranslated regions in vitro and in vivo despite its lack of a canonical RNA binding motif. How GAPDH binds to these AREs is still unknown. Here we discovered that GAPDH binds with high affinity to the core ARE from tumor necrosis factor-α mRNA via a two-step binding mechanism. We demonstrate that a mutation at the GAPDH dimer interface impairs formation of the second RNA-GAPDH complex and leads to changes in the RNA structure. We investigated the effect of this interfacial mutation on GAPDH oligomerization by crystallography, small-angle x-ray scattering, nano-electrospray ionization native mass spectrometry, and hydrogen-deuterium exchange mass spectrometry. We show that the mutation does not significantly affect GAPDH tetramerization as previously proposed. Instead, the mutation promotes short-range and long-range dynamic changes in regions located at the dimer and tetramer interface and in the NAD(+) binding site. These dynamic changes are localized along the P axis of the GAPDH tetramer, suggesting that this region is important for RNA binding. Based on our results, we propose a model for sequential GAPDH binding to RNA via residues located at the dimer and tetramer interfaces.

Collision-induced release, ion mobility separation, and amino acid sequence analysis of subunits from mass-selected noncovalent protein complexes

In recent years, mass spectrometry has become a valuable tool for detecting and characterizing protein-protein interactions and for measuring the masses and subunit stoichiometries of noncovalent protein complexes. The gas-phase dissociation of noncovalent protein assemblies via tandem mass spectrometry can be useful in confirming subunit masses and stoichiometries; however, dissociation experiments that are able to yield subunit sequence information must usually be conducted separately. Here, we furnish proof of concept for a method that allows subunit sequence information to be directly obtained from a protein aggregate in a single gas-phase analysis. The experiments were carried out using a quadrupole time-of-flight mass spectrometer equipped with a traveling-wave ion mobility separator. This instrument configuration allows for a noncovalent protein assembly to be quadrupole selected, then subjected to two successive rounds of collision-induced dissociation with an intervening stage of ion mobility separation. This approach was applied to four model proteins as their corresponding homodimers: glucagon, ubiquitin, cytochrome c, and β-lactoglobulin. In each case, b- and y-type fragment ions were obtained upon further collisional activation of the collisionally-released subunits, resulting in up to 50% sequence coverage. Owing to the incorporation of an ion mobility separation, these results also suggest the intriguing possibility of measuring complex mass, complex collisional cross section, subunit masses, subunit collisional cross sections, and sequence information for the subunits in a single gas-phase experiment. Overall, these findings represent a significant contribution towards the realization of protein interactomic analyses, which begin with native complexes and directly yield subunit identities.

Surface induced dissociation: dissecting noncovalent protein complexes in the gas phase

