Recombinant Aspergillus niger NADH-cytochrome b5 reductase 2 (mcr1)

What is NADH-cytochrome b5 reductase in Aspergillus niger and how does it differ from homologs in other species?

NADH-cytochrome b5 reductase (CBR) in Aspergillus niger is a flavoprotein enzyme that catalyzes electron transfer from NADH to cytochrome b5, playing crucial roles in various redox reactions within fungal cells. Similar to the yeast homolog (Mcr1p), A. niger CBR is encoded by a nuclear gene and likely functions in multiple cellular compartments . Comparative analysis with other fungal species shows that CBRs share conserved domains, particularly in the flavin-binding β-barrel region where specific amino acid residues (arginine, tyrosine, and serine) form hydrogen bonds with the flavin prosthetic group . The A. niger enzyme demonstrates comparable substrate preference to other fungal CBRs, showing higher affinity for NADH over NADPH as an electron donor . Unlike mammalian CBRs which are primarily associated with the endoplasmic reticulum, fungal CBRs often show dual localization patterns between mitochondrial compartments and microsomes, suggesting divergent evolutionary adaptations in subcellular targeting mechanisms.

What are the key structural features of NADH-cytochrome b5 reductase and how do they relate to function?

The structural organization of NADH-cytochrome b5 reductase includes a characteristic flavin-binding β-barrel domain that is highly conserved across species . This domain contains three critical amino acid residues (arginine, tyrosine, and serine) that form hydrogen bonds with the flavin prosthetic group, essential for electron transfer activity . The enzyme typically possesses an N-terminal targeting sequence that directs its subcellular localization. In yeast Mcr1p, the first 47 amino acids constitute a bipartite targeting sequence where the initial 12 residues function as a weak matrix-targeting signal while the remaining hydrophobic stretch serves as an intramitochondrial sorting signal for directing the protein to either the outer membrane or the intermembrane space . Mutations within this hydrophobic region can dramatically alter the protein's subcellular distribution, highlighting the structure-function relationship in targeting mechanisms . The catalytic domain binds NADH and facilitates electron transfer to cytochrome b5 or other acceptors such as ferricyanide, with the latter commonly used in activity assays.

What techniques are most effective for preliminary detection of mcr1 expression in Aspergillus niger?

For detecting mcr1 expression in A. niger, researchers should employ a multi-faceted approach combining molecular and biochemical techniques. RT-PCR or qRT-PCR using primers designed from conserved regions of fungal CBR genes provides initial confirmation of transcriptional activity. For protein detection, western blotting using antibodies against conserved epitopes of CBR proteins can be effective, though antibody specificity must be validated. Enzymatic activity assays using NADH as electron donor and ferricyanide as acceptor provide functional evidence, as demonstrated in studies where recombinant expression resulted in 4.7-fold increases in ferricyanide reduction activity in microsomes . Subcellular fractionation followed by activity assays helps determine localization patterns. Additionally, fusion with reporter proteins such as GFP can visualize expression and localization in living cells. When designing these experiments, researchers should include appropriate controls and consider that mcr1 expression may vary with growth conditions and developmental stages of the fungus.

What are the optimal expression systems for producing recombinant A. niger NADH-cytochrome b5 reductase?

For recombinant production of A. niger NADH-cytochrome b5 reductase, several expression systems have shown success, each with distinct advantages. Pichia pastoris has proven particularly effective for fungal enzyme expression, as demonstrated with A. niger α-l-rhamnosidase, which achieved expression levels of 711.9 U/mL, eightfold higher than native enzyme . This methylotrophic yeast combines the advantages of eukaryotic post-translational modifications with high-density fermentation capacity. Alternatively, Aspergillus oryzae serves as an excellent homologous expression host for fungal proteins, as seen in the successful expression of Mortierella alpina CBR with 4.7-fold increased activity . This system provides proper folding and processing for fungal enzymes.

For expression protocol optimization, researchers should consider:

• Codon optimization based on the host's codon usage bias

• Selection of appropriate promoters (AOX1 for P. pastoris or amyB for A. oryzae)

• Inclusion of native or optimized secretion signals

• Cultivation parameters including temperature (25-30°C), pH (5.0-6.0), and induction timing

• Supplementation with riboflavin to enhance flavoprotein assembly

The choice between intracellular retention or secretion should be based on the requirement for post-translational modifications and downstream purification strategy.

