Recombinant Human Aquaporin-3 (AQP3) is synthesized using heterologous expression systems such as Escherichia coli or mammalian cell lines (e.g., HEK293T). This protein retains the native ability to transport water, glycerol, urea, and hydrogen peroxide (HO) across cell membranes .
AQP3 facilitates bidirectional transport of multiple solutes, validated through assays like stopped-flow light scattering and gene-editing studies .
| Solute | Permeability | Inhibitors | Assay |
|---|---|---|---|
| Water | High | HgCl | Osmotic swelling |
| Glycerol | Moderate | Phloretin | Radiolabeled uptake |
| HO | Confirmed | N/A | Fluorescence |
Knockout models (e.g., AQP3 mice) show impaired epidermal hydration, wound healing, and tumor resistance .
Mechanism: AQP3 overexpression enhances migration/invasion in trophoblasts (via PDGF-B/PI3K-AKT pathways) and cancer cells (via ERK1/2 and NF-κB) .
Cancer Link: Correlates with poor prognosis in breast, gastric, and colorectal cancers .
Hydration: AQP3 mice exhibit reduced stratum corneum elasticity .
Disease Role: Elevated in atopic eczema but reduced in psoriasis .
Diarrhea/Constipation: Modulates water transport; downregulated during viral enteritis (e.g., PEDV) .
Oxidative Stress: Mediates HO transport, influencing intestinal barrier function .
Human Aquaporin-3 is a membrane channel protein belonging to the aquaglyceroporin subfamily that facilitates the transport of water, glycerol, and some small neutral solutes across cell membranes . The protein has a molecular weight of approximately 31.4 kDa and consists of multiple transmembrane domains that form a central pore for selective transport . AQP3 is expressed primarily in the basolateral membranes of collecting duct cells in the kidney, as well as in the skin, gastrointestinal tract, and other tissues .
Unlike classical aquaporins that exclusively transport water, AQP3 has dual functionality as both a water and glycerol channel, which makes it particularly important in processes requiring osmotic balance and lipid metabolism . The protein features several functional domains that contribute to its selectivity and transport mechanisms, including a central pore lined with hydrophilic residues that facilitate water passage and regions that allow glycerol transport .
Two primary expression systems have demonstrated effectiveness for producing recombinant human AQP3:
HEK293T Mammalian Expression System:
This system yields properly folded human AQP3 with appropriate post-translational modifications, making it suitable for studies requiring native-like protein characteristics . The HEK293T system typically produces moderate protein yields but with high biological activity and proper membrane integration .
Cell-Free (CF) Expression System:
For higher yield requirements, an Escherichia coli extract-based cell-free system has been developed that can produce milligram quantities of functional AQP3 . This system utilizes the non-ionic detergent Brij-98 during protein synthesis to maintain proper protein folding and functionality . The CF approach offers significant advantages in terms of speed, scalability, and the ability to produce membrane proteins that might be toxic when expressed in living cells .
| Expression System | Advantages | Disadvantages | Typical Yield | Applications |
|---|---|---|---|---|
| HEK293T | Native-like PTMs, Proper folding | Moderate yield, Higher cost | Microgram range | Structural studies, Functional assays |
| Cell-Free (E. coli extract) | High yield, Rapid production, Scalable | May lack some PTMs | Milligram range | Large-scale purification, Reconstitution experiments |
Achieving high-purity recombinant AQP3 typically involves a multi-step purification process:
Affinity Chromatography:
The initial purification step often utilizes affinity tags such as histidine (His) or DDK (FLAG) tags that are engineered into the recombinant protein . For His-tagged AQP3 (hAQP3-6His), immobilized metal affinity chromatography (IMAC) using Ni-NTA resin is highly effective . Similarly, anti-DDK affinity columns can be used for DDK-tagged versions of the protein .
Conventional Chromatography:
Following affinity purification, additional chromatography steps are recommended to achieve higher purity levels . These may include:
Size exclusion chromatography (SEC) to separate monomeric AQP3 from aggregates and other contaminants
Ion exchange chromatography to remove impurities based on charge differences
Hydrophobic interaction chromatography for further refinement
The combination of affinity capture followed by conventional chromatography steps can yield AQP3 preparations with greater than 80% purity as determined by SDS-PAGE and Coomassie blue staining . For functional studies, it's essential to maintain the protein in an appropriate detergent environment throughout the purification process to preserve its native conformation and activity .
Maintaining the stability and functionality of purified recombinant AQP3 requires specific storage conditions:
Temperature:
Store purified AQP3 at -80°C for long-term preservation . This ultra-low temperature minimizes protein degradation and maintains structural integrity. For short-term storage (less than one week), -20°C may be sufficient if the protein is in an appropriate buffer with stabilizing agents.
Buffer Composition:
The recommended storage buffer typically contains:
25 mM Tris-HCl as the primary buffer component
100 mM glycine to maintain protein solubility
pH 7.3 to mimic physiological conditions
Handling Recommendations:
Avoid repeated freeze-thaw cycles as they significantly reduce protein stability and activity
Consider aliquoting the purified protein into single-use volumes before freezing
When thawing, do so rapidly at room temperature or in a water bath at 25°C
For cell culture applications, filter the protein solution before use to ensure sterility
Several complementary approaches can validate the functional activity of recombinant AQP3:
Proteoliposome-Based Water and Glycerol Transport Assays:
The gold standard for functional characterization involves reconstituting purified AQP3 into liposomes and measuring transport activities using stopped-flow light scattering techniques . This approