- Open Access
In vitro anti-plasmodial activity of Dicoma anomala subsp. gerrardii (Asteraceae): identification of its main active constituent, structure-activity relationship studies and gene expression profiling
© Becker et al; licensee BioMed Central Ltd. 2011
- Received: 29 July 2011
- Accepted: 11 October 2011
- Published: 11 October 2011
Anti-malarial drug resistance threatens to undermine efforts to eliminate this deadly disease. The resulting omnipresent requirement for drugs with novel modes of action prompted a national consortium initiative to discover new anti-plasmodial agents from South African medicinal plants. One of the plants selected for investigation was Dicoma anomala subsp. gerrardii, based on its ethnomedicinal profile.
Standard phytochemical analysis techniques, including solvent-solvent extraction, thin-layer- and column chromatography, were used to isolate the main active constituent of Dicoma anomala subsp. gerrardii. The crystallized pure compound was identified using nuclear magnetic resonance spectroscopy, mass spectrometry and X-ray crystallography. The compound was tested in vitro on Plasmodium falciparum cultures using the parasite lactate dehydrogenase (pLDH) assay and was found to have anti-malarial activity. To determine the functional groups responsible for the activity, a small collection of synthetic analogues was generated - the aim being to vary features proposed as likely to be related to the anti-malarial activity and to quantify the effect of the modifications in vitro using the pLDH assay. The effects of the pure compound on the P. falciparum transcriptome were subsequently investigated by treating ring-stage parasites (alongside untreated controls), followed by oligonucleotide microarray- and data analysis.
The main active constituent was identified as dehydrobrachylaenolide, a eudesmanolide-type sesquiterpene lactone. The compound demonstrated an in vitro IC50 of 1.865 μM against a chloroquine-sensitive strain (D10) of P. falciparum. Synthetic analogues of the compound confirmed an absolute requirement that the α-methylene lactone be present in the eudesmanolide before significant anti-malarial activity was observed. This feature is absent in the artemisinins and suggests a different mode of action. Microarray data analysis identified 572 unique genes that were differentially expressed as a result of the treatment and gene ontology analysis identified various biological processes and molecular functions that were significantly affected. Comparison of the dehydrobrachylaenolide treatment transcriptional dataset with a published artesunate (also a sesquiterpene lactone) dataset revealed little overlap. These results strengthen the notion that the isolated compound and the artemisinins have differentiated modes of action.
The novel mode of action of dehydrobrachylaenolide, detected during these studies, will play an ongoing role in advancing anti-plasmodial drug discovery efforts.
- Sesquiterpene Lactone
- Exocyclic Methylene
- Main Active Constituent
The most critical problem facing malaria treatment today is resistance to anti-plasmodial drugs. The emerging resistance of Plasmodium falciparum to the only affordable anti-malarials, chloroquine and sulphadoxine/pyrimethamine, and now even the last effective class of antimalarials, the artemisinins [1, 2], undermines efforts to eliminate or even manage effectively this deadly disease. Hence, there is continued interest in the discovery of bioactive natural compounds with unique structures that may lead to anti-malarial drugs with novel modes of action [3–5].
South Africa boasts a rich biodiversity with more than 22,600 indigenous plants, representing about 9% of all higher plants on Earth . There is also a long history of the use of plants in African traditional healthcare systems. This natural resource and indigenous knowledge, together with the historical success of the plant-derived anti-malarials (i.e. quinine, artemisinin) and the universal need for new drugs, prompted a national consortium initiative to discover novel anti-plasmodial agents from South African plants .
One of the plants selected for this study was Dicoma anomala, an erect, suberect or prostrate herb bearing aromatic semi-woody tubers at the base of a woody subterranean stem. This grassland species is widely distributed in sub-Saharan Africa, and is morphologically diverse, resulting in the recognition of several infraspecific taxa. Two subspecies occur in South Africa: D. anomala subsp. anomala and D. anomala subsp. gerrardii .
The numerous ethnomedicinal uses of D. anomala, which range from the treatment of coughs and colds, fevers, ulcers, dermatosis, venereal diseases, labour pains, dysentery, intestinal parasites, stomach pains, toothache and internal worms, can be linked to several pharmacological properties: anti-bacterial, anti-helmintic, anti-viral, anti-plasmodial, anti-spasmodic, wound healing, analgesic and anti-inflammatory [8–11]. A previous study reported the anti-bacterial and anti-inflammatory properties of the root extracts of D. anomala . Another study demonstrated in vitro anti-cancer activity of extracts of a related species, Dicoma capensis [12, 13].
Plant collection and extraction
Collection of rootstocks of D. anomala subsp. gerrardii was undertaken in the Brits region of the North West Province of South Africa during February 2008. A voucher (BP 01455) was deposited at the National Herbarium of South Africa (Pretoria), and the identity of this taxon confirmed by Dr E. Retief.
A total of 5.6 kg of fresh rootstock was oven dried (30°C) and ground with a hammer mill to yield 3.7 kg of finely processed plant material. Of this, 3.4 kg of the processed material was consecutively extracted with 3 volumes of EtOAc (15 L) at room temperature over 3 days. The filtered extract was concentrated under reduced pressure on a rotary evaporator at 60°C and further dried in a vacuum desiccator for 96 h to remove all traces of solvent. The extraction yielded 48 g of brown gum (1.3% w/w of dry plant material).
Isolation and identification of dehydrobrachylaenolide
Solvent partitioning of the crude extract was used to divide the extract into three fractions with different polarities. The extract (1 g) was dissolved in 100 mL of aqueous methanol (MeOH/H2O 9:1, v/v) and extracted with hexane (3 × 100 mL). MeOH was removed from the aqueous methanolic layer under vacuum on a rotary evaporator; the remaining solution was diluted to 100 mL with H2O and extracted with dichloromethane (DCM) (3 × 100 mL). The DCM layers were combined and dried over anhydrous Na2SO4, filtered and concentrated under vacuum on a rotary evaporator to give a DCM-soluble fraction. This process was scaled up for the remaining crude extract.
Large-scale purification of the DCM-soluble fraction was performed by liquid chromatography in batches of 5 - 10 g of extract on 400 - 500 g of silica gel 60 (0.063 - 0.2 mm) under reduced pressure, using EtOAc/hexane/DCM/MeOH and acetone/DCM/MeOH gradients. Pooled fractions were combined on the basis of similarity of chemical profile as determined by thin-layer chromatography (TLC). Crude fractions 1A-1L were concentrated under vacuum on the rotary evaporator. Fractions 1D-1H were combined (3.5 g) on the basis of similarity of their TLC profile and subjected to further column chromatography using a 90 cm column packed with silica gel and eluted with an EtOAc/hexane/DCM/MeOH isocratic solvent mixture (9:45:45:1, v/v) to give fractions 2A-2N. The fractions were combined on the basis of similarity of the chemical composition determined by TLC analysis. Further fractionation of 2F (0.4 g) was achieved by means of flash chromatography, using a 40 cm flash column, packed with flash silica gel (silica gel 60) and eluted with a hexane/DCM/EtOAc/MeOH isocratic solvent mixture (45:45:9:1, v/v). This yielded compound 1, which was recrystallized from 2-propanol to yield 400 mg (0.013% w/w of dry plant material) of white orthorhombic crystals.
Compound 1 was identified using standard one- and two-dimensional nuclear magnetic resonance spectroscopic (NMR) experiments; electrospray-ionization mass spectrometry (ESI-MS); X-ray crystallography and by direct comparison with published spectral data [19–21].
NMR analysis was carried out on a Varian 400 MHz Unity spectrometer. The mass spectral data were obtained from a hyphenated HPLC-UV/MS instrument (HPLC Waters Alliance 2690 system, equipped with a Waters 996 photodiode array detector and a triple quadrupole Quattro LC Micro mass spectrometer). The mass spectrometer was set to operate in both the ESI- and ESI+ modes (49 - 478 amu) with a gain of 10; the cone voltage was varied between 20 and 70 eV; the desolvation temperature was 450°C; and the source block temperature was set at 120°C. Crystallography experiments were conducted on an Oxford Diffraction Excalibur-2 CCD area detector diffractometer, using Mo-Kα X-radiation and a graphite-crystal monochromator. Optical rotations were measured in chloroform at room temperature on a Perkin-Elmer 241 polarimeter at 589 nm (Na D-line) using a 1 dm cell.