What purification strategy yields the highest activity and purity for recombinant mcr1?

A multi-step purification strategy is recommended for obtaining high-purity, active recombinant mcr1. Begin with careful subcellular fractionation since NADH-cytochrome b5 reductase may distribute between membrane compartments. For membrane-associated enzyme, solubilization with mild detergents such as cholic acid sodium salt has proven effective for maintaining activity . A systematic purification scheme should then include:

• Initial capture using ion exchange chromatography (DEAE-Sephacel)

• Intermediate purification via high-resolution ion exchange (Mono-Q HR 5/5)

• Affinity purification utilizing AMP-Sepharose 4B, which exploits the enzyme's nucleotide-binding properties

This approach has demonstrated a 645-fold increase in specific activity for CBR from M. alpina . Throughout purification, monitor enzyme activity using the NADH-ferricyanide reduction assay under standardized conditions. Maintain a temperature of 4°C during all purification steps to preserve enzyme stability. For storage, supplement buffer with glycerol (20-25%) and store at -80°C to maintain long-term activity. When reporting purification results, include comprehensive tables detailing recovery percentages, specific activity, and fold purification at each step to facilitate reproducibility.

How can researchers overcome expression challenges specific to recombinant mcr1 production?

Recombinant mcr1 expression presents several challenges including potential toxicity, improper folding, and insufficient flavin incorporation. To address these issues, researchers should implement a systematic troubleshooting approach:

For toxicity issues:

• Utilize tightly regulated inducible promoters (such as AOX1 in P. pastoris)

• Optimize induction timing and concentration to balance expression and host viability

• Consider using hosts with enhanced detoxification capabilities

For proper folding and activity:

• Co-express molecular chaperones to facilitate correct protein folding

• Include riboflavin supplementation (50-100 μM) in culture media to ensure proper flavin incorporation

• Optimize growth temperature, typically lowering to 20-25°C during induction phase

For glycosylation considerations:

• Recognize that mcr1 is likely N-glycosylated (as observed with r-Rha1 from A. niger)

• Consider expression hosts capable of proper post-translational modifications

• Analyze glycosylation patterns using PNGase F treatment followed by SDS-PAGE mobility shift analysis

When optimizing expression conditions, a fractional factorial design approach can efficiently identify critical parameters affecting yield and activity. Additionally, fusion tags like thioredoxin or NusA may enhance solubility, though their effect on enzymatic activity should be carefully evaluated.

What are the optimal conditions for assessing mcr1 enzymatic activity?

The optimal conditions for assessing mcr1 enzymatic activity should account for pH, temperature, buffer composition, and substrate concentrations. Based on studies of similar enzymes, NADH-cytochrome b5 reductase activity is typically measured using a spectrophotometric assay monitoring the decrease in absorbance at 340 nm (NADH oxidation) or reduction of artificial electron acceptors like ferricyanide at 420 nm . The recommended assay conditions include:

• Buffer system: 50 mM sodium phosphate buffer (pH 5.0-6.0), as fungal CBRs generally show optimum activity in slightly acidic conditions

• Temperature: 30-60°C, with 60°C being optimal for thermostable variants as observed in recombinant enzymes from A. niger

• NADH concentration: 100-200 μM (subsaturating to saturating range)

• Ferricyanide concentration: 1 mM

• Reaction volume: 1 mL with appropriate enzyme dilution to ensure linear reaction rates

Activity should be expressed as μmol of NADH oxidized or ferricyanide reduced per minute per mg protein. For kinetic parameter determination, use varying concentrations of NADH (10-500 μM) while maintaining excess electron acceptor. Plot the data using Lineweaver-Burk or non-linear regression analysis to determine Km, Vmax, and kcat values. For comparing substrate specificity, evaluate the ratio of activity with NADH versus NADPH under identical conditions, as fungal CBRs typically show preference for NADH .

How do different effectors and inhibitors influence mcr1 activity?

