Publications
2015
P. Kramberger, U. Lidija, A. Štrancar
Human Vaccines & Immunotherapeutics, 11:4 (2015) 1010-1021
Downstream processing of nanoplexes (viruses, virus-like particles, bacteriophages) is characterized by complexity of the starting material, number of purification methods to choose from, regulations that are setting the frame for the final product and analytical methods for upstream and downstream monitoring. This review gives an overview on the nanoplex downstream challenges and chromatography based analytical methods for efficient monitoring of the nanoplex production.
A. G. Lopes
FBP-461, Food and Bioproducts Processing (2014)
As the biopharmaceutical industry matures, the trend towards increased flexibility and productivity, faster time tomarket and greater profitability are driving the replacement of traditional stainless steel equipment by single-use technology (SUT). The use of SUT in the biopharmaceutical industry can significantly impact the manufacturing process efficiency by reducing capital costs, improving plant flexibility, reducing start-up times and costs, and elim-inating both non-value added process steps and the risk of cross-contamination. In addition it significantly reduces process liquid waste, labour costs and on-site quality and validation requirements. This paper reviews the current status of the technology and the impact of SUT in the biopharmaceutical industry, with the aim of identifying the challenges and limitations that still need to be addressed for further adoption of these technologies. Even tough SUT has a multitude of systems available, its components and assemblies have little standardisation as well as alack of harmonised tests and procedures among suppliers, with an array of guidelines from a variety of sourcesand no critical limits have been established. In addition, the use of SUT has new validation requirements such as leachables and extractables, suppliers’ qualification and SUT lot-to-lot variability. The lack of expertise in these areas and the new training requirements when using SUT also need to be addressed. To date the majority of the avail-able literature regarding SUT is found in trade journals where typically suppliers are the main contributors. There is still a lack of engagement of the academic community, which contributes to very limited scientific proof from independent peer-reviewed research to support performance of SUT. This is particularly the case during operation and integrity testing of SUT, during for example on-site testing, transport and disposal. Another area where no work has been undertaken concerns conceptual approaches for facility clean-room requirement and appropriate layout design using SUT. Investment in novel technologies, research, standardisation and training is paramount for further development and implementation of SUTs across all sectors of the biopharmaceutical industry.
Urh Černigoj, Urška Martinuč, Sara Cardoso, Rok Sekirnik, Nika Lendero Krajnc, Aleš Štrancar
Sample displacement chromatography (SDC) is a chromatographic technique that utilises different rela-tive binding affinities of components in a sample mixture and has been widely studied in the context ofpeptide and protein purification. Here, we report a use of SDC to separate plasmid DNA (pDNA) isoformsunder overloading conditions, where supercoiled (sc) isoform acts as a displacer of open circular (oc) orlinear isoform. Since displacement is more efficient when mass transfer between stationary and mobilechromatographic phases is not limited by diffusion, we investigated convective interaction media (CIM)monoliths as stationary phases for pDNA isoform separation. CIM monoliths with different hydrophobic-ities and thus different binding affinities for pDNA (CIM C4 HLD, CIM-histamine and CIM-pyridine) weretested under hydrophobic interaction chromatography (HIC) conditions. SD efficiency for pDNA isoformseparation was shown to be dependent on column selectivity for individual isoform, column efficiencyand on ammonium sulfate (AS) concentration in loading buffer (binding strength). SD and negative modeelution often operate in parallel, therefore negative mode elution additionally influences the efficiencyof the overall purification process. Optimisation of chromatographic conditions achieved 98% sc pDNAhomogeneity and a dynamic binding capacity of over 1 mg/mL at a relatively low concentration of AS.SDC was successfully implemented for the enrichment of sc pDNA for plasmid vectors of different sizes,and for separation of linear and and sc isoforms, independently of oc:sc isoform ratio, and flow-rate used.This study therefore identifies SDC as a promising new approach to large-scale pDNA purification, whichis compatible with continuous, multicolumn chromatography systems, and could therefore be used toincrease productivity of pDNA production in the future.