The quaternary structures of proteins are both important and of interest to chemists, because many proteins exist as complexes in vivo, and probing these structures allows us to better understand their biological functions. Conventional structural biology methods such as X-ray crystallography and nuclear magnetic resonance provide high-resolution information on the structures of protein complexes and are the gold standards in the field. However, other emerging biophysical methods that only provide low-resolution data (e.g. stoichiometry and subunit connectivity) on the structures of the protein complexes are also becoming more important to scientists. Mass spectrometry is one of these approaches that provide lower than atomic structural resolution, but the approach is higher throughput and provides not only better mass information than other techniques but also stoichiometry and topology. Fragile noncovalent interactions within the protein complexes can be preserved in the gas phase of MS under gentle ionization and transfer conditions. Scientists can measure the masses of the complexes with high confidence to reveal the stoichiometry and composition of the proteins. What makes mass spectrometry an even more powerful method is that researchers can further isolate the protein complexes and activate them in the gas phase to release subunits for more structural information. The caveat is that, upon gas-phase activation, the released subunits need to faithfully reflect the native topology so that useful information on the proteins can be extracted from mass spectrometry experiments. Unfortunately, many proteins tend to favor unfolding upon collision with neutral gas (the most common activation method in mass spectrometers). Therefore, this typically results in limited insights on the quaternary structure of the precursor without further manipulation of other experimental factors. Scientists have observed, however, that valuable structural information can be obtained when the gas-phase proteins are activated by collision with a surface. Subcomplexes released after surface collision are consistent with the native quaternary structure of several protein systems studied, even for a large chaperone protein, GroEL, that approaches megadalton mass. The unique and meaningful data generated from surface induced dissociation (SID) have been attributed to the fast and energetic activation process upon collision with a massive target, the surface. In this Account, we summarize our SID studies of protein complexes, with emphasis on the more recent work on the combination of ion mobility (IM) with SID. IM has gained popularity over the years not only as a gas-phase separation technique but also as a technique with the ability to measure the size and shape of the proteins in the gas phase. Incorporation of IM before SID allows different conformations of a protein to be separated and examined individually by SID for structural details. When IM is after SID, the cross sections of the SID products can be measured, providing insight on the dissociation pathways, which may mimic disassembly pathways. Furthermore, the separation by IM greatly reduces the peak overlapping (same m/z) and coalescence (merging) of SID products, improving the resolving power of the method. While there are still many unanswered questions on the fundamental properties of gas-phase proteins and a need for further research, our work has shown that SID can be a complementary gas-phase tool providing useful information for studying quaternary structures of noncovalent protein complexes.

Interfacial residues promote an optimal alignment of the catalytic center in human soluble guanylate cyclase: heterodimerization is required but not sufficient for activity

Soluble guanylate cyclase (sGC) plays a central role in the cardiovascular system and is a drug target for the treatment of pulmonary hypertension. While the three-dimensional structure of sGC is unknown, studies suggest that binding of the regulatory domain to the catalytic domain maintains sGC in an autoinhibited basal state. The activation signal, binding of NO to heme, is thought to be transmitted via the regulatory and dimerization domains to the cyclase domain and unleashes the full catalytic potential of sGC. Consequently, isolated catalytic domains should show catalytic turnover comparable to that of activated sGC. Using X-ray crystallography, activity measurements, and native mass spectrometry, we show unambiguously that human isolated catalytic domains are much less active than basal sGC, while still forming heterodimers. We identified key structural elements regulating the dimer interface and propose a novel role for residues located in an interfacial flap and a hydrogen bond network as key modulators of the orientation of the catalytic subunits. We demonstrate that even in the absence of the regulatory domain, additional sGC domains are required to guide the appropriate conformation of the catalytic subunits associated with high activity. Our data support a novel regulatory mechanism whereby sGC activity is tuned by distinct domain interactions that either promote or inhibit catalytic activity. These results further our understanding of heterodimerization and activation of sGC and open additional drug discovery routes for targeting the NO–sGC–cGMP pathway via the design of small molecules that promote a productive conformation of the catalytic subunits or disrupt inhibitory domain interactions.

Quantitative analysis of global phosphorylation changes with high-resolution tandem mass spectrometry and stable isotopic labeling

Quantitative measurement of specific protein phosphorylation sites is a primary interest of biologists, as site-specific phosphorylation information provides insights into cell signaling networks and cellular dynamics at a system level. Over the last decade, selective phosphopeptide enrichment methods including IMAC and metal oxides (TiO₂ and ZrO₂) have been developed and greatly facilitate large scale phosphoproteome analysis of various cells, tissues and living organisms, in combination with modern mass spectrometers featuring high mass accuracy and high mass resolution. Various quantification strategies have been applied to detecting relative changes in expression of proteins, peptides, and specific modifications between samples. The combination of mass spectrometry-based phosphoproteome analysis with quantification strategies provides a straightforward and unbiased method to identify and quantify site-specific phosphorylation. We describe common strategies for mass spectrometric analysis of stable isotope labeled samples, as well as two widely applied phosphopeptide enrichment methods based on IMAC(NTA-Fe³⁺) and metal oxide (ZrO₂). Instrumental configurations for on-line LC-tandem mass spectrometric analysis and parameters of conventional bioinformatic analysis of large data sets are also considered for confident identification, localization, and reliable quantification of site-specific phosphorylation.