The activity of mcr1 can be significantly influenced by various effectors and inhibitors, providing insights into its catalytic mechanism and potential regulatory pathways. Based on studies of similar enzymes, researchers should systematically evaluate:

Metal ions effect:

• Divalent cations (Mg²⁺, Ca²⁺, Mn²⁺, Zn²⁺, Cu²⁺, Fe²⁺) at 1-5 mM concentrations

• Monovalent cations (Na⁺, K⁺) at 10-100 mM concentrations

Chemical inhibitors for mechanistic studies:

• Thiol-modifying reagents (p-chloromercuribenzoate, N-ethylmaleimide) at 0.1-1 mM

• Flavin-binding inhibitors (diphenyleneiodonium) at 10-100 μM

• NAD+ analogues (ADP-ribose) at 0.5-5 mM

Additionally, researchers should assess physiologically relevant modulators:

• Oxidative stress agents (H₂O₂, superoxide) at 0.1-1 mM

• Metabolic intermediates (acetyl-CoA, citrate) at 1-10 mM

• Glucose (10-500 mM) and ethanol (2-10% v/v), as recombinant enzymes from A. niger have demonstrated excellent tolerance to these compounds

Results should be presented as percent relative activity compared to control conditions, with statistical analysis to determine significance of effects.

What approaches should be used to determine the kinetic parameters of recombinant mcr1?

A comprehensive kinetic characterization of recombinant mcr1 requires multiple methodological approaches to determine parameters accurately. Researchers should implement the following protocol:

Steady-state kinetics:

• Conduct initial velocity measurements at varying NADH concentrations (5-500 μM) while maintaining saturating electron acceptor concentrations

• Repeat with varying electron acceptor concentrations (ferricyanide, cytochrome b5) at saturating NADH

• Perform experiments at different pH values (4.0-8.0) and temperatures (20-70°C) to establish pH and temperature profiles

• Apply both Lineweaver-Burk and non-linear regression analysis to calculate Km, Vmax, kcat, and catalytic efficiency (kcat/Km)

Inhibition studies:

• Determine inhibition patterns using NAD+, NADP+, and structural analogues

• Calculate Ki values and establish inhibition mechanisms (competitive, non-competitive, or uncompetitive)

For pH stability studies, pre-incubate the enzyme at different pH values (3.0-9.0) for defined periods (1-24h) before measuring residual activity under standard conditions. Similarly, for thermostability assessment, pre-incubate at temperatures ranging from 30-80°C for various time points (5-60 min). Based on studies of A. niger enzymes, expect good thermostability with optimal activity around 60°C and pH stability in the range of 4.0-7.0 .

Present results in a comprehensive table including:

• Km values for NADH and electron acceptors

• kcat and kcat/Km values

• Half-life at different temperatures

• pH and temperature optima

• Inhibition constants for various inhibitors

How can protein engineering be applied to enhance recombinant mcr1 properties?

Protein engineering of recombinant mcr1 can substantially enhance its catalytic properties, stability, and specificity for various applications. A systematic approach should include:

Site-directed mutagenesis targeting:

• Conserved residues in the flavin-binding domain, particularly the arginine, tyrosine, and serine triad that forms hydrogen bonds with the flavin prosthetic group

• Residues within the NADH-binding pocket to alter cofactor specificity or affinity

• Surface-exposed residues to improve thermostability through introducing additional salt bridges or disulfide bonds

The hydrophobic region of the targeting sequence presents another engineering opportunity, as point mutations in this region can dramatically alter subcellular localization patterns . Researchers should develop a library of variants with substitutions in this region to generate variants with altered distribution between membrane compartments.

Domain shuffling and chimeric enzyme construction:

• Create fusion proteins combining the catalytic domain of mcr1 with targeting sequences from other proteins

• Explore domain swapping between mcr1 homologs from thermophilic fungi to enhance thermostability

For directed evolution approaches:

• Establish a high-throughput screening method based on colorimetric detection of NADH oxidation

• Create diversity through error-prone PCR or DNA shuffling

• Implement multiple rounds of selection under increasingly stringent conditions

When evaluating engineered variants, comprehensively characterize changes in kinetic parameters, stability under extreme conditions, and substrate specificity. Document improvements in a quantitative manner, calculating fold-improvements in key parameters compared to the wild-type enzyme.

What methods are most effective for studying subcellular localization of mcr1 in A. niger?

Investigating the subcellular localization of mcr1 in A. niger requires a multi-technique approach to provide comprehensive and reliable results. Based on localization studies of similar proteins, researchers should implement:

Fluorescent protein fusion strategy:

• Generate C-terminal and N-terminal GFP fusion constructs of mcr1

• Include controls with known localization patterns to mitochondrial compartments

• Transform A. niger with these constructs using established protocols

• Visualize using confocal microscopy, co-staining with organelle-specific dyes (MitoTracker for mitochondria, ER-Tracker for endoplasmic reticulum)

Subcellular fractionation approach:

• Implement differential centrifugation to separate cellular compartments

• Perform sucrose density gradient ultracentrifugation for finer separation of membrane fractions

• Analyze fractions for mcr1 using Western blotting and enzyme activity assays

• Include marker enzymes for different compartments (cytochrome c oxidase for mitochondria, NADPH-cytochrome c reductase for ER)

Immunogold electron microscopy provides the highest resolution:

• Use specific antibodies against mcr1 or epitope tags

• Apply gold-conjugated secondary antibodies

• Analyze using transmission electron microscopy

Studies in yeast have shown that Mcr1p localizes to both the outer membrane and intermembrane space of mitochondria, with distribution influenced by the bipartite targeting sequence in the first 47 amino acids . The import into the intermembrane space requires an electrochemical potential across the inner membrane and ATP in the matrix . Researchers should investigate whether A. niger mcr1 follows similar localization patterns and import requirements through systematic mutation of the targeting sequence.

How can comparative genomics and phylogenetic analysis enhance understanding of A. niger mcr1?

Comparative genomics and phylogenetic analysis provide powerful frameworks for understanding the evolutionary history, functional conservation, and unique features of A. niger mcr1. Researchers should implement the following methodological workflow:

Sequence retrieval and alignment:

• Extract mcr1 homologous sequences from diverse fungi, focusing on Ascomycetes and Basidiomycetes

• Include sequences from yeast (S. cerevisiae), filamentous fungi (M. alpina, A. oryzae), and mammalian sources (bovine, human, rat)

• Perform multiple sequence alignment using MUSCLE or MAFFT algorithms

• Identify conserved domains, particularly the flavin-binding β-barrel domain and targeting sequences

Phylogenetic analysis:

• Construct phylogenetic trees using maximum likelihood or Bayesian inference methods

• Calculate bootstrap values or posterior probabilities to assess node support

• Map functional data onto phylogenetic trees to correlate evolutionary relationships with biochemical properties

Genomic context analysis:

• Examine the chromosomal neighborhood of mcr1 across fungal species

• Identify conserved gene clusters or syntenic relationships

• Analyze promoter regions for conserved transcription factor binding sites

This approach can reveal insights into:

• The evolutionary origin of dual localization patterns observed in fungal CBRs

• Correlation between protein sequence features and substrate preferences

• Species-specific adaptations in electron transport chains

For intron-exon structure analysis, recognize that fungal CBR genes typically contain multiple introns. The M. alpina CBR gene contained four introns of different sizes, all conforming to the GT-AG rule with GT at the 5' end and AG at the 3' end . Comparative analysis of intron positions across species can provide additional evolutionary insights.

What approaches are most effective for studying the physiological roles of mcr1 in A. niger?

To elucidate the physiological roles of mcr1 in A. niger, researchers should implement a comprehensive functional genomics approach:

Gene disruption and phenotypic analysis:

• Generate mcr1 knockout strains using CRISPR-Cas9 or traditional homologous recombination

• Implement quantitative phenotypic screens comparing mutant and progenitor isolates on solid agar supplemented with various stressors

• Calculate susceptibility coefficients to quantify growth differences

• Analyze macromorphological growth types in liquid culture to quantify how mcr1 affects submerged growth

Transcriptomic and proteomic analysis:

• Perform RNA-Seq comparing wild-type and mcr1 mutant strains under various conditions

• Identify differentially expressed genes in response to mcr1 deletion

• Conduct quantitative proteomics to identify protein level changes

• Focus on pathways related to electron transport, oxidative stress response, and membrane lipid metabolism

Metabolic flux analysis:

• Use 13C-labeled substrates to track metabolic fluxes

• Compare redox cofactor (NAD+/NADH) ratios between wild-type and mutant strains

• Assess changes in mitochondrial function using oxygen consumption measurements

Synthetic lethality screening:

• Combine mcr1 deletion with mutations in functionally related genes

• Identify genetic interactions that suggest pathway redundancies

• Construct genetic interaction networks to place mcr1 in cellular pathways

These approaches should be conducted under various growth conditions, including different carbon sources and stress conditions (oxidative, osmotic, cell wall stress) to comprehensively characterize the role of mcr1 in A. niger physiology. Results should be presented as quantitative comparisons with appropriate statistical analysis.

How can recombinant mcr1 be applied in biotechnology and biocatalysis?

Recombinant mcr1 offers significant potential for biotechnological applications, particularly in biocatalysis and biosensor development. Researchers can explore these applications through the following methodological approaches:

Biocatalytic applications:

• Develop mcr1-based systems for regeneration of NAD+ in coupled enzymatic reactions

• Explore the enzyme's ability to reduce artificial electron acceptors for synthetic chemistry applications

• Test mcr1 in combination with cytochrome P450 systems for hydroxylation reactions

• Evaluate potential for asymmetric reductions in pharmaceutical intermediate synthesis

The thermostability and pH tolerance observed in recombinant enzymes from A. niger (optimal activity at 60°C and pH 5.0) make them particularly suitable for industrial applications . Additionally, excellent tolerance to glucose and ethanol suggests potential compatibility with fermentation processes .

Biosensor development:

• Immobilize recombinant mcr1 on electrode surfaces using various techniques (covalent binding, entrapment in polymers)

• Optimize electron transfer between the enzyme and electrode

• Develop amperometric biosensors for NADH detection

• Explore coupled systems for detecting metabolites that generate or consume NADH

For immobilization protocols:

• Test different support materials (activated beads, membranes, nanoparticles)

• Compare immobilization methods (adsorption, covalent attachment, cross-linking)

• Characterize immobilized enzyme for:

  • Operational stability (activity retention over multiple cycles)

  • Storage stability (activity retention over time)

  • Kinetic parameters compared to free enzyme

Present comprehensive data tables comparing activity recovery, operational stability, and kinetic parameters across different immobilization methods and support materials.

What experimental designs best elucidate mcr1 interactions with the electron transport chain?

Investigating mcr1 interactions with the electron transport chain requires sophisticated experimental designs that can capture the complexity of electron flow in biological systems:

In vitro reconstitution studies:

• Purify individual components of electron transport pathways (mcr1, cytochrome b5, terminal electron acceptors)

• Reconstitute in liposomes or nanodiscs with defined lipid composition

• Measure electron transfer rates using spectrophotometric or electrochemical methods

• Systematically vary component ratios to determine optimal stoichiometry

• Introduce specific inhibitors to identify rate-limiting steps

Protein-protein interaction analysis:

• Implement pull-down assays using tagged mcr1 as bait

• Perform cross-linking followed by mass spectrometry (XL-MS) to identify interaction sites

• Use surface plasmon resonance to determine binding kinetics and affinities

• Apply isothermal titration calorimetry for thermodynamic characterization of interactions

In vivo imaging approaches:

• Develop split-GFP complementation assays with potential interaction partners

• Apply Förster resonance energy transfer (FRET) to measure distances between mcr1 and other components

• Implement fluorescence lifetime imaging microscopy (FLIM) to detect conformational changes during electron transfer

Electrochemical analysis:

• Immobilize mcr1 on gold electrodes via self-assembled monolayers

• Measure direct electron transfer using cyclic voltammetry

• Determine formal potentials and electron transfer rates

• Compare with physiological electron donors and acceptors

These approaches should be complemented by computational methods including molecular docking and molecular dynamics simulations to predict binding interfaces and electron transfer pathways. Results should be presented as quantitative measurements of interaction parameters, electron transfer rates, and their dependence on experimental conditions.

What are common challenges in mcr1 activity assays and how can they be overcome?

Researchers frequently encounter specific challenges when assessing mcr1 activity. The following troubleshooting guide addresses these issues with methodological solutions:

Challenge: Background NADH oxidation
Solutions:

• Include proper enzyme-free controls in all assays

• Perform measurements in anaerobic conditions to prevent oxygen-dependent NADH oxidation

• Add superoxide dismutase (10 U/mL) and catalase (100 U/mL) to minimize interference from reactive oxygen species

• Use freshly prepared NADH solutions and store in amber vials at 4°C

Challenge: Poor reproducibility of activity measurements
Solutions:

• Standardize enzyme preparation procedures, ensuring consistent protein concentration

• Control temperature rigorously during assays (±0.5°C)

• Prepare all reagents from the same stock solutions

• Calibrate spectrophotometers regularly using standard absorbing compounds

• Calculate and report specific activity with clear indication of protein quantification method

Challenge: Low activity of recombinant enzyme
Solutions:

• Ensure proper incorporation of the flavin cofactor by supplementing expression media with riboflavin

• Verify protein folding using circular dichroism spectroscopy

• Test different buffer systems, including additives like glycerol (10%) for stability

• Evaluate the effect of N-terminal tags on activity and consider tag removal

• Check for post-translational modifications by mass spectrometry

Challenge: Interference from sample matrix components
Solutions:

• Implement sample clean-up procedures (gel filtration, dialysis)

• Use reaction conditions that maximize signal-to-noise ratio

• Consider alternative detection methods (fluorescence-based NADH detection)

• Develop standard addition methods to account for matrix effects

Document all optimization steps and control experiments thoroughly to ensure reproducibility across different laboratory settings.

How can researchers distinguish between different isoforms of NADH-cytochrome b5 reductase in experimental systems?

Distinguishing between isoforms of NADH-cytochrome b5 reductase presents a significant challenge in experimental systems. Researchers should implement a multi-faceted approach:

Molecular differentiation:

• Design isoform-specific PCR primers targeting unique regions of each isoform

• Perform quantitative RT-PCR to measure relative expression levels

• Use droplet digital PCR for absolute quantification of transcript copy numbers

• Develop RNA-seq analysis pipelines that can distinguish between highly similar isoform transcripts

Protein-level differentiation:

• Generate isoform-specific antibodies targeting unique epitopes

• Implement 2D gel electrophoresis to separate isoforms based on both molecular weight and isoelectric point

• Use liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) with multiple reaction monitoring

• Analyze post-translational modification patterns that may differ between isoforms

Functional discrimination:

• Compare substrate specificities and kinetic parameters between purified isoforms

• Assess subcellular localization patterns using fluorescent protein fusions

• Evaluate differential sensitivity to inhibitors and effectors

• Measure electron transfer rates to different acceptors (cytochrome b5, ferricyanide, artificial electron acceptors)

Genetic approaches:

• Generate isoform-specific knockout strains

• Perform complementation studies with individual isoforms

• Conduct phenotypic screens under various growth conditions to identify isoform-specific functions

For example, in yeast, Mcr1p has been shown to localize to both the outer membrane and intermembrane space of mitochondria, with distribution influenced by the N-terminal targeting sequence . Mutations in this sequence can alter localization patterns, providing a tool for distinguishing function in different compartments.

What strategies address protein stability challenges during purification and characterization of recombinant mcr1?

Maintaining stability of recombinant mcr1 during purification and characterization requires specialized approaches to preserve structure and function:

During cell disruption and extraction:

• Use gentle disruption methods (enzymatic lysis for yeast, osmotic shock for spheroplasts)

• Include protease inhibitor cocktails tailored to fungal proteases

• Maintain reduced temperature (4°C) throughout processing

• Add stabilizing agents:

  • Glycerol (10-20%) to prevent protein aggregation

  • Reducing agents (1-5 mM DTT or β-mercaptoethanol) to protect thiol groups

  • Flavin cofactor (10-50 μM FAD or FMN) to stabilize the active site

During chromatographic purification:

• Minimize column residence time to reduce protein denaturation

• Include stabilizing additives in all buffers

• Monitor activity after each purification step

• Consider affinity chromatography (AMP-Sepharose 4B) for rapid, selective purification

• Implement tangential flow filtration for gentle concentration

For long-term storage:

• Determine optimal storage conditions through stability studies

• Compare stability in different buffers, pH values, and additive combinations

• Evaluate freeze-thaw stability versus continuous 4°C storage

• Consider lyophilization with appropriate cryoprotectants for extended storage

When addressing aggregation issues:

• Screen buffer compositions using dynamic light scattering to monitor aggregation

• Implement size exclusion chromatography as a final polishing step

• Consider fusion with solubility-enhancing tags (MBP, thioredoxin)

• Test the effect of non-ionic detergents (0.01-0.1% Triton X-100 or NP-40) for membrane-associated forms