• Introduction
  • The need for new insecticides
  • Spider toxins as novel insecticide candidates
  
  
• ArachnoServer
  • Requirements
  • Database Design and Implementation
  • Interface and Functionality
  
  
• Bacterial expression system
  • Experimental procedures
    • Materials
    • Common abbreviations
    • Plasmid design
    • Test expressions
    • Production of isotopically-labelled toxins
    • Toxin purification
    • RP–HPLC
    • NMR and MALDI–TOF MS
  • Results
  
  
• Speeding Up Heteronuclear NMR
  • Rationale
    • Spider Toxins and NMR
    • Multidimensional NMR and Indirect Dimensions
    • Time Acquisition Problem, Toxin Structures and NUS
    • Maximum Entropy Reconstruction (MaxEnt)
    • NUS Pre-Selection Problem
  • Finding a Minimal M
    • Previous work: HSQC
    • Current Work: CbCa(CO)NH
    • Determining Spectral Quality
      • Automatic Peak-Picking and Verification
      • Quality factor
    • Monitoring MaxEnt parameters
    • Experiment
      • Input Dataset (data)
      • Random seed (RND seed)
      • Generating sampling schedules (NUS)
      • Setting of MaxEnt parameters (MaxEnt)
      • Spectral Reconstructions (spectra)
    • Analysis of Spectral Quality
      • Information Quality (Peak Counting)
      • Inherent Spectral Quality (Q_f)
      • Noise and Spectral Quality
    • MaxEnt parameters
  
  
• Conclusions
  • Arachnoserver
  • Bacterial Expression System
  • Speeding Up Heteronuclear NMR
  • Structural Venomics Pipeline

Chapter 1.  Introduction

1.1  The need for new insecticides

The world is currently experiencing a major food crisis^1-5, with more than one billion people estimated to be living in hunger in 2009. The rising world population continues to increase the demand for food, while decreasing the amount of free arable land per capita^{1; 3}. The global food supply is further being threatened by global warming^{2; 4; 5}. Climate change is predicted to create a significant net decrease in fertile land area worldwide^{2; 4}, and global temperature rises are expected to increase the population and spread of many agricultural pests². Modern agriculture is dependent on the use of insecticides to maintain current supply levels, with current yields and crop quality predicted to decrease dramatically if the use of existing pesticides were abandoned. However, the efficacy of several insecticides has decreased, with pest populations becoming increasingly resistant^6-8. Furthermore, in addition to their effect on their intended targets, many existing pesticides are capable of adversely affecting the health of humans, livestock and the environment⁹. A significant share of the insecticides in use today were developed decades ago during the golden age of pesticide development, when there was less concern about resistance, and health and environmental issues⁷. While the prospective loss of ineffectual and unsafe insecticides looks to have a detrimental impact on food supply, the development of novel insecticides against a range of insect pests could be a major boon to global food security. Yet despite modern demand for new, safe and effective insecticides, few have been developed in recent years⁷ .

Similar problems are faced in efforts to control arthropod-borne diseases. Human population growth and migration have facilitated the spread of insect vectors, threatening disease outbreaks in previously unaffected areas^{8; 10-14}. Containment and eradication strategies for these diseases rely heavily upon the use of insecticides^{8; 15}. However, the number of vector populations showing resistance to current insecticides is increasing, and novel replacements are lacking^{6; 8; 16; 17}. The use of chemical insecticides with adverse health or environmental effects is necessitated in several countries due to the lack of effective alternatives, and resistance to these chemicals is increasing. The small number of compounds able to control certain insect vectors frustrates resistance-prevention strategies, which often rely upon rotational use of different compounds¹⁷. Warnings have been made that new insecticides for disease vector control will be required to avert or combat health crises^{8; 18-20}.

1.2  Spider toxins as novel insecticide candidates

Spiders have been natural predators of insects for millions of years^{21; 22}. Most spiders are venomous creatures^{21; 23}, producing venom comprising numerous different types of peptide toxins²⁴. (Non-proteinaceous toxins are also produced, but they will not be discussed here.) Spider toxins characteristically possess fairly short peptide chains of about 40–60 amino acids, which are folded into very stable globular conformations due to a common post-translational modification involving the formation of a disulphide bond between two cystine residues. Spider toxins typically contain 3–5 disulphide bonds often arranged to produce a knot-like geometry, resulting in highly stable molecules capable of withstanding much of the biochemical insults they may be exposed to in an envenomated organism. Collectively, toxins are active against a diverse range of targets within numerous species. Modes of action vary, with neurotoxic, haemolytic, antiarrhythmic and cytolytic activity being some examples of lethal and non-lethal activity exhibited.²⁵ Interest in spider-venom peptides as potential insecticide candidates is growing^{26; 27}, and several potent toxins with high insecticidal activity have already been isolated^28-30. Considering that there are currently ~41,000 species of spider classified³¹, and it is estimated that each species could produce over one thousand unique toxins, the potential pool of molecules with insecticidal activity may be several millions^{28; 32}. This contrasts the meagre 521 spider toxins that have thus far been isolated and published²⁵. Fortunately, however, the number of toxins discovered each year is rising exponentially³⁴ (see Fig. 1.1). This dramatic expansion necessitates a depository for the storage and interrogation of the ever-growing accumulation of data. Ideally, such a database would include information on each toxinʼs amino acid sequence, three-dimensional structure, disulphide-bonding pattern, biological activity, molecular target, phyletic specificity, and, where available, pharmacophore and genomic information. The development of such a database is considered in Chapter 2.

The process of translating an insecticidal spider toxin into a novel insecticide involves detailed biochemical and biophysical characterisation of the toxin at an atomic level. A very important part of this process is the production of pure toxins; Chapter 3 will discuss the available technologies for this purpose. Finally, to produce stable and effective, small molecule, insecticides from these toxins requires detailed knowledge of the three-dimensional (3D) structures of the toxins (as will be discussed in Chapter 4). This information can then be used to guide the chemical synthesis of potent mimetics, which may be mass-produced and utilized using conventional agricultural methods.

Currently this approach is greatly hampered by the lack of toxin structures available (currently only 39²⁵ structures of spider-venom peptides have been deposited in the Protein DataBank (PDB)^{27; 33}). Unfortunately, the exponential rise seen in the number sequences discovered annually (Fig. 1.1) has not been translated a greater number of toxin structures being determined, as illustrated in Fig. 1.2.²⁵. The preferred method for high-resolution structures determination of toxins is by nuclear magnetic resonances. The largest prohibiting factors to high-throughput structure determination are the time-consuming data acquisition and analysis steps. Chapter 4 will discuss novel approaches to data acquisition capable of significantly reducing the time requirements, and making NMR analysis a viable high-throughput method in structural studies of proteins. The various components which will be discussed in this thesis are part of what is emerging as a new field dubbed “Structural Venomics” ²⁷.