Asexual P. falciparum chloroquine-sensitive 3D7 and D10 cultures, as well as chloroquine-resistant K1 strain cultures, were maintained and synchronized according to established methods [22, 23] in an atmosphere consisting of 5% oxygen, 5% carbon dioxide and 90% nitrogen. The parasites were maintained at a 5% haematocrit in RPMI 1640 medium supplemented with 25 mM HEPES, 22 mM glucose, 0.0088% hypoxanthine, 40 ug/mL gentamycin (all Sigma) and 0.5% Albumax (Invitrogen).
In vitro anti-malarial assay
The anti-plasmodial activities of the extracts and pure compounds were determined against the chloroquine-sensitive D10 and the chloroquine-resistant K1 strains via the parasite lactate dehydrogenase (pLDH) assay . All test substances were stored at -20°C prior to testing. Stock solutions of test substances were prepared in 10% MeOH or 10% DMSO (in water), depending on the solubility, and diluted in Millipore water to prepare 2 mg/mL solutions, which were stored at -20°C. Chloroquine diphosphate (Sigma) was used as a reference drug in all experiments. The test substances were evaluated as ten serial two-fold dilutions (0.2 - 100 μg/mL final concentration) in medium (two replicates per concentration point) in duplicate wells. The highest concentration of organic solvent that the parasites were exposed to was 0.5%, which was shown to have no measurable effect on parasite viability . Test solutions were mixed with suspensions of infected human red blood cells to achieve a final haematocrit of 1% and parasitaemia of 2% and incubated for 48 h in microtitre plates (250 uL final volume). Incubation conditions were as described above for the routine maintenance of the P. falciparum cultures. The IC50 values, serving as a measure for anti-plasmodial activities, were calculated by non-linear regression dose-response analysis using GraphPad Prism v.4.0 software.
In vitro cytotoxicity assay
Compounds were tested for in vitro cytotoxicity against a Chinese hamster ovary (CHO) cell line using the MTT [3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide] assay . The CHO cells were cultured in DMEM: Hams F-12 medium (1:1) supplemented with 10% heat-inactivated foetal calf serum (FCS) and gentamycin (0.04 μg/mL) (Highveld Biological, RSA). Samples were dissolved in 10% MeOH. Stock solutions (2 mg/mL) were prepared and were stored at -20°C until use. The samples were added to CHO cells as five ten-fold serial dilutions ranging from 100 - 0.01 μg/mL. A serial dilution of emetine (100 - 0.001 μg/mL) was used as a positive control. Cells were seeded in 96-well plates at a concentration of 105/mL (100 μL per well) and incubated at 37°C for 24 h in a humidified 5% CO2-air atmosphere. The medium was subsequently aspirated from the wells and replaced with 200 μL of the test compound dilutions. The microplates were incubated at 37°C for 48 h, after which 25 μL of sterile MTT (5 mg/mL in PBS) was added to each well and incubation was continued for 4 h at 37°C. Formazan crystals formed by viable cells were dissolved in DMSO and quantitated by measuring absorbance at 540 nm in a microtitre plate reader (Cambridge Technologies). Cell viabilities were calculated relative to reference wells containing no test compounds (positive cell controls) and no cells (background controls), plotted against log[test sample] and IC50 values derived by non-linear regression analysis using GraphPad Prism v.4.0 software.
Generation of synthetic analogues of compound 1
Information on the synthesis of compound 1 analogues for structure-activity relationship studies is provided [see Additional file 1].
Parasite drug treatment and RNA extraction
P. falciparum 3D7 cultures were treated with 12.5 μM of compound 1, corresponding to an inhibitory concentration of IC99 as determined from dose-response curves. A morphological comparison between compound 1 treated versus untreated parasites was performed to assess the effect of treatment and to establish sampling times, by examining the stage-specific progression of parasites across the intra-erythrocytic development cycle. The solvent (DMSO) or compound 1 was added in the window shortly after red blood cell (RBC) invasion and parasite development was monitored 6 hourly over a 48 h period using conventional Giemsa-stained smears. Fresh cultures were scaled up to 50 ml (5% hematocrit, 10% parasitemia), synchronized twice and treated with compound 1 in the window around invasion. Fifteen milliliters of culture was harvested at each of the stages used for transcriptional analyses (2, 6 and 12 hpt). Similar volumes were harvested from untreated P. falciparum 3D7 control cultures at the same time points. Parallel drug treatments were conducted, serving as biological replicates. RNA was extracted from the frozen erythrocyte pellets as described .