Attachments
2013
A. A. Shukla, U. Gottschalk
Trends in Biotechnology (2012) 1-8
The manufacture of protein biopharmaceuticals is conducted under current good manufacturing practice (cGMP) and involves multiple unit operations for upstream production and downstream purification. Until recently, production facilities relied on the use of relatively inflexible, hard-piped equipment including large stainless steel bioreactors and tanks to hold product intermediates and buffers. However, there is an increasing trend towards the adoption of single-use technologies across the manufacturing process. Technical advances have now made an end-to-end single-use manufacturing facility possible, but several aspects of single-use technology require further improvement and are continually evolving. This article provides a perspective on the current state-of-the-art in single-use technologies and highlights trends that will improve performance and increase the market penetration of disposable manufacturing in the future.
M. Li, Y. X. Qiu
Vaccine 31 (2013) 1264-1267
An effective downstream bio-processing of vaccine products requires complete chemical knowledge of the contaminants that may arise from a given vector expression system. Whether the vaccine is made from the traditional egg-based or the new cell-cultured process, it is the expression system that determines the types of impurities that need to be identified and removed from the vaccine product.
There are mechanical and chemical factors that can either reduce the yield or render a vaccine product to be irreversibly inactive. The choice of equipment and solvents is therefore important in minimizing product loss, and for maintaining an efficient and optimized manufacturing process.
The frequent out-of-specification, irreproducible data and inefficiency in the manufacturing of biologics were the basis for FDA to propose the “cGMP for the 21st Century” initiative in the year of 2000. Effective 2004, the concept of quality by design (QbD) has been imposed in the manufacturing of biologics. To facilitate the implementation of QbD FDA has encouraged the use of process analytical technology (PAT). Further, FDA believes that an optimized manufacturing scheme requires one to identify and to control the variables that can negatively affect the yield and quality of the desired product, and PAT can reveal wrongful data and alert the operator for immediate correction during processing.
E. Mota, A. Sousa, U. Černigoj, J. A. Queiroz, C. T. Tomaz, F. Sousa
Journal of Chromatography A (2013)
The demand for high-purity supercoiled plasmid DNA to be applied as a vector for new therapeutic strategies, such as gene therapy or DNA vaccination has increased in the last years. Thus, it is necessary to implement an analytical technique suitable to control the quality of the supercoiled plasmid as a pharmaceutical product during the manufacturing process. The present study describes a new methodology to quantify and monitor the purity of supercoiled plasmid DNA by using a monolithic column based on anion-exchange chromatography. This analytical method with UV detection allows the separation of the plasmid isoforms by combining a NaCl stepwise gradient. The specificity, linearity, accuracy, reproducibility and repeatability of the method have been evaluated, and the lower quantification and detection limits were also established. The validation was performed according to the guidelines, being demonstrated that the method is precise and accurate for a supercoiled plasmid concentration up to 200 μg/mL. The main advantage achieved by using this monolithic column is the possibility to quantify the supercoiled plasmid in a sample containing other plasmid topologies, in a 4 min experiment. This column also permits the assessment of the supercoiled plasmid DNA present in more complex samples, allowing to control its quality throughout the bioprocess. Therefore, these findings strengthen the possibility of using this monolithic column associated with a powerful analytical method to control the process development of supercoiled plasmid DNA production and purification for therapeutic applications.
S. Haberl, M. Jarc, A. Štrancar, M. Peterka, D. Hodžić, D. Miklavčič
J Membrane Biol, DOI 10.1007/s00232-013-9580-5
The use of plasmid DNA (pDNA) as a pharmaceutical tool has increased since it represents a safer vector for gene transfer compared to viral vectors. Different pDNA extraction methods have been described; among them is alkaline lysis, currently the most commonly used. Although alkaline lysis represents an established method for isolation of pDNA, some drawbacks are recognized, such as entrapment of pDNA in cell debris, leading to lower pDNA recovery; the time-consuming process; and increase of the volume due to the buffers used, all leading to increased cost of production. We compared the concentration of extracted pDNA when two methods for extracting pDNA from Escherichia coli were used: alkaline lysis and a method based on membrane electroporation, electroextraction. At the same time, we also studied the effect of different pulse protocols on bacterial inactivation. The concentration of pDNA was assayed with anion exchange chromatography. When alkaline lysis was used, two incubations of lysis time (5 and 10 min) were compared in terms of the amount of isolated pDNA. We did not observe any difference in pDNA concentration regardless of incubation time used. In electroextraction, different pulse protocols were used in order to exceed the pDNA concentration obtained by alkaline lysis. We show that electroextraction gives a higher concentration of extracted pDNA than alkaline lysis, suggesting the use of electroporation as a potentially superior method for extracting pDNA from E. coli. In addition, electroextraction represents a quicker alternative to alkaline lysis for extracting pDNA.
B. Gabor, U. Černigoj, M. Barut, A. Štrancar
Journal of Chromatography A, 1311 (2013) 106-114
HPLC based analytical assay is a powerful technique that can be used to efficiently monitor plasmid DNA (pDNA) purity and quantity throughout the entire purification process. Anion exchange monolithic and non-porous particle based stationary phases were used to study the recovery of the different pDNA isoforms from the analytical column. Three differently sized pDNA molecules of 3.0 kbp, 5.2 kbp and 14.0 kbp were used. Plasmid DNA was injected onto columns under the binding conditions and the separation of the isoforms took place by increasing the ionic strength of the elution buffer. While there was no substantial decrease of the recovered supercoiled and linear isoforms of the pDNA with the increase of the plasmid size and with the increase of the flow rate (recoveries in all cases larger than 75%), a pronounced decrease of the oc isoform recovery was observed. The entrapment of the oc pDNA isoform occurred under non-binding conditions as well. The partial oc isoform elution from the column could be achieved by decreasing the flow rate of the elution mobile phase. The results suggested a reversible entrapment of the oc isoform in the restrictions within the pores of the monolithic material as well as within the intra-particle space of the non-porous particles. This phenomenon was observed on both types of the stationary phase morphologies and could only be connected to the size of a void space through which the pDNA needs to migrate. A prediction of reversible pDNA entrapment was successfully estimated with the calculation of Peclet numbers, Pe, which defines the ratio between a convective and diffusive mass transport.
M. Limonta, N. Lendero Krajnc, U. Vidic, L. Zumalacárregui
Biochemical Engineering Journal 80 (2013) 14-18
The pIDKE2 plasmid is the main component of the CIGB's candidate vaccine against Hepatitis C virus (HVC), which is being used in HCV chronically-infected individuals during clinical trials phase 1 and 2. The designed downstream process of pIDKE2 plasmid produces up to 179 g/year. In order to conduct further improvements, modelling of the downstream process was performed. A methodology based on process analysis tools, such as experimental design and modelling was established to identify factors with the highest influence on production cost and the amount of annual plasmid. Taking into account that the pIDKE2 downstream process designed is in its initial stages of development, CIM technology was evaluated as a new manufacturing process on lab scale. Purity and recovery of CIM technology was better than porous particle matrix, thus SuperPro Designer was used in order to simulate the purification process. Cost efficiency optimization of the pIDKE2 downstream process was done with the simulation model.
E. Maksimova, E. Vlakh, E. Sinitsyna, T. Tennikova
J. Sep. Sci. 2013, 36, 3741–3749
Ultrashort monolithic columns (disks) were thoroughly studied as efficient stationary phases for precipitation–dissolution chromatography of synthetic polymers. Gradient elution mode was applied in all chromatographic runs. The mixtures of different flexible chain homopolymers, such as polystyrenes, poly(methyl methacrylates), and poly(tert-butylmethacrylates) were separated according to their molecular weights on both commercial poly(styrene-co divinylbenzene).
disks (12 id × 3 mm and 5 × 5 mm) and lab-made monolithic columns (4.6 id × 50 mm) filled with supports of different hydrophobicity. The experimental conditions were optimized to reach fast and highly efficient separation. It was observed that, similar to the separation of monoliths of other classes of (macro)molecules (proteins, DNA, oligonucleotides), the length of column did not affect the peak resolution.
A comparison of the retention properties of the poly(styrene-co-divinylbenzene) diskshaped monoliths with those based on poly(lauryl methacrylate-co-ethylene dimethacrylate), poly(butyl methacrylate-co-ethylene dimethacrylate), and poly(glycidyl methacrylate-co-ethylene dimethacrylate) supports demonstrated the obvious effect of surface chemistry on the resolution factor. Additionally, the results of the discussed chromatographic mode on the fast determination of the molecular weights of homopolymers used in this study were compared to those established by SEC on columns packed with sorbent beads of a similar nature to the monoliths.