Spider-venom peptides are also of interest as lead compounds for drug development^{21; 27}. Isolated toxins have been found to target a variety of ion channels and receptors of pharmacological interest^{21; 35; 36}, and they are currently being investigated for the treatment of atrial fibrillation³⁷, erectile dysfunction³⁸ and acute and neuropathic pain³⁹. Although the results and methods developed herein are equally applicable to such toxins, the focus of this thesis will be insecticidal toxins.

Chapter 2.  ArachnoServer

Ongoing mapping of spider venomes (i.e. a complete catalogue of all peptides and proteins in the venom of a spider) will result in the accrual of a wealth of diverse yet interrelated information on numerous spider toxins. Information on amino acid sequence, three-dimensional structure, disulphide-bonding pattern, biological activity, molecular target, phyletic specificity, pharmacophore, and genomic information are expected to be collected for the continually-increasing range of identified toxins (see Section 1.2). Some of this information will be a prerequisite for collecting other remaining data (e.g. knowledge of the amino acid sequence is generally required before the 3D structure can be determined). This information will also be crucial for selecting candidates for insecticide and drug development. Ideally, this information should be readily and freely accessible to all researchers, stored in a manner that is easy to query and highly scalable (see estimated number of toxins in Section 1.2).

Online databases containing some of this information are already available. Tox-Prot (www.expasy.ch/sprot/tox-prot) and the Animal Toxin Database (protchem.hunnu.edu.cn/toxin) are two repositories designed to hold information on all animal toxins. generality of these databases makes them useful for comparing toxins between lineages and species, but they do not allow for the detailed storage of rich, manually curated information that is critical for spider toxin research focussed on insecticide and drug development. An example of such a species-specific database, tailored for research on a particular class of venoms, is ConoServer (www.conoserver.org), a database of peptide toxins from venomous marine cone snails. An analogous database that provided detailed information on all characterised spider toxins would greatly assist with structural venomics research and insecticide/drug development. For these reasons, a web-based database was built to serve as a central repository for information on proteinaceous spider toxins²⁵. Named ArachnoServer (to allow for future expansion from Araneae-sourced toxins to toxins from all Arachnida), it can be accessed online at http://www.arachnoserver.org .

2.1  Requirements

Certain requirements would need to be met in order for this database to be an invaluable component of the venomics pipeline. It would need the capability to logically store all information generally relevant to such research, along with citations for all provided information. Foremost, each toxins data record would need to describe the property that makes it unique, namely its mature toxin sequence. Data for (potentially) multiple precursor sequences would also need to be included, as well as notable sequence features for each precursor (including signal peptide, propeptide, and excised regions). Also important would be information on features of the mature toxins such as post-translational modifications, pharmacophores, and disulphide-bonding pattern. In the case of disulphide bonds, an indication of how the bond connectivity was determined (i.e. by experiment, homology, or theoretical modelling) would need to be indicated without exception for each disulphide bridge, to assist with assessing this informations reliability; most other databases do not include this information. The ability to include genetic information in the form of DNA, cDNA, and mRNA sequences is also required.

In order to easily find and compare toxins, entries would need to be stored using a suitable classification system. This would best be done by following the recently devised rational nomenclature for spider-venom peptides, which names each toxin on the basis of molecular target, channel or receptor type, toxin family (grouping similar toxins), source spider (genus/species), and isoform⁵⁷. The location where the source spider was collected and its taxonomy could assist with collecting samples and searching for toxins that have yet to be isolated. Importantly, the database would also need to store or link to structural information. Ideally, an online viewer would be incorporated to allow for an immediate examination of each solved 3D structure for a particular toxin. Structure files should also be available for download in Brookhaven PDB format, given its widespread use.

Information on toxicity would also be required. All applicable modes of action (such as whether a toxin is neurotoxic or antimicrobial) would need to be included. Inclusion of molecular targets and quantitative measures of efficacy such as the inhibitory concentration (IC₅₀), dissociation constant (K_d), and effective dose (ED₅₀) for each target would be of extreme importance for insecticide and drug development. Furthermore, biological activity on a per-species basis would be required, with lethal dose (LD₅₀), paralytic dose (PD₅₀), and further qualitative information included as relevant for the induced effect.

The above were deemed key features needed to make the database a comprehensive repository consistent with the needs of mapping the spider venome. While the above would allow for much useful information to be stored, it was recognised that certain studies could require information beyond the capabilities and scope of the completed database. The inclusion of accessions to external databases would provide links to more specialised information stored elsewhere, and a flexible data structure would allow later upgrades to include additional information.

2.2  Database Design and Implementation

A database structure was devised, based upon the requirements outlined in the previous section (see figure 2.1). A relational database model was selected, with unique primary and foreign key pairs used to ensure data integrity. A more normalised data structure was favoured, though not always possible due to the complex nature and relationships between the data being stored. The database schematic can be seen in figure 2.3 .

The initial database was implemented using MySQL (mysql.com). The final application was built with a Model View Controller (MVC) architecture using the Spring (springsource.org) framework. A MySQL database was selected for a storage backend, with Hibernate (hibernate.org) Object Relational Mapping (ORM) used to create an abstraction layer for the controller. With the mapping of database table to Plain Old Java Object (POJO) beans, the ORM layer was capable of generating all required SQL statements for querying and modifying the database. This approach simplifies future alterations to the data structure. A web application interface was designed for the view, using JavaServer Pages (JSP) and Asynchronous JavaScript and XML (AJAX) to serve content. A Spring service layer connects the interface to the ORM abstraction layer, facilitating the viewing, searching and curation of database content.

The database was initially populated from existing records in the UniProt (www.uniprot.org), EMBL/GenBank (http://www.ebi.ac.uk/embl/) and PDB databases. Initial records were created by import scripts, populating fields supported by the external databases. Manual curation verified imported data and added information from other literature sources, in addition to populating remaining fields. Source spider information was obtained from the World Spider Catalog³¹, and post-translational modifications to mature toxins were classified using a system based upon that implemented for ConoServer (www.conoserver.org). A new ontology was developed for classifying molecular targets, conforming with International Union of Basic & Clinical Pharmacology recommendations⁶³, with targets able to be classified at the subtype level of receptors or ion channels.

2.3  Interface and Functionality

For visualisation purposes, repository data was grouped into spider toxin records (STR), with a STR for each entry in the TOXIN table of the database (see figure 2.1). Information on individual toxins are displayed in an STR card (an example is shown in figure 2.2). The initial view displays basic descriptive information at the top of the card, including the toxin name, source species (together with location and a photograph), discovery year and basic descriptive information. A dynamically-generated display of the mature toxin sequence is prominently displayed. This display graphically marks the locations of any disulphide bonds (differentiating between bonding patterns determined experimentally, by homology or predicted), pharmacophoric residues (distinguishing between predicted and determined) and post-translational modifications (together with modification type). Hovering a cursor over the image provides further information, including residue number (with respect to the mature sequence) and full residue name.

Below the default view items, the STR card holds a number of expandable sections, in which all other information on that toxin is grouped. The sections are carefully categorised so that researchers need only view information relevant to their discipline or project stage. The Taxonomy section provides the full taxonomy of the source spider, as well as any historical taxonomy and alternate or deprecated names for the species. Biological Activity provides mode of action, toxicity in different species, and activity for specific molecular targets and subtargets. Accessions provides hyperlinks and accessions relevant to this toxin in external databases, such as links to PDB entries. Literature References cites other source information, including original publications. Protein Information displays annotated precursor sequences and includes a table displaying disulphide bond connectivity. Sequences contains peptide, precursor and genetic sequences in FASTA format, with links to perform BLAST (www.ncbi.nlm.nih.gov/BLAST/) searches with each sequence. Toxin Synonyms contains common, alternate and historical names for toxins (important due to the the new rational nomenclature system being relatively new). Toxin Structure contains a Jmol (http://www.jmol.org/) applet which can be used to interactively view each available toxin structure. Placeholder headers for expandable sections are only displayed if some or all of the relevant database records for the section are populated.

An important feature of the Spring interface is its advanced search capability. While basic keyword searches can be performed across key fields, advanced searches allow for multi-clause conditional queries across several data fields. Most displayable database fields can be searched with a set of different operators depending on data type. Additional clauses can be dynamically added to the search page, then grouped and joined by Boolean operators. The advanced search capabilities allow researchers to quickly locate potential lead compounds or find other toxins of interest. An example search shown in Figure 2.2 reveals all toxins with known structure exhibiting antimicrobial activity against Escherichia coli.

Chapter 3.  Bacterial expression system

The production of toxins on the scale required for structural venomics studies is said to be the “greatest remaining bottleneck” ²⁷ preventing realisation of the full potential benefits of animal venoms. For spider toxins, sufficient quantities for the full range of structural and functional studies cannot be obtained from milking or sacrificing spiders. Methods such as bacterial expression⁵⁸, solid-phase peptide synthesis in combination with native chemical ligation⁵⁹ and insect cell expression⁶⁰ can be used to produce toxins in vivo. However, structural studies require these toxins be in their native conformation. Spider toxins typically contain between three and five disulphide bonds^{24 ; 28}; as this results in between 15 and 945 possible isomers after disulphide-bridge formation, care must be taken to ensure that the produced toxins have the correct disulphide-bonding pattern prior to attempting structural and functional studies.

Production of recombinant toxins in bacteria was selected as the method of production for the structural venomics pipeline. The bacterial species chosen was Escherichia coli as it has been studied extensively, it is most commonly used method for recombinant protein expression, and allows for relatively quick, uncomplicated peptide expression. The periplasm of E. coli contains sophisticated molecular machinery for ensuring correct disulphide-bond formation, and it was surmised that this machinery could be utilised to produce toxins with the correct disulphide-bonding pattern.

Furthermore, E. coli is an ideal system for the production of uniformly ¹⁵N/¹³C-labelled toxin for 3D triple resonance NMR experiments. The native isotopes of carbon and nitrogen are not suitable for NMR studies as ¹²C has zero spin-quantum number, and hence is not NMR-active⁵⁶, whereas ¹⁴N is a highly insensitive quadrupolar nucleus. Thus, replacing these nuclei with the stable isotopes ¹³C and ¹⁵N, both sensitive spin-1/2 nuclei, opens up a range of additional 3D and 4D NMR experiments that both aids resonance assignments and leads to higher-quality structures. In order to make isotopically-labelled proteins, E. coli is gown in minimal medium containing ¹⁵NH₄Cl as the sole nitrogen source and, if ¹³C labelling is also required, with [U-¹³C₆]glucose as the sole carbon source for growth. So long as appropriate vitamins and minerals are provided in the minimal medium, the levels of protein expression are typically not significantly different to those of bacteria grown in a nutrient-rich medium.

In order to test the bacterial expression pipeline, five test toxins with potential as bioinsecticides were selected from ArachnoServer. Each toxin was required to have proven insecticidal activity, possess no more than five disulphide bonds, and be less than 70 amino acid residues in length. Sequences that were likely to encode novel 3D structures were also given high priority. From these five, the following two were selected for my thesis project:

Toxin name: U₂-segestritoxin-Sf1a (Sf1a)

Source: Segestria florentina (Tube-web spider)

Sequence: KECMTDGTVCYIHNHNDCCGSCLCSNGPIARPWEMMVGNCMCGPKA

Number of disulphide bonds: 4

Toxin name: U₁-agatoxin-Ta1a (Ta1a)

Source: Tegenaria agrestis (Hobo spider)

Sequence: EPDEICRARMTHKEFNYKSNVNGCGDQVAACEAECFRNDVYTACHEAQK

Number of disulphide bonds: 3

3.1  Experimental procedures

(See also Low, C.F. (2009). Development of an efficient bacterial expression system for production of disulfide-rich toxins for structural venomics, MSc PROJECT REPORT, Uni. of Queensland.)

3.1.1  Materials

Synthetic genes, with codons optimised for E. coli expression, were synthesised by GENEART (BioPark, Regensburg, Germany), cloned into the pLICC expression plasmid (see Section 3.1.3), and sequenced to ensure fidelity with the supplied amino acid sequence. Acid (TFA) was sourced from Auspep Pty Ltd (Vic., Australia). -grade acetonitrile was sourced from Lab-Scan Analytical Sciences (Lab-Scan Co. Ltd, Bangkok, Thailand). BenchMark^TM Prestained Protein Ladder was obtained from Invitrogen (Vic., Australia). Ni-NTA Superflow column resin was sourced from Qiagen (Vic., Australia). -Bertani (LB) broth and agar was obtained from United States Biochemical (Ohio, USA). Ampicillin (Amp), Tris hydrochloride (Tris-HCl) and isopropyl β-D-1-thiogalacto-pyranoside (IPTG) were obtained from Astral Scientific (NSW, Australia). Ethylenediamine-tetraacetic acid (EDTA) was obtained from Fisher Scientific (Vic., Australia).

3.1.2  Common abbreviations

• LB/Amp refers to 100 μg of ampicillin mixed into 5.0 mL of Luria-Bertani media.
• TSA buffer refers to 30 mM Tris-HCl pH 7.2, 40% sucrose and 2 mM EDTA
• TNG buffer refers to a 20 mM Tris pH 8.0, 200 mM NaCl and 10% glycerol solution
• Redox buffer refers to 6mM reduced and 0.6mM oxidised glutathione in TNG

3.1.3  Plasmid design

Each toxin gene was cloned into the pLICC plasmid vector by GENEART to allow for periplasmic expression in E. coli. In this plasmid vector, the toxin is encoded as a MalE-His₆-MBP-toxin fusion protein, with a tobacco etch virus (TEV) protease site engineered between the MBP and toxin coding regions. The MalE signal sequence at the beginning of the construct is used to ensure that the protein is exported to the periplasm (the signal sequence is cleaved off during this process). The hexahistidine tag enables purification of the MBP-toxin fusion protein using nickel affinity chromatography. The MBP (maltose binding protein) is used to aid folding and solubility. The TEV cleavage site enables the pure recombinant toxin to be realised from the MBP fusion protein. The pLICC vector contains an ampicillin resistance gene (AmpR) for selection, and expression of the target gene is inducible with IPTG via a T7 promoter. The plasmid map for the pLICC:Sf1a vector used to produce recombinant U₂-segestritoxin-Sf1a expression is shown in Fig. 3.1.

3.1.4  Test expressions

The following was performed in duplicate for each of the two plasmid vectors. vectors obtained from GENEART were transformed into E. coli strain BL21(λDE3) using the heat-shock method. L of 10 mg/μL plasmid was added to 50 μL of competent cells, then the mixture was vortexed and incubated on ice for 30 min. The culture was heated for 55 s at 42℃, then chilled on ice for 2 min. Transformed BL21(λDE3) cells were incubated at 37℃ in 1.0 mL LB media for 1–3 h, then centrifuged at 8,000 rpm. The pellets were then separated from the supernatant and resuspended in a further 50–100 µL LB. The resuspended pellets and media were streaked onto LB/Amp plates that had been preheated to 37℃; these were then incubated at 37℃ overnight. Six colonies were selected, suspended in LB/Amp, and again incubated overnight at 37℃. 500 µL of the BL21(λDE3) culture was transferred to new LB/Amp and incubated at 37℃ with shaking until an OD₆₀₀ between 0.8 and 1.3  (w.r.t. pure LB) was attained. A 1.0 mL aliquot of each culture was induced with 1 μL of 1M IPTG and incubated for 3 h at 37℃ with shaking. An additional 1.0 mL aliquot of each were taken as negative controls, and incubated under the same conditions without being induced by IPTG. Cells were then harvested from induced samples and controls after 10 min of centrifugation at 8,000 rpm.

The pellets from the induced samples were resuspended in 100 μL TSA buffer. A 30 μL aliquot of each suspension (hereafter referred to as “whole cell extract – induced” or simply “WC induced”) was removed and set aside, and the remainder was centrifuged at 12,000 rpm for 10 min. The pellets were resuspended in 100 μL ice-chilled water to induce hypotonic shock and break the outer membrane, then again centrifuged at 12,000 rpm for a further 10 min. A 30 μL sample of the supernatant was collected (hereafter referred to as “periplasmic cell extract – induced” or simply “PE”). The pellets were then resuspended in 100 μL SDS-PAGE running buffer, and a 30 μL aliquot was retained (henceforth referred to as “cytoplasmic cell extract – induced” or simply “CE”). The pellets from the control samples were resuspended in 100 μL SDS-PAGE running buffer; a 30 μL sample (hereafter referred to as “whole cell extract – uninduced” or simple “WC uninduced”) was retained. 30 μL of 2× SDS-PAGE loading dye was mixed into each of the WC induced, WC uninduced, PE and CE samples, then boiled for 5 min prior to PAGE analysis on a 12.5% polyacrylamide gel using a running potential of 200 V.

3.1.5  Production of isotopically-labelled toxins

The PE samples of each toxin that were shown to have the highest level of expression based on SDS-PAGE analysis of the test expressions, were selected for the production of uniformly ¹⁵N-labelled toxins. The protocol used was adapted from a previously published method⁵⁶. of the solutions prescribed in the original publication – a thymine-uracil solution and solution containing tricine and MOPS buffer – were not used for the following expressions.

Vitamin solution, metal stock solution, O solution, SBMX solution, S solution and thiamine solution were prepared as described in the literature⁵⁶. growth media was prepared for each toxin by mixing 40 mL SBMX solution, 1 mL S solution, and 940 mL distilled water into a 5 L baffled conical flask and autoclaving. The selected E. coli transformants were streaked on fresh LB/Amp plates and incubated overnight at 37℃. colonies selected from the plate were inoculated into 5 mL LB/Amp media to produce starter cultures that were then incubated at 37℃ with shaking. 2 mL O solution, 1 mL vitamin solution, and 1 mL thiamine solution were then mixed, filter sterilised, and added to the growth medium. -sterilised solutions of 4 g glucose in 10 mL of water and 1 g ¹⁵NH₄Cl in 5 mL of water were also added to the medium, followed by 1 mL of 100 mg/mL ampicillin. Conical flasks with 50 mL of minimal media were prepared for each of the starter cultures, then inoculated with 0.4 mL of the culture after 4 h. The cultures were incubated at 37℃ with shaking until an OD₆₀₀ between 2 and 3 was reached. The 50-mL cultures were then added to the remaining minimal medium for that toxin. Once each suspension reached an OD₆₀₀ of 0.8, 1 mL of 1 M IPTG was added to induce toxin expression. After 3 h cells were harvested by centrifugation at 8,000rpm for 10 min; the pellets were retained and stored at -80℃.

3.1.6  Toxin purification

Toxin purifications were carried out on ice with pre-chilled buffers. The pellets obtained from enriched media culture were defrosted on ice and resuspended in 60 mL TSA buffer. The mixtures were centrifuged at 12,000 rpm for 20 min at 4℃, then the pellets were resuspended in 60 mL chilled water. 5.4 mL of 20 mM magnesium chloride was mixed into the suspension, prior to 10 min incubation followed by centrifugation at 12,000 rpm for 20 min at 4℃. 650 μL TNG buffer was added to the extracted supernatant. 6 mL Ni⁺-equilibrated Ni-NTA Superflow resin was added to the solution, and mixed for 1 h prior to setting in an empty column. After four washes with 50 mL TNG mixed with 15 mM imidazole in order to remove unbound proteins, 20 mL TNG mixed with 250 mM imidazole was used to elute the fusion protein from the resin matrix. The eluate was concentrated down to 5 mL using an Amicon Ultra 3 kDa centrifugal filter, then diluted with 10–12mL TNG buffer prior to recconcentration to 5 mL. The concentrate was then made up to 10 mL by the addition of redox buffer. 1 mg/mLTEV protease was added to the solution, before incubation for 12–13 h with shaking, in order to release the recombinant toxin from the MBP fusion proteins. , the solution was passed over the Ni-NTA Superflow matrix in order to capture the His₆-MBP. The column was washed with TNG, and purified recombinant peptide toxin was collected in TNG buffer.

3.1.7  RP–HPLC

Reverse-phase high pressure liquid chromatography (RP-HPLC) was used to further purify the recombinant toxin. Shimadzu Prominence HPLC system fitted with a Vydac analytical C₁₈ RP-HPLC column (218TP54 series, 5 μm, 4.6  mm × 250 mm) was utilised for all purifications, with a Shimadzu Prominence SPD-20 UV/Vis detector operating at 214nm and 280nm used to monitor peptide elution. Trials with small amounts of peptide were used to determine optimal concentration gradients for purification. 0.1% TFA in water was used as solvent A, while solvent B comprised 0.09% TFA, 90% acetonitrile and 9.91% H₂O. toxins were eluted at a flow rate of 1 ml/min using the following gradient profiles: 5–25% solvent B over 10 min, 25–65% solvent B over 40 min, then 80% solvent B over 5 min for Sf1a; 5–18% solvent B over 5 min, 18-35% solvent B over 26 min then 35–80% solvent B over 5 min for Ta1a. toxins were purified to >98% homogeneity.

3.1.8 NMR and MALDI–TOF MS

Toxin samples were analysed using both NMR and mass spectrometry. 2D ¹H-¹⁵N HSQC NMR spectra were acquired on a Bruker 900 MHz NMR spectrometer equipped with cryogenic triple resonance probe. Sf1a (54.4   μM at pH 5.0) and Ta1a (43.5  μM at pH 6.0) were used for NMR data collection. Matrix-Assisted Laser Desorption Ionisation–Time of Flight mass spectrometry (MALDI-TOF) mass spectra were acquired using an Applied Biosystems 4700 Proteomics Bioanalyser with 5 mg/mL α-cyano-4-hydroxycinnamic acid in 1:1 acetonitrile/H₂O as the matrix.

3.2  Results

Uniformly ¹⁵N-labelled U₂-segestritoxin-Sf1a and U₁-agatoxin-Ta1a were both successfully produced using the E. coli periplasmic expression system. An SDS-PAGE gel showing overexpression and initial purification of the toxins can be seen in Fig. 3.2 . of the whole-cell extracts before IPTG induction (lane 1, labelled “WC” in black) and after IPTG induction (lane 2 for U₂-segestritoxin-Sf1a and lane 3 for U₁-agatoxin-Ta1a, labelled “WC” in red) reveals that an intense band at ~48 kDa, consistent with the expected size of the His₆-MBP-toxin fusion protein, is only present after IPTG induction. Moreover, as expected, this protein is found predominantly in the periplasmic fraction (labelled “PE”), with only minimal amounts, if any, present in the cytoplasmic extract (labelled “CE”). was conclude that the MBP-toxin fusion proteins have been highly overexpressed and are found almost exclusively in the periplasm.

Following nickel affinity chromatography and TEV cleavage of the fusion protein, the recombinant toxins were eluted from the Ni-NTA column and further purified using RP-HPLC. The resulting HPLC chromatograms (see Fig. 3.3) show that a single disulphide-bond isoform of each peptide was isolated (retention times of ~27 min and ~18 min for U₂-segestritoxin-Sf1a and U₁-agatoxin-Ta1a, respectively). The insets shown in Fig. 3.3  are MALDI-TOF mass spectra of the collected peaks and they indicate that the correct toxins were produced and isolated based on mass parity. The peaks eluting at ~40 min are presumed to be MBP.

The 2D ¹H-¹⁵N HSQC spectra obtained for each of the recombinant toxins (Figs 3.4 and 3.5 for U₂-segestritoxin-Sf1a and U₁-agatoxin-Ta1a, respectively), indicates that the peptides have folded into well-ordered structures based on the excellent chemical shift dispersion in both the ¹⁵N and ¹H frequency dimensions. Moreover, each HSC spectrum contains the expected number of backbone amide peaks based on the known amino acid sequence. The expected number of peaks is the total number of amino acid residues minus the number of prolines (which do not have a backbone amide proton and therefore do not give rise to correlations in ¹H-¹⁵N HSQC spectra) minus the N-terminal residue (the amide group of this residue is not involved in a peptide bond and hence these the amide protons exchange rapidly with those of the solvent are broadened beyond the level of detection).

Chapter 4.  Speeding Up Heteronuclear NMR

4.1  Rationale

4.1.1  Spider Toxins and NMR

The two most prominent methods for protein structure determination are X-ray crystallography and Nuclear Magnetic Resonance (NMR) spectroscopy⁶⁴. X-ray crystallography is viewed as a more mature technique^{26; 65; 66}. However unlike X-Ray crystallography, NMR spectroscopy does not require complex crystallisations^{64; 66}, can be used on proteins in solution^{46; 50; 64; 69}, and is better suited for molecules with molecular weight under ~30 kDa.

Peptide toxins from insect venoms are generally small, tightly conformed molecules less than 10kDa in size. of the three-dimensional structures of toxins in the Protein DataBank were obtained using Nuclear Magnetic Resonance (NMR) spectroscopy²⁷. Spider toxins are no exception, with all but one published structure obtained via solution NMR (see Appendix A).

Structure determination with NMR spectroscopy uses resonance data to create a set of structural restraints. nucleus with spin s and gyromagnetic ratio γ will possess a magnetic moment μ=ħs, where ħ is the reduced Planck constant. placed inside a magnetic field B₀, this moment will experience a torque and its angular momentum will process about B₀ at its Larmor frequency ω= γB_net ^{67; 68}. the same nuclear isotope, spins in different chemical environments will resonate at differing frequencies, due to locally induced magnetic fields contributing to B_net at each nucleiʼs location^{70; 71}. detector coil on an axis normal to B₀ can measure the relaxation of the net magnetisation vector M = ∑ μ_i. contribution from each moment is a decaying sinusoid; the relaxation or free induction decay (FID) observed from the magnetisation vector is the superposition of this signals. this reason NMR spectra are usually viewed in Fourier space, with unique moments and resonance effects viewed as separate signal peaks.

4.1.2  Multidimensional NMR and Indirect Dimensions

For more complex molecules such as proteins, there is often too much signal overlap for a spectrum with only one frequency dimension, or a 1D spectrum, to be useful in isolation. frequency dimensions may be added by via additional time delays (evolution times) between the excitation of nuclei and data acquisition. set of n-dimensional data points can be obtained by using n different time series, corresponding to the evolution times for each dimension. a two-dimensional case, a standard 1D dataset for the first dimension is acquired for each evolution time of the second dimension, resulting in a spectrum with two frequency dimensions in Fourier space. first dimension is referred to as a direct dimension and the second as an indirect dimension, due to the methods by which data for each has been acquired⁸. indirect dimensions may be added by introducing another time series of evolution times, for all data points in lower dimensions⁴¹. allows for heteronuclear experiments to be conducted, with resonances for separate nuclei being recorded in each dimension.