Universal Reference RNA (URR) pool, cDNA synthesis and hybridization
The URR pool was constructed from mixed-stage cultures as described . cDNA synthesis and hybridizations was as described in , with the exception that 40 pmoles of each dye was hybridized to each array, utilising Cy3 (sample) and Cy5 (reference) dyes from GE Healthcare (#RPN5661), specifically optimized for nucleic acid labelling.
Microarray data analysis and real-time quantitative PCR (RT-qPCR)
Generation of GenePix results (gpr) files, LIMMA and MARRAY analysis in the R computing environment, calculation of Pearson correlation coefficients and determination of differentially expressed genes were performed as detailed in . RT-qPCR was performed on an Applied Biosystems 7500 Fast cycler (Carlsbad, California, USA) as described . qPCR primers were designed using Primer3 Plus  and sequences are available on request. PCR efficiencies for each sample were calculated using LinRegPCR, software described in . Fluorescence data per cycle of each sample is exported from the Applied Biosystems 7500 Fast cycler, from which the efficiencies of individual samples were calculated. These efficiencies were used to calculate relative expression in a mathematical model described by Pfaffl . Gene ontology analyses were performed using the Micro Array Data Interface for Biological Annotation (MADIBA) software .
Isolation and identification of compound 1
In the search for novel anti-malarials from South African plants, an EtOAc extract of D. anomala subsp. gerrardii was screened against the chloroquine-sensitive D10 strain of P. falciparum using the pLDH assay. The extract exhibited an IC50 of 1.4 μg/mL .
A phytochemical investigation of this extract resulted in the isolation of a major compound, compound 1. NMR analysis revealed the presence of an α-methylene-γ-lactone moiety and two fused cyclohexane rings forming the skeleton of the eudesmanolide-type sesquiterpene lactone. The A ring was found to possess a 1,2-endocyclic double bond, a carbonyl at C-3 and an additional exocyclic methylene at C-4. Compound 1 was subsequently identified as 3-oxoeudesma-1,4(15),11(13)-triene-12,6α-lide, which was identical to the structure of dehydrobrachylaenolide (Figure 1, see Additional file 2), previously isolated from Brachylaena transvaalensis , Hieracium intybaceum  and various Dicoma species , all of the Asteraceae family. A successful chemical synthesis, which confirmed the structure and absolute configuration of dehydrobrachylaenolide, has been reported .
The relative configuration of the asymmetric centres at C-5, C-6 and C-7 was deduced to be trans based on the size of the observed 1H NMR coupling constants and NOE correlations. This was in good agreement with previously reported configuration data for dehydrobrachylaenolide [16, 32], and was subsequently confirmed by X ray crystallography and optical rotation studies .
In vitro anti-plasmodial activity of dehydrobrachylaenolide and its synthetic analogues
In vitro activity of dehydrobrachylaenolide against P. falciparum.
n = 8
n = 4
n = 2
The compound had an IC50 of 1.865 μM (0.455 μg/mL) against the chloroquine-sensitive D10 strain and 4.095 μM (1.0 μg/mL) against the chloroquine-resistant K1 strain when tested in vitro [see Additional file 3]. Dehydrobrachylaenolide can therefore be considered a hit, because it complies with the basic criteria for anti-parasitic drug discovery  with an in vitro IC50 against whole protozoa of ≤ 1 μg/ml and a selectivity of close to ten-fold more against the chloroquine-sensitive parasites than against the CHO cells (see therapeutic index, Table 1).
Analogues generated for determination of active sub-structures.