Roy N D‘Souza, Ana M Azevedo, M Raquel Aires-Barros, Nika Lendero Krajnc, Petra Kramberger, Maria Laura Carbajal, Mariano Grasselli, Roland Meyer & Marcelo Fernández-Lahore
Vol. 1, No. 5, Pharmaceutical Bioprocessing (2013)
Downstream processing is currently the major bottleneck for bioproduct generation. In contrast to the advances in fermentation processes, the tools used for downstream processes have struggled to keep pace in the last 20 years. Purification bottlenecks are quite serious, as these processes can account for up to 80% of the total production cost. Coupled with the emergence of new classes of bioproducts, for example, virus-like particles or plasmidic DNA, this has created a great need for superior alternatives. In this review, improved downstream technologies, including aqueous two-phase systems, expanded bed adsorption chromatography, convective flow systems, and fibre-based adsorbent systems, have been discussed. These adaptive methods are more suited to the burgeoning downstream processing needs of the future, enabling the cost-efficient production of new classes biomaterials with a high degree of purity, and thereby hold the promise to become indispensable tools in the pharmaceutical and food industries.
A. Ghanem, R. Healey, F. G. Adly
Analytica Chimica Acta 760 (2013) 1-15
Abstract
Plasmid DNA (pDNA)-based vaccines offer more rapid avenues for development and production if compared to those of conventional virus-based vaccines. They do not rely on time- or labour-intensive cell culture processes and allow greater flexibility in shipping and storage. Stimulating antibodies and cellmediated components of the immune system are considered as some of the major advantages associated with the use of pDNA vaccines. This review summarizes the current trends in the purification of pDNA vaccines for practical and analytical applications. Special attention is paid to chromatographic techniques aimed at reducing the steps of final purification, post primary isolation and intermediate recovery, in order to reduce the number of steps necessary to reach a purified end product from the crude plasmid.
A. Romanovskaya, L. P. Sarina, D. H. Bamford, M. M. Poranen
Journal of Chromatography A (2013)
Recent advances in the field of RNA interference and new cost-effective approaches for large-scale double-stranded RNA (dsRNA) synthesis have fuelled the demand for robust high-performance purification techniques suitable for dsRNA molecules of various lengths. To address this issue, we developed an improved dsRNA purification method based on anion exchange chromatography utilizing convective interaction media (CIM) monolithic columns. To evaluate column performance we synthesized a selection of dsRNA molecules (58–1810 bp) in a one-step enzymatic reaction involving bacteriophage T7 DNA-dependent RNA polymerase and phi6 RNA-dependent RNA polymerase. In addition, small interfering RNAs (siRNAs) of 25–27 bp were generated by Dicer digestion of the genomic dsRNA of bacteriophage phi6. We demonstrated that linearly scalable CIM monolithic quaternary amine (QA) columns can be used as a fast and superior alternative to standard purification methods (e.g. LiCl precipitation) to obtain highly pure dsRNA preparations. The impurities following Dicer treatment were quickly and efficiently removed with the QA CIM monolithic column, yielding siRNA molecules of high purity suitable for potential therapeutic applications. Moreover, baseline separation of dsRNA molecules up to 1 kb in non-denaturing conditions was achieved.
2012
J. Lee, H. T. Gan, S. M. Abdul Latiff , C. Chuah, W. Y. Lee, Y.-S. Yang, B. Loo, S. K. Ng, P. Gagnon
Journal of Chromatography A, 1270 (2012) 162-170
We introduce a chromatography method for purification of large proteins and viruses that works by capturing them at a non-reactive hydrophilic surface by their mutual steric exclusion of polyethylene glycol (PEG). No direct chemical interaction between the surface and the target species is required. We refer to the technique as steric exclusion chromatography. Hydroxyl-substituted polymethacrylate monoliths provide a hydrophilic surface and support convective mass transport that is unaffected by the viscosity of the PEG. Elution is achieved by reducing PEG concentration. Selectivity correlates with molecular size, with larger species retained more strongly than smaller species. Retention increases with PEG size and concentration. Salts weaken retention in proportion to their concentration and Hofmeister ranking. Retention is enhanced near the isoelectric point of the target species. Virus binding capacity was measured at 9.9 × 1012 plaque forming units per mL of monolith. 99.8% of host cell proteins and 93% of DNA were eliminated. Mass recovery exceeded 90%. IgM capacity was greater than 60 mg/mL. 95% of host cell proteins were eliminated from IgM produced in protein-free media, and mass recovery was up to 90%. Bioactivity was fully conserved by both viruses and antibodies. Process time ranged from less than 30 min to 2 h depending on the product concentration in the feed stream.