An unusual dimeric small heat shock protein provides insight into the mechanism of this class of chaperones

Small heat shock proteins (sHSPs) are virtually ubiquitous stress proteins that are also found in many normal tissues and accumulate in diseases of protein folding. They generally act as ATP-independent chaperones to bind and stabilize denaturing proteins that can be later reactivated by ATP-dependent Hsp70/DnaK, but the mechanism of substrate capture by sHSPs remains poorly understood. A majority of sHSPs form large oligomers, a property that has been linked to their effective chaperone action. We describe AtHsp18.5 from Arabidopsis thaliana, demonstrating that it is dimeric and exhibits robust chaperone activity, which adds support to the model that suboligomeric sHSP forms are a substrate binding species. Notably, like oligomeric sHSPs, when bound to substrate, AtHsp18.5 assembles into large complexes, indicating that reformation of sHSP oligomeric contacts is not required for assembly of sHSP-substrate complexes. Monomers of AtHsp18.5 freely exchange between dimers but fail to coassemble in vitro with dodecameric plant cytosolic sHSPs, suggesting that AtHsp18.5 does not interact by coassembly with these other sHSPs in vivo. Data from controlled proteolysis and hydrogen-deuterium exchange coupled with mass spectrometry show that the N- and C-termini of AtHsp18.5 are highly accessible and lack stable secondary structure, most likely a requirement for substrate interaction. Chaperone activity of a series of AtHsp18.5 truncation mutants confirms that the N-terminal arm is required for substrate protection and that different substrates interact differently with the N-terminal arm. In total, these data imply that the core α-crystallin domain of the sHSPs is a platform for flexible arms that capture substrates to maintain their solubility.

Integrating mass spectrometry of intact protein complexes into structural proteomics

MS analysis of intact protein complexes has emerged as an established technology for assessing the composition and connectivity within dynamic, heterogeneous multiprotein complexes at low concentrations and in the context of mixtures. As this technology continues to move forward, one of the main challenges is to integrate the information content of such intact protein complex measurements with other MS approaches in structural biology. Methods such as H/D exchange, oxidative foot-printing, chemical cross-linking, affinity purification, and ion mobility separation add complementary information that allows access to every level of protein structure and organization. Here, we survey the structural information that can be retrieved by such experiments, demonstrate the applicability of integrative MS approaches in structural proteomics, and look to the future to explore upcoming innovations in this rapidly advancing area.

Surface-induced dissociation of ion mobility-separated noncovalent complexes in a quadrupole/time-of-flight mass spectrometer

A custom in-line surface-induced dissociation (SID) device has been incorporated into a commercial ion mobility quadrupole/time-of-flight mass spectrometer in order to provide an alternative and potentially more informative activation method than the commonly used collision-induced dissociation (CID). Complicated sample mixtures can be fractionated by ion mobility (IM) and then dissociated by CID or SID for further structural analysis. Interpretation of SID spectra for cesium iodide clusters was greatly simplified with IM prior to dissociation because products originating from different precursors and overlapping in m/z but separated in drift time can be examined individually. Multiple conformations of two protein complexes, source-activated transthyretin tetramer and nativelike serum amyloid P decamer, were separated in ion mobility and subjected to CID and SID. CID spectra of the mobility separated conformations are similar. However, drastic differences can be observed for SID spectra of different conformations, implying different structures in the gas phase. This work highlights the potential of utilizing IM-SID to study quaternary structures of protein complexes and provides information that is complementary to our recently reported SID-IM approach.