D10 strain IC50
n = 2
n = 2
CHO IC50 (μM)
n = 2
Transcriptome analysis of dehydrobrachylaenolide inhibition
Culturing, drug treatment and RNA extraction
Gene expression profiling of P. falciparum treated with dehydrobrachylaenolide
A microarray reference design experimental strategy, similar to that described in  was employed to ascertain global gene expression in parasites perturbed with dehydrobrachylaenolide. Labelled cDNA was hybridized to Operon oligonucleotide microarrays, interrogating 4585 unique genes. All data has been deposited in the NCBI's Gene Expression Omnibus (GEO) database, GEO number GSE29874. Pearson correlation coefficient values for both technical and biological variation were calculated in Microsoft Excel. Technical variation across all arrays was calculated to be 0.89 ± 0.13; whereas biological variation across all slides was calculated as 0.78 ± 0.16. Datasets were collated into untreated (UT2, UT6 and UT12) and treated (T2, T6 and T12) samples at each time point before calculation of Pearson correlation coefficients between drug-treated and control samples. Correlation coefficients suggested that parasites remained in similar states across the different time points after dehydrobrachylaenolide treatment, as can be gauged from coefficients between T2 and T6 (0.88) and T6 and T12 (0.91). The correlation between T2 and T12 was calculated as 0.82, indicating a growth delay close to or around 6 hpt. This notion is strengthened by the fact that Pearson correlation between UT6 and T12 was 0.70, while the parallel comparison (UT12 and T12) was calculated at 0.57. For differential gene expression analyses, T2 parasites were contrasted to UT2, and T12 and T6 parasites contrasted to UT6. A full table of correlation values between all collated samples is provided [see Additional file 4]. A total of 572 unique genes were differentially regulated (cumulatively across all time points) at least two-fold and with a false discovery rate (FDR) cut off of 5% following parasite perturbation with dehydrobrachylaenolide (all genes listed in Additional file 5). The number of differentially regulated genes represents 12.5% of the genes present on the array. Of these, 297 were upregulated (52% of the total), and 275 downregulated (48% of the total). The number of differentially expressed transcripts increased with time following drug addition, as expected from Pearson correlations, which indicates a drug effect on parasite transcription at approximately 6 hpt. Affected transcripts for T2, T6 and T12 were 134, 291 and 378, respectively. Several transcripts were differentially expressed at more than one time point (e.g. T2 and T6 or T6 and T12). Due to the cytocidal nature of sesquiterpene lactones [39, 40], the high treatment dose (IC99) and the rapid time of action of dehydrobrachylaenolide, the transcriptional changes observed at the last time point (T = 12) were regarded as less informative concerning mode of action and were not analysed further. In a related transcriptome investigation of P. falciparum parasites treated with lethal doses of artesunate (a derivative of the sesquiterpene lactone artemisinin), time points were harvested after 90 minutes and 3 hours resulting in 398 differentially affected genes .
Differentially expressed transcripts were validated by analysing their expression by real-time quantitative PCR (RT-qPCR). The expression of three transcripts (MAL7P1.93 (mitochondrial ribosomal protein S8, putative), MAL7P1.175 (hypothetical protein) and PFL0055 c (protein with DNAJ domain (resa-like), putative)) was evaluated by qPCR, utilising PFL0625 c (eukaryotic translational initiation factor 3) as an endogenous control, as described previously .
Comparison of expression values (log2)* as determined by transcriptome analysis and RT-qPCR.
MADIBA analyses for metabolic pathways enriched following drug perturbation indicated that several metabolic pathways were involved in the parasite's response to perturbation with dehydrobrachylaenolide. At T2, transcripts involved in 20 metabolic pathways were affected; at T6, this increased to 26. The only metabolic pathway with an appreciable p-value (in Fisher's contingency test in MADIBA) was "Biosynthesis of type II polyketide backbone", affected at T6 (p = 0.190). However, there is scant information regarding this pathway in the parasite. Higher p-values are expected from these analyses, since all affected transcripts at a given time point are submitted for analyses, without clustering, as described .
Gene Ontology terms enriched following addition of dehydrobrachylaenolide at 2 and 6 hours post-treatment (at p < 0.05).
Time post treatment
(false discovery rate, p < 0.05)
pepsin A activity
The EtOAc extract of D. anomala subsp. gerrardii showed sufficient activity against P. falciparum to warrant further investigation. Compound 1, dehydrobrachylaenolide, isolated as a major component of this extract, was subsequently screened for its anti-plasmodial activity and found to exhibit some activity against a chloroquine-sensitive D10 strain and a chloroquine-resistant K1 strain of P. falciparum. This is the first report of anti-malarial activity associated with this compound.
Dehydrobrachylaenolide was originally isolated from the roots of Brachylaena transvaalensis, from which its name was derived . Several biological activities were reported for this natural product. These included inhibitory activity toward induction of intracellular adhesion molecule-1 (ICAM-1)  and anti-bacterial properties . It was also shown to have significant anti-cancer activity in the NCI's 60-cell line panel, with a selectivity trend towards the leukaemia sub-panel .