4.1.3  Time Acquisition Problem, Toxin Structures and NUS

The Nyquist theorem holds that if a spectrum contains a maximum frequency f_max, then that spectrum should be sampled at a frequency greater or equal to twice f_max to avoid aliasing⁴². results in a need to frequently collect data for long periods⁴³. a sample must be taken every t_i ≤ f_max ^-1, i ∈ [0, t_max] for each indirect dimension, the temporal cost for increasing the dimensionality of an NMR experiment increases exponentially with each additional indirect dimension⁴⁴. In addition the accuracy with which a frequency component can be measured i.e. the resolution of the spectrum is related to t_max, which is the total length of the data record. And the total number of points (N) required to achieve a given resolution whilst sampling at the Nyquist rate is N = t_max / Δt, where Δt is 1/2 f_max ^-1 (also referred to as the dwell time).

Both the Nyquist theorem and the need to obtain data over large time intervals apply for each indirect dimension in multidimensional NMR⁴⁵. , the temporal cost for increasing the dimensionality of an NMR experiment increases exponentially with each additional indirect dimensions⁴⁴. Figure 4.1 shows a list of NMR experiments commonly used to collect through-bond restraint data for a peptide or protein (i.e., to assign all resonances in the structures), along with an estimate of the NMR time required for each experiment. experiments are heteronuclear, and all but one require two indirect dimensions and well over a day of NMR time. further two to three days would be required to collect through-space restraints with NOESY experiments. can see that over two weeks of NMR data collection is required to determine the structure of just one spider toxin. are potentially millions of spider toxins with undetermined structure (see Section 1.2). it is predicted that spider toxins are structurally based upon a limited number of folds⁵⁷, at the least several hundred experimentally determined toxin structures would be required to map the structural scaffold of the venome.

Fortunately, conventional NMR experiments often result in highly redundant data sets being obtained. data tends to be sparse, meaning that there are few signals dispersed in a large volume; it is not uncommon for several orders of magnitude of data being collected than is strictly required for the required information to be extracted⁴⁶. is due to the requirement of high resolution in all dimensions whilst conforming to the Nyquist condition, resulting in very large densely sampled data. New processing techniques have been developed that do not require data from indirect dimensions to be obtained at the Nyquist interval, but can instead utilise spectral data sampled non-uniformly in each indirect dimension^{42; 45; 47; 48}. number of samples taken (M) is typically less than the total number prescribed by the Nyquist theorem (N) to achieve the desired resolution. -uniform sampling (NUS) allows sampling to be spread over a wide domain, but concentrated in regions that have high signal to noise or more likely to contain unique data⁴³. -uniform sampling can allow for a subset of the data to be sampled at appropriate locations, meaning enough data to reconstruct an NMR spectrum can be collected in a fraction of the experimental time taken for DFT methods^46-50.

There are several methods for reducing the temporal cost of heteronuclear NMR data collection using NUS. include G-matrix Fourier Transform-NMR (GFT-NMR)⁴⁴; Three-Way Decomposition (TWD),also known as muti-dimensional NMR spectra interpretation (MUNIN)^{46; 51} ; Back-Projection Reconstrucion⁵², Maximum Likelihood Reconstruction⁵³ and Maximum Entropy Reconstruction⁵⁴.

4.1.4  Maximum Entropy Reconstruction (MaxEnt)

Perhaps the most prominent⁴⁶ of the aforemention methods, MaxEnt is a reconstruction method that uses a least-information approach to rebuild a spectrum from a subset of the data required to produce a conventional spectrum. allows for accurate reconstructions with high sensitivity, which is able to produce usable spectra in situations where DFT produces spurious or unusable results⁴⁹. algorithm effectively uses entropy as a smoothing function⁴⁸, reducing the relative size of noise and artifact peaks while preserving the sharpness of signal peaks^48-50. A Lagrange multiplier is used to balance producing spectra with the maximum possible entropy, and retaining fidelity with experimental data. A solution is obtained by maximising for Q(f) in the following function:

where f is the frequency set or spectrum being produced by the algorithm, λ is the Lagrange multiplier, S(f) is the entropy function and Cf provides the experimental constraint⁴¹. Here, C(f) produces a χ² statistic by taking f into the time domain and comparing it to the set of data d collected during the NMR experiment:

where IDFT is used for the inverse DFT⁴⁹. A global maximum exists, due to the convex nature of the entropy function^{41; 49}. C₀ is often referred to as aim, and λ spelt out as lambda, when discussing computational implementations of MaxEnt; that convention will be followed here.

As one of the oldest NUS techniques, and perhaps the best studied, thus the peculiarities and potential problems with this method appear to be the best understood⁴⁹. this reason, this project will use MaxEnt as the method for reconstructing spectra from NUS datasets.

(For more on the principles behind and algorithms for MaxEnt reconstruction, the following^{41; 49; 54} are recommended reading.)

4.1.5  NUS Pre-Selection Problem

While many of the techniques used for processing of non-uniformly sampled data differ greatly in terms of their underlying principles or implementations, it has been shown that similar reconstructions can be obtained with each if like NUS sampling schedules are employed⁴⁸. This indicates that the sample size and distribution of sample points is more important than the technique selected. However there is presently no way in which to predict the minimum set of samples required to produce an accurate reconstruction, with any of the NUS-NMR techniques⁵⁵.

4.2  Finding a Minimal M

Non-uniform sampling looks to be a promising way to speed up structure NMR studies for determining the three-dimensional structure of spider toxins. With reductions in data collection time directly related to the number of samples discarded from the full Nyquist grid in the indirect dimensions, the exact temporal gain is dependent on the sampling schedules used. NUS-NMR is already being employed for some NMR experiments on arachnid toxins. However the values of M are deliberately selected to be far larger than required as the limitations of the method are unknown, and the manner in which the method decays is also poorly understood⁷².

In order to harness the full potential of NUS-NMR for high throughput NMR studies of spider toxins, a solution for the pre-selection problem is required. This would allow the smallest possible dataset – resulting in the greatest possible temporal saving – to be collected which still results in a suitable NMR spectrum. In the absence of any reliable model for predicting this sample set, a comprehensive empirical study on the effects of varying the sampling schedule of a NUS-NMR experiment was performed. MaxEnt reconstructions of data from the same NMR experiment would be performed with varying sample sizes and distributions, followed by analysis of all the resulting spectra. NUS-NMR data collection was simulated by taking a full dataset, and discarding data not in a specified sampling schedule. It was hoped a means would be found of either predicting the minimal sample set prior to the NMR experiment, or (by monitoring data as it is collected) determining when sufficient samples have been obtained. Remarkably , no such study has thus far been published despite more than two decades of research and speculation on NUS-NMR.