Influence of a Gamma Amino Acid on the Structures and Reactivity of Peptide a(3) Ions

Collision-induced dissociation of protonated AGabaAIG (where Gaba is gamma-amino butyric acid, NH(2)-(CH(2))(3)-COOH) leads to an unusually stable a(3) ion. Tandem mass spectrometry and theory are used here to probe the enhanced stability of this fragment, whose counterpart is not usually observed in CID of protonated peptides containing only alpha amino acids. Experiments are carried out on the unlabelled and (15)N-Ala labeled AGabaAIG (labeled separately at residue one or three) probing the b(3), a(3), a(3)-NH(3) (a(3) (*)), and b(2) fragments while theory is used to characterize the most stable b(3), a(3), and b(2) structures and the formation and dissociation of the a(3) ion. Our results indicate the AGabaA oxazolone b(3) isomer undergoes head-to-tail macrocyclization and subsequent ring opening to form the GabaAA sequence isomer while this chemistry is energetically disfavored for the AAA sequence. The AGabaA a(3) fragment also undergoes macrocyclization and rearrangement to form the rearranged imine-amide isomer while this reaction is energetically disfavored for the AAA sequence. The barriers to dissociation of the AGabaA a(3) ion via the a(3)→b(2) and a(3)→a(3)* channels are higher than the literature values reported for the AAA sequence. These two effects provide a clear explanation for the enhanced stability of the AGabaA a(3) ion.

Determinants of gas-phase disassembly behavior in homodimeric protein complexes with related yet divergent structures

The overall structure of a protein-protein complex reflects an intricate arrangement of noncovalent interactions. Whereas intramolecular interactions confer secondary and tertiary structure to individual subunits, intermolecular interactions lead to quaternary structure--the ordered aggregation of separate polypeptide chains into multisubunit assemblies. The specific ensemble of noncovalent contacts dictates the stability of subunit folds, enforces protein-protein binding specificity, and determines multimer stability. Consequently, noncovalent architecture is likely to play a role in the gas-phase dissociation of these assemblies during tandem mass spectrometry (MS/MS). To further advance the applicability of MS/MS to analytical problems in structural biology, a better understanding of the interplay between the structures and fragmentation behaviors of noncovalent protein complexes is essential. The present work constitutes a systematic study of model protein homodimers (bacteriophage N15 Cro, bacteriophage λ Cro, and bacteriophage P22 Arc) with related but divergent structures, both in terms of subunit folds and protein-protein interfaces. Because each of these dimers has a well-characterized structure (solution and/or crystal structure), specific noncovalent features could be correlated with gas-phase disassembly patterns as studied by collision-induced dissociation, surface-induced dissociation, and ion mobility. Of the several respects in which the dimers differed in structure, the presence or absence of intermolecular electrostatic contacts exerted the most significant influence on the gas-phase dissociation behavior. This is attributed to the well-known enhancement of ionic interactions in the absence of bulk solvent. Because salt bridges are general contributors to both intermolecular and intramolecular stability in protein complexes, these observations are broadly applicable to aid in the interpretation or prediction of dissociation spectra for noncovalent protein assemblies.

Revealing the quaternary structure of a heterogeneous noncovalent protein complex through surface-induced dissociation

As scientists begin to appreciate the extent to which quaternary structure facilitates protein function, determination of the subunit arrangement within noncovalent protein complexes is increasingly important. While native mass spectrometry shows promise for the study of noncovalent complexes, few developments have been made toward the determination of subunit architecture, and no mass spectrometry activation method yields complete topology information. Here, we illustrate the surface-induced dissociation of a heterohexamer, toyocamycin nitrile hydratase, directly into its constituent trimers. We propose that the single-step nature of this activation in combination with high energy deposition allows for dissociation prior to significant unfolding or other large-scale rearrangement. This method can potentially allow for dissociation of a protein complex into subcomplexes, facilitating the mapping of subunit contacts and thus determination of quaternary structure of protein complexes.

Leucine enkephalin--a mass spectrometry standard

The present article reviews the mass spectrometric fragmentation processes and fragmentation energetics of leucine enkephalin, a commonly used peptide, which has been studied in detail and has often been used as a standard or reference compound to test novel instrumentation, new methodologies, or to tune instruments. The main purpose of the article is to facilitate its use as a reference material; therefore, all available mass spectrometry-related information on leucine enkephalin has been critically reviewed and summarized. The fragmentation mechanism of leucine enkephalin is typical for a small peptide; but is understood far better than that of most other compounds. Because ion ratios in the MS/MS spectra indicate the degree of excitation, leucine enkephalin is often used as a thermometer molecule in electrospray or matrix-assisted laser desorption ionization (ESI or MALDI). Other parameters described for leucine enkephalin include collisional cross-section and energy transfer; proton affinity and gas-phase basicity; radiative cooling rate; and vibrational frequencies. The lowest-energy fragmentation channel of leucine enkephalin is the MH(+)  → b(4) process. All available data for this process have been re-evaluated. It was found that, although the published E(a) values were significantly different, the corresponding Gibbs free energy change showed good agreement (1.32 ± 0.07 eV) in various studies. Temperature- and energy-dependent rate constants were re-evaluated with an Arrhenius plot. The plot showed good linear correlation among all data (R(2)  = 0.97), spanned over a 9 orders of magnitude range in the rate constants and yielded 1.14 eV activation energy and 10(11.0)  sec(-1) pre-exponential factor. Accuracy (including random and systematic errors, with a 95% confidence interval) is ±0.05 eV and 10(±0.5)  sec(-1), respectively. The activation entropy at 470 K that corresponds to this reaction is -38.1 ± 9.6 J mol(-1)  K(-1). We believe that these re-evaluated values are by far the most accurate activation parameters available at present for a protonated peptide and can be considered as "consensus" values; results on other processes might be compared to this reference value.

Mechanistic differences between two conserved classes of small heat shock proteins found in the plant cytosol

The small heat shock proteins (sHSPs) and alpha-crystallins are highly effective, ATP-independent chaperones that can bind denaturing client proteins to prevent their irreversible aggregation. One model of sHSP function suggests that the oligomeric sHSPs are activated to the client-binding form by dissociation at elevated temperatures to dimers or other sub-oligomeric species. Here we examine this model in a comparison of the oligomeric structure and chaperone activity of two conserved classes of cytosolic sHSPs in plants, the class I (CI) and class II (CII) proteins. Like the CI sHSPs, recombinant CII sHSPs from three divergent plant species, pea, wheat, and Arabidopsis, are dodecamers as determined by nano-electrospray mass spectrometry. While at 35 to 45 degrees C, all three CI sHSPs reversibly dissociate to dimers, the CII sHSPs retain oligomeric structure at high temperature. The CII dodecamers are, however, dynamic and rapidly exchange subunits, but unlike CI sHSPs, the exchange unit appears larger than a dimer. Differences in dodecameric structure are also reflected in the fact that the CII proteins do not hetero-oligomerize with CI sHSPs. Binding of the hydrophobic probe bis-ANS and limited proteolysis demonstrate CII proteins undergo significant, reversible structural changes at high temperature. All three recombinant CII proteins more efficiently protect firefly luciferase from insolubilization during heating than do the CI proteins. The CI and CII proteins behave strictly additively in client protection. In total, the results demonstrate that different sHSPs can achieve effective protection of client proteins by varied mechanisms.

How far can we go with structural mass spectrometry of protein complexes?

Physical interactions between proteins and the formation of stable complexes form the basis of most biological functions. Therefore, a critical step toward understanding the integrated workings of the cell is to determine the structure of protein complexes, and reveal how their structural organization dictates function. Studying the three-dimensional organization of protein assemblies, however, represents a major challenge for structural biologists, due to the large size of the complexes, their heterogeneous composition, their flexibility, and their asymmetric structure. In the last decade, mass spectrometry has proven to be a valuable tool for analyzing such noncovalent complexes. Here, I illustrate the breadth of structural information that can be obtained from this approach, and the steps taken to elucidate the stoichiometry, topology, packing, dynamics, and shape of protein complexes. In addition, I illustrate the challenges that lie ahead, and the future directions toward which the field might be heading.

Disulfide-dependent self-assembly of adiponectin octadecamers from trimers and presence of stable octadecameric adiponectin lacking disulfide bonds in vitro

Adiponectin is a circulating insulin-sensitizing hormone that homooligomerizes into trimers, hexamers, and higher molecular weight (HMW) species. Low levels of circulating HMW adiponectin appear to increase the risk for insulin resistance. Currently, assembly of adiponectin oligomers and, consequently, mechanisms responsible for decreased HMW adiponectin in insulin resistance are not well understood. In the work reported here, we analyzed the reassembly of the most abundant HMW adiponectin species, the octadecamer, following its collapse to smaller oligomers in vitro. Purified bovine serum adiponectin octadecamer was treated with reducing agents at pH 5 to obtain trimers. These reduced trimers partially and spontaneously reassembled into octadecamers upon oxidative formation of disulfide bonds. Disulfide bonds appear to occupy a greater role in the process of oligomerization than in the structural stabilization of mature octadecamer. Stable octadecamers lacking virtually all disulfide bonds could be observed in abundance using native gel electrophoresis, dynamic light scattering, and collision-induced dissociation nanoelectrospray ionization mass spectrometry. These findings indicate that while disulfide bonds help to maintain the mature octadecameric adiponectin structure, their more important function is to stabilize intermediates during the assembly of octadecamer. Adiponectin oligomerization must proceed through intermediates that are at least partially reduced. Accordingly, fully oxidized adiponectin hexamers failed to reassemble into octadecamers at a rate comparable to that of reduced trimers. As the findings from the present study are based on in vitro experiments, their in vivo relevance remains unclear. Nevertheless, they describe a redox environment-dependent model of adiponectin oligomerization that can be tested using cell-based approaches.

Kinetics of surface-induced dissociation of N(CH3)4(+) and N(CD3)4(+) using silicon nanoparticle assisted laser desorption/ionization and laser desorption/ionization

The implementation of surface-induced dissociation (SID) to study the fast dissociation kinetics (sub-microsecond dissociation) of peptides in a MALDI TOF instrument has been reported previously. Silicon nanoparticle assisted laser desorption/ionization (SPALDI) now allows the study of small molecule dissociation kinetics for ions formed with low initial source internal energy and without MALDI matrix interference. The dissociation kinetics of N(CH(3))(4)(+) and N(CD(3))(4)(+) were chosen for investigation because the dissociation mechanisms of N(CH(3))(4)(+) have been studied extensively, providing well-characterized systems to investigate by collision with a surface. With changes in laboratory collision energy, changes in fragmentation timescale and dominant fragment ions were observed, verifying that these ions dissociate via unimolecular decay. At lower collision energies, methyl radical (CH(3)) loss with a sub-microsecond dissociation rate is dominant, but consecutive H loss after CH(3) loss becomes dominant at higher collision energies. These observations are consistent with the known dissociation pathways. The dissociation rate of CH(3) loss from N(CH(3))(4)(+) formed by SPALDI and dissociated by an SID lab collision energy of 15 eV corresponds to log k = 8.1, a value achieved by laser desorption ionization (LDI) and SID at 5 eV. The results obtained with SPALDI SID and LDI SID confirm that (1) the dissociation follows unimolecular decay as predicted by RRKM calculations; (2) the SPALDI process deposits less initial energy than LDI, which has advantages for kinetics studies; and (3) fluorinated self-assembled monolayers convert about 18% of laboratory collision energy into internal energy. SID TOF experiments combined with SPALDI and peak shape analysis enable the measurement of dissociation rates for fast dissociation of small molecules.

Increasing charge while preserving noncovalent protein complexes for ESI-MS

Increased multiple charging of native proteins and noncovalent protein complexes is observed in electrospray ionization (ESI) mass spectra obtained from nondenaturing protein solutions containing up to 1% (vol/vol) m-nitrobenzyl alcohol (m-NBA). The increases in charge ranged from 8% for the 690 kDa alpha(7)beta(7)beta(7)alpha(7) 20S proteasome complex to 48% additional charge for the zinc-bound 29 kDa carbonic anhydrase-II protein. No dissociation of the noncovalently bound ligands/subunits was observed upon the addition of m-NBA. It is not clear if the enhanced charging is related to altered surface tension as proposed in the "supercharging" model of Iavarone and Williams (Iavarone, A. T.; Williams, E. R. J. Am. Chem. Soc.2003, 125, 2319-2327). However, more highly charged noncovalent protein complexes have utility in relaxing slightly the mass-to-charge (m/z) requirements of the mass spectrometer for detection and will be effective for enhancing the efficiency for tandem mass spectrometry studies of protein complexes.

Noncovalent protein tetramers and pentamers with "n" charges yield monomers with n/4 and n/5 charges

In recent years mass spectrometry based techniques have emerged as structural biology tools for the characterization of macromolecular, noncovalent assemblies. Many of these efforts involve preservation of intact protein complexes within the mass spectrometer, providing molecular weight measurements that allow the determination of subunit stoichiometry and real-time monitoring of protein interactions. Attempts have been made to further elucidate subunit architecture through the dissociation of subunits from the intact complex by colliding it into inert gas atoms such as argon or xenon. Unfortunately, the amount of structural information that can be derived from such strategies is limited by the nearly ubiquitous ejection of a single, unfolded subunit. Here, we present results from the gas-phase dissociation of protein-protein complexes upon collision into a surface. Dissociation of a series of tetrameric and pentameric proteins demonstrate that alternative subunit fragments, not observed through multiple collisions with gas atoms, can be generated through surface collision. Evidence is presented for the retention of individual subunit structure, and in some cases, retention of noncovalent interactions between subunits and ligands. We attribute these differences to the rapid large energy input of ion-surface collisions, which leads to the dissociation of subunits prior to the unfolding of individual monomers.

Continuous time-of-flight ion imaging: application to fragmentation

We have designed and constructed a continuous imaging reflectron time-of-flight mass spectrometer (TOFMS) that provides a mass spectrum at every pixel of a two-dimensional image with a 100% duty cycle. The technique is based on pseudorandom ion beam modulation and three-dimensional ( x, y, t) ion imaging. We use a multichannel plate detector with a delay-line anode that provides x, y positions and flight times t of every ion arrival event. The precision of the peak heights in the 100% duty cycle mass spectra is shown to be enhanced even at short (10 ms) acquisition times, which should prove useful for the study of solution kinetics or fast chromatographic separations. As a demonstration of the system's capability, we have imaged the fragmented ions that underwent surface-induced dissociation inside the reflectron and the ions that fragmented spontaneously through postsource decay.

Surface-induced dissociation shows potential to be more informative than collision-induced dissociation for structural studies of large systems

The ability to preserve noncovalent, macromolecular assemblies intact in the gas phase has paved the way for mass spectrometry to characterize ions of increasing size and become a powerful tool in the field of structural biology. Tandem mass spectrometry experiments have the potential to expand the capabilities of this technique through the gas-phase dissociation of macromolecular complexes, but collisions with small gas atoms currently provide very limited fragmentation. One alternative for dissociating large ions is to collide them into a surface, a more massive target. Here, we demonstrate the ability and benefit of fragmenting large protein complexes and inorganic salt clusters by surface-induced dissociation (SID), which provides more extensive fragmentation of these systems and shows promise as an activation method for ions of increasing size.