The activity of dehydrobrachylaenolide against the chloroquine-sensitive strain (IC50 = 1865 nM) is within an order of magnitude of that of quinine (IC50 = 194 nM) . Furthermore, against the chloroquine-sensitive strain, the compound has a therapeutic index of 9.2, which is close to the acceptable value of 10 for potential development .
To establish the chemical moieties responsible for the inhibition of P. falciparum inhibition by dehydrobrachylaenolide, synthetic analogues of dehydrobrachylaenolide were tested against P. falciparum utilising the pLDH assay. From these studies, it was concluded that the anti-malarial activity was mainly attributable to the conjugate acceptor properties of the methylene lactone and the methylene ketone (in the A-ring, Figure 1). The natural product possessed two readily accessible acceptor groups of this type and the absence or inaccessibility of the methylene ketone was responsible for a ten-fold enhancement in activity without concomitant increase in toxicity (or, possibly, a two-fold reduction in toxicity), suggesting that toxic liabilities were largely associated with the methylene lactone. Further examinations relating to the role of A-ring geometry and functionalization could be warranted.
Previously, the authors successfully applied a functional genomics approach to study the effects on the P. falciparum transcriptome of treatment with cytostatic drugs (i.e. DFMO/MDL73811 co-inhibition  and cyclohexylamine ). In the study presented here, gene expression profiling was performed on a parasitic cytocidal compound, dehydrobrachylaenolide, subsequent to its isolation, identification, demonstrated anti-malarial activity and structure-activity relationship (SAR) studies. Gene expression profiling of another sesquiterpene lactone, artesunate , reported 398 genes that were differentially expressed compared to untreated P. falciparum parasites. Further to the SAR analyses, comparison of the artesunate dataset with the dehydrobrachylaenolide dataset of 340 genes (unique genes differentially expressed at T2 and T6), resulted in only 7.65% (26 genes of the 340) overlap. This marked difference underscores their probable different modes of action, particularly since, despite being a sesquiterpene lactone, deydrobrachylaenolide does not contain the endoperoxide bridge that is characteristic of the artemisinins and key to their biological activity . In contrast, the α-methylene-γ-lactone moiety, as well as the conformation of the A-ring (Figure 1) of dehydrobrachylaenolide, which is absent in the artemisinins, is significant for various biological activities of the eudesmane sesquiterpene lactones [11, 46]. The structure-activity relationship studies performed for dehydrobrachylaenolide confirmed this.
In this investigation the active constituent of Dicoma anomala subsp. gerrardii was isolated and identified as dehydrobrachylaenolide, an eudesmanolide-type sesquiterpene lactone. The compound demonstrated in vitro anti-malarial activity against a chloroquine-sensitive strain of P. falciparum. Structure-activity relationship studies indicated that exocyclic methylene residues on both the lactone and A-ring appear to be responsible for the observed anti-malarial activity . This methylene lactone moiety is absent in the artemisinin anti-malarials, indicating a differentiated mode of action to the artemisinins. Gene expression profiling via microarray strengthened the notion that dehydrobrachylaenolide displays a different mode of action compared to artesunate .
In light of the development of resistance against standard anti-malarials (now also including the artemisinins [1, 2]) and the quest for new drugs with novel modes of action, this finding is significant and underscores the potential of dehydrobrachylaenolide as a potential drug lead. Some recent examples of so-called pro-drugs of sesquiterpene lactones, namely ambrosin, arglabin, parthenin and parthenolide, demonstrate the value of sesquiterpene lactones as lead compounds for the development of pharmaceuticals [47–52].
It can be concluded that dehydrobrachylaenolide could play a valuable role as a drug lead. Further mechanistic studies and an in vivo dose response toxicity study would be necessary to gain in-depth knowledge of the structural requirements for selectivity, with respect to the desired biological activity, and systemic toxicity.
Acknowledgements and Funding
The project was funded by the South African Department of Science and Technology, the NRF Innovation fund (NDDP) (Grant Number TM1002FP) and CSIR Parliamentary Grant. Synthetic and bioactivity evaluation work was abstracted from a thesis presented in the fulfilment of the requirements for an MSc by MM van der Merwe. The authors wish to thank Heinrich Hoppe for critical revision of the manuscript.
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