4.2.1  Previous work: HSQC

A trial study had previously been undertaken out using data from a two-dimensional HSQC experiment⁷². An unpublished 41-residue toxin from an Australian arachnid, currently designated P1, was used as test subject (see Figure 4.2 for sequence). A two-dimensional ¹H-¹⁵N-HSQC experiment, with one indirect dimension containing 400 points (fully sampled) was collected with a Bruker 900MHz ARX spectrometer. sampling schedules with M sample points on the Nyquist grid were created for selected M, 0 < M ≤ 400. For each schedule, mock NUS-NMR experiments were conducted by ‘samplingʼ from the full dataset. NUS data sets were reconstructed using MaxEnt as implemented in the Rowland NMR Toolkit (RNMRTK)⁷³, and the number of HSQC signal peaks retained for each M was determined. The signal peaks from these spectra were then compared to those present in a conventional (DFT) spectrum produced from the full dataset. It was shown that all expected signal peaks (viz, all signal peaks in the full DFT spectrum) were present in reconstructed spectra, except where M was below a threshold value (see Figure 4.2). This value was ~40 sample points, or 10% of the Nyquist grid.

Similar results could be expected for HSQC experiments on other spider toxins, due to the nature of the HSQC experiment. HSQC spectra of proteins result in a predictable number of peaks within a well-defined area. One peak is observed per amino acid residue other than proline, with additional resonances for amide side chains (see Figures 3.4 and 3.5). The co-ordinate of each peak is within a well-known chemical shift range, dependent on amino acid residue type. Substituting P1 for another spider toxin of like size would affect the co-ordinates of signal peaks, but not significantly alter other properties of the spectrum. Thus the results of this test case could be deemed representative for all ¹⁵N-¹H HSQC spectra with this peptide size (at the measured sample concentration) in that only ~40 data points are required to reconstruct a satisfactory spectrum. As a precaution against small variations from this minimum (due either to a physical property of a peptide, or a random factor such as noise) a minimum sample size of M=80 is recommended for HSQC experiments on toxins containing similar number of residues. This cautious doubling of the ‘thresholdʼ would still result in a temporal saving of ca. 2 h, cutting NMR time by 80%.

4.2.2  Current Work: CbCa(CO)NH

While beneficial, the results from the above HSQC analysis cannot be directly applied to any of the other experiments required for resonance assignment (see Figure 4.1). Firstly the complexity, dimensionality and quality of spectra from the other experiments all differ from that of HSQC spectra, such that the temporal requirements are vastly different. However, it was predicted that a similar behaviour would be observed in terms of number of peaks found before and after a threshold M. Also, while data for the above experiment explored many different sample sizes, it did not investigate the distribution of sample points for each particular size; for more complicated spectra, the location as well as number of points may be key to finding a minimum sample set.

The work described in the remainder of this chapter is on data collected with a 3D CbCa(CO)NH NMR experiment. The CbCa(CO)NH spectrum is vital for the sequential assignment of backbone resonances, which in turn is required for the protein structure determination process (see Figure 4.1). This requires the collection of data in two indirect dimensions, one for ¹³C shifts and another for ¹⁵N (with ¹H frequencies in the direct dimension). NUS can be employed in both the ¹³C and¹⁵N dimensions, potentially allowing for a far greater time saving than a two-dimensional experiment such as HSQC (see sections 4.1.2  and 4.1.3  above).

In many NMR experiments, the signal to noise ration (S/N) is higher for some data points than others⁷⁶, which adds more complexity to the situation of which samples to acquire and whether to bias NUS for certain regions. However, this particular experiment employs a particular type of data acquisition mode known as constant time acquisition, where the total length of the decay period in the indirect dimensions is kept constant. Theoretically, this would result in a constant S/N value for all data points, allowing another unknown to be eliminated.

4.2.3  Determining Spectral Quality

4.2.3.1  Automatic Peak-Picking and Verification

The standard methods for evaluating the quality of reconstructed spectra are all based upon peak-picking. Peak-picking involves the identification of signal or real peaks within a spectrum, based upon the line shape, intensity or chemical shift co-ordinates of spectral features. the above experiment, quality was measured in terms of the number of signal peaks identified. The number and co-ordinates of peaks in the spectrum was extracted using an automated peak-picking tool. Then, the number of peaks retained in relation to a reference peak list (extracted using the full dataset) was used as an indication of spectral quality.

A similar approach was used with the CbCa(CO)NH analysis to reveal the quality of reconstructed spectra in terms of how much signal information was retained. The automated peak-picker employed, PEAKY, is one that operates within the software platform used (Rowland NMR Toolkit). The program performs lineshape analysis to reject noise spikes or baseline errors. However this approach may result in rejection of real peaks due to failures in the fitting procedure, where peaks are assumed to have a mixed Lorentz-Gaussian shape. While one would expect signal peaks to theoretically conform to this behaviour⁴¹ this is not always borne through in experiment as a result of deviations from homogeneity in the reference field B₀ due to inadequate shimming or choice of RF pulses, and resolution enhancements⁷⁵.

No automatic peak-picker has thus far been proven to select all signal peaks, without false positive or negatives, and the human eye is still seen by some as the best way of identifying peaks in spectra. However, manually finding peaks in all of the spectra created during the course of this work is not remotely feasible. the use of a reference list spurious peaks can be filtered out, and manual checking can be used to uncover consistent false negatives.

4.2.3.2  Quality factor

While peak-picking provides a useful measure of information content, it does not provide a measure of the inherent quality of a spectrum. A spectrum may contain most or all desired signal peaks, yet still be useless if one cannot distinguish them from noise or artifact peaks. Currently , there is no quantitative definition of spectral quality in the literature. For the purposes of this analysis, a quality factor (Q_f) was defined to fit this role:

where amp is an abbreviation for amplitude. If either the peak or signal count is below 10 for a given spectrum, zero-intensity peaks of the appropriate type and quantity are introduced to make up the count. Q_f is intended to quantify the relative dominance of signal peaks over artifact peaks when comparing two different spectra from similar experiments. As can be seen from the definition Q_f tends towards unity as signals become more distinguishable from artifacts and background noise. If Q_f ~ 0.5, then there exist signal peaks which cannot be distinguished from artifacts.

For the purposes of calculating Q_f, artifacts were deemed to be any peaks identified by the peak-picker but not present in the reference list. The rationale behind this is that any artifact not mistakenly classified as a signal after lineshape analysis, could no longer be considered a spurious peak. remaining artifacts would be identifiable as such, and thus not considered to have an impact on spectral quality.