P. Gagnon
Journal of Chromatography A, 1221 (2012) 57-70(2012) 57-70
This article reviews technology trends in antibody purification. Section 1 discusses non-chromatography methods, including precipitation, liquid–liquid extraction, and high performance tangential flow filtration. The second addresses chromatography methods. It begins with discussion of fluidized and fixed bed formats. It continues with stationary phase architecture: diffusive particles, perfusive particles, membranes and monoliths. The remainder of the section reviews recent innovations in size exclusion, anion exchange, cation exchange, hydrophobic interaction, immobilized metal affinity, mixed-mode, and bioaffinity chromatography. Section 3 addresses an emerging trend of formulating process buffers to prevent or correct anomalies in the antibodies being purified. Methods are discussed for preventing aggregate formation, dissociating antibody-contaminant complexes, restoring native antibody from aggregates, and conserving or restoring native disulfide pairing.
M. Žorž
ChemieXtra 3/2012 pp 30-33
Sartorius BIA Separations produziert und vertreibt kurze monolithischen Chromatografiesäulen, die auf der CIM-Convective Interaction Media-Technologie basieren. CIM-Säulen eignen sich vor allem für die Reinigung von grossen Biomolekülen wie etwa Viren (virale Vektoren und Impfstoffe), DNA (Plasmid-DNA) und grössere Proteine (Immunglobuline G und M, pegylierte Proteine). Sie weisen einzigartige Eigenschaften in Bezug auf operative Flussraten, Adsorptionsfähigkeit und Trennung grosser Biomoleküle auf. Die Säulen werden in Forschung, Labor, Pilot- und industriellen Produktionsstufen eingesetzt und sind extrem einfach zu handhaben.
R. Milačič, D. Ajlec, T. Zuliani, D. Žigon, J. Ščančar
Talanta 101 (2012) 203-210
In human milk zinc (Zn) is bound to proteins and low molecular mass (LMM) ligands. Numerous investigations demonstrated that Zn bioavailability in human milk is for infant much higher than in cow's milk. It was presumed that in the LMM human milk fraction highly bioavailable Zn-citrate prevails. However, literature data are controversial regarding the amount of Zn-citrate in human milk since analytical procedures reported were not quantitative. So, complex investigation was carried out to develop analytical method for quantitative determination of this biologically important molecule. Studies were performed within the pH range 5–7 by the use of synthetic solutions of Zn-citrate prepared in HEPES, MOPS and MES buffers. Zn-citrate was separated on weak anion-exchange convective interaction media (CIM) diethylaminoethyl (DEAE) monolithic chromatographic column using NH4NO3 as an eluent. Separated Zn species were determined by flame atomic absorption spectrometry (FAAS) or inductively coupled plasma mass spectrometry (ICP-MS). Quantitative separation of Zn-citrate complexes ([Zn(Cit)]- and [Zn(Cit)2]4-; column recoveries 94–102%) and good repeatability and reproducibility of results with relative standard deviation (RSD±3.0%) were obtained. In fractions under the chromatographic peaks Zn-binding ligand was identified by electrospray ionization tandem mass spectrometry (ESI-MS-MS). Limits of detection (LOD) for determination of Zn-citrate species by CIM DEAE-FAAS and CIM DEAE-ICP-MS were 0.01 μg Zn mL-1 and 0.0005 μg Zn mL-1, respectively. Both techniques were sensitive enough for quantification of Zn-citrate in human milk. Results demonstrated that about 23% of total Zn was present in the LMM milk fraction and that LMM-Zn corresponded to Zn-citrate. The developed speciation method represents a reliable analytical tool for investigation of the percentage and the amount of Zn-citrate in human milk.
J. Ruščić, I. Gutierrez-Aguirre, L. Urbas, P. Kramberger, N. Mehle, D. Škorić, M. Barut, M. Ravnikar, M. Krajačić
Journal of Chromatography A, 1274 (2013) 129-136
Potato spindle tuber viroid (PSTVd) is the causal agent of a number of agriculturally important diseases. It is a single-stranded, circular and unencapsidated RNA molecule with only 356–360 nucleotides and no coding capacity. Because of its peculiar structural features, it is very stable ex vivo and it is easily transmitted mechanically by contaminated hands, tools, machinery, etc. In this work, we describe the development and optimization of a method for concentrating PSTVd using Convective Interaction Media (CIM) monolithic columns. The ion-exchange chromatography on diethylamine (DEAE) monolithic analytical column (CIMac DEAE-0.1 mL) resulted in up to 30% PSTVd recovery whilst the hydrophobic interaction chromatography on C4 monolithic analytical column (CIMac C4-0.1 mL) improved it up to 60%. This was due to the fact that the binding of the viroid to the C4 matrix was less strong than to the highly charged anion-exchange matrix and could be easier and more completely eluted under the applied chromatographic conditions. Based on these preliminary results, a C4 HLD-1 (High Ligand Density) 1 mL monolithic tube column was selected for further experiments. One-litre-water samples were mixed with different viroid quantities and loaded onto the column. By using reverse transcription quantitative polymerase chain reaction (RT-qPCR), the viroid RNA was quantified in the elution fraction (≈5 mL) indicating that 70% of the viroid was recovered and concentrated by at least two orders of magnitude. This approach will be helpful in screening irrigation waters and/or hydroponic systems’ nutrient solutions for the presence of even extremely low concentrations of PSTVd.
2011
S. H. Lubbad, M. R. Buchmeiser
Journal of Chromatography A, 1218 (2011) 2362-2367
Ring-opening metathesis polymerization- (ROMP) derived monoliths were prepared from 5-norborn-2-enemethyl bromide (NBE-CH2Br) and tris(5-norborn-2-enemethoxy)methylsilane ((NBE-CH2O)3SiCH3) within the confines of surface-silanized borosilicate columns (100 × 3 mm I.D.), applying Grubbs’ first generation benzylidene-type catalyst [RuCl2(PCy3)2(CHPh)]. Monoliths were converted into weak anion exchangers via reaction with diethyl amine. The resulting monolithic anion exchangers demonstrated a very good potential for the anion-exchange separation of nucleic acids applying a phosphate buffer (0.05 mol/L, pH 7) and NaCl (1.0 mol/L) as a gradient former. Fast and efficient separations, indicated by sharp and highly symmetric analyte peaks, were established. Except for the 267 and 298 base pair fragments, the eleven fragments of a ds-pUC18 DNA Hae III digest were baseline separated within ∼8 min. Nineteen fragments of a ds-pBR322 Hae III digest were separated within ∼12 min. There, only the 192 and 213 base pair fragments and the 458, 504 and 540 base pair fragments coeluted. A ds-pUC18 DNA Hae III digest was used as a control analyte in evaluating the influence of organic additives on the mobile phase such as methanol and acetonitrile on nucleic acid separation. Methanol, and even better, acetonitrile improved the separation efficiency and shortened the analysis time.
S. Yamamoto, T. Okada, M. Abe, N. Yoshimoto
Journal of Chromatography A, 1218 (2011) 2460-2466
The peak spreading of DNAs of various sizes [12-mer, 20-mer, 50-mer and 95-mer poly(T)] in linear gradient elution (LGE) chromatography with a thin monolithic disk was investigated by using our method developed for determining HETP in LGE. Electrostatic interaction-based chromatography mode (ion-exchange chromatography, IEC) was used. Polymer-based monolithic disks of two different sizes (12 mm diameter, 3 mm thickness and 0.34 mL; 5.2 mm diameter, 4.95 mm thickness and 0.105 mL) having anion-exchange groups were employed. For comparison, a 15-μm porous bead IEC column (Resource Q, 6.4 mm diameter, 30 mm height and 0.97 mL) was also used. The peak width did not change with the flow velocity for the monolithic disks where as it became wider with increasing velocity. For the monolithic disks the peak width normalized with the column bed volume was well-correlated with the distribution coefficient at the peak position KR. HETP values were constant (ca. 0.003–0.005 cm) when KR > 5. Much higher HETP values which are flow-rate dependent were obtained for the porous bead chromatography. It is possible to obtain 50–100 plates for the 3 mm monolithic disk. This results in very sharp elution peaks (standard deviation/bed volume = 0.15) even for stepwise elution chromatography, where the peak width is similar to that for LGE of a very steep gradient slope.