4.2.4  Monitoring MaxEnt parameters

Although these are good measures of spectral quality, they are not ideal if one wishes to analyse and determine the quality of a spectrum as it is being acquired. Techniques such as MaxEnt are compatible with incremental acquisition⁷⁴, and one could theoretically peak-pick spectra created ‘on the flyʼ, but without an existing reference list the above measures cannot be used. Any alternative measure of quality that is based upon peak counts would instead require an a priori method of verifying peaks. However, the end-state values of MaxEnt parameters used to arrive at a reconstructed spectrum could provide an alternate real-time measure of quality. It was hypothesised that since entropy is a measure of information content, it may be a suitable and independent variable to monitor as a guide for when to terminate the experiment.

It was thought that the investigation of other reconstruction parameters might also reveal information on spectral quality. MaxEnt algorithm operates in one of two different modes — one in which aim is held constant during optimisation, allowing lambda to vary freely, and another where lambda is constrained an aim may vary. It has been proposed that the constant lambda mode results in better continuity in incrementally acquired spectra⁶¹. Performing reconstructions in both of these modes would allow one to monitor the values of lambda (with constant aim) and aim (with constant lambda) determined by the algorithm. As an alternative to manually specifying a value for either parameter, an approach (hereafter referred to as auto mode) has been described where in situ data is used to automatically set a value for lambda through inspection of the experimental data⁶².

It was decided that the values of the entropy (S), aim and lambda parameters would be monitored, to assess their suitability as monitors of spectral quality. It was hoped that a ‘quality critical pointʼ, or other indication that sufficient samples had been collected to produce a quality spectrum, would be revealed.

4.2.5  Experiment

The study was designed in a similar manner to that used in the 2D case for the HSQC experiment, in that a full 60×80 (N=4800) dataset was acquired from which subsets of size M were extracted. The variability in the absolute distribution of M was monitored by generating sampling schedules using different random seeds (4 seeds used). Values of M were taken at intervals of 50 from 4800 to 50 (resulting in 96 values of M). Spectra were then reconstructed from these datasets via MaxEnt, with three sets of initial parameters. The output parameters (aim, lambda and entropy (S)) were monitored for all datasets. In addition, the spectra were peak-picked and verified, and an inherent quality factor value (Q_f) assigned to each spectrum. A schematic of the analysis system can be seen in Figure 4.3, and each step of the process is detailed below.

4.2.5.1  Input Dataset (data)

P1 was again used as a study toxin. A Nyquist-sampled CbCa(CO)NH dataset was collected with a Bruker 900MHz spectrometer. 1200 points were collected in the ¹H (direct) dimension, 60 in the ¹⁵N dimension and 80 in the ¹³C dimension. The maximum number of sample points, N, is 60×80=4800 (points are always collected in direct dimensions).

4.2.5.2  Random seed (RND seed)

The program sched3d (described here⁷⁷) was selected as the means of generating sampling schedules. The program outputs a schedule containing a user-specified number of samples. The sample co-ordinates chosen are selected with the use of a pseudo-random number generator (PRNG), hence, changing the input seed (s) alters the spread of the output sample set. Further, this means that for a particular seed, a sampling schedule for M points would contain all samples specified in a schedule with M-1 points, allowing one to simulate incremental acquisition. Four three-digit seeds were obtained, in order to evaluate the effect of sample distribution. The seeds were themselves provided by an entropy-seeded PRNG (/dev/random from a Linux kernel).

4.2.5.3  Generating sampling schedules (NUS)

Non-uniform sampling schedules were produced using each of the random seed values. The samples were all on points specified by the 60×80 Nyquist grid. were created for each M = 50x, 1 ≤ x ≤ 96 .

4.2.5.4  Setting of MaxEnt parameters (MaxEnt)

The MaxEnt algorithm (see section 4.1.4  of this chapter) requires either aim or lambda to be user-specified. The aim parameter is related to the noise in the experimental data, and lambda determines the weighting between the entropy minimisation constraint and the requirement for the reconstructed spectrum to match the experimentally-collected data. Three sets of reconstructions were performed for each NUS schedule — one where aim was fixed to 100.0, one where lambda was kept constant at 0.5, and a third using auto. This method is quite convenient, removing the requirement to carefully set a value of aim or lambda. The value 100.0 was taken from the noise level in the collected dataset (determined by inspection). 0.5 was used for constant lambda experiments, as this was found to be the average value of lambda achieved during constant aim reconstructions.

4.2.5.5  Spectral Reconstructions (spectra)

Reconstructed spectra were obtained for each random seed, sample size and MaxEnt setting, resulting in 1152 different spectra being collected. The Rowland NMR Toolkit (RNMRTK)⁷³ implementation of the MaxEnt algorithm was used for all reconstructions. While many spectra were examined by eye, it was readily apparent that manual inspection of all spectra and collected information could not be done in a timely and reliable manner. From here a set of automated tests were conducted to examine the quality of the reconstructed spectra (quality), and search for any trends in MaxEnt parameters for the reconstructions (param), as specified above.

4.2.6  Analysis of Spectral Quality

The quality of all spectra generated was assessed using the two aforementioned measures: counts of identified signal peaks, and the quality factor Q_f. The former was seen to be a good measure of how much sought or required information (viz, signal peaks) was reconstructed by MaxEnt from the NUS data. Q_f was seen as an effective way of evaluating the quality inherent in a spectrum, independent of the presence or absence of any expected information. Plots for spectra reconstructed in both constant aim and constant lambda mode can be seen in Figure 4.4 . Similar results were also obtained for auto, though were not included in the figure for redundancy reasons.

4.2.6.1  Information Quality (Peak Counting)

A peak-picker was used to create lists of real peaks in reconstructed spectra. This list was then compared with a standard peaklist, obtained from a conventional (DFT) CaCb(CO)NH spectrum produced with this dataset. Tolerances of ± 0.28 ppm for ¹H, ± 0.55 ppm for ¹⁵N and ± 1.2 ppm for ¹³C chemical shift values were used to determine matches, with each tolerance being equal to five times the step size in its respective dimension. The greater the number standard peaks identified as real peaks in a reconstructed spectrum, the greater the information quality of that spectrum was perceived to be.

In a manner similar to that shown for HSQC experiments, the number of signal peaks reconstructed remained fairly constant for spectra recreated with more than a threshold number of data points. Below this value, the number of signal peaks found tended sharply to zero with decreasing M. This threshold value (hereafter referred to as M₀) appears to be around M=150, varying by 50 depending on the random seed used. For these analyses, the range of available sample sizes was covered in increments of 50 samples; if a smaller step size M_i was used (such as M_i=1) this variance could potentially have been found to be smaller.

Examining the amino acid sequence of P1, one will notice that the maximum number of peaks identified is lower than the 71 one might expect. In fact, spectra with M greater than 400 were selected randomly and manually checker for peaks; there appear to be two weak signal peaks present in several reconstructions, but consistently not identified by the peak-picker. An exception to this occurs for reconstructions using s=123 when M is close to 800, where the peak is identified as such by the peak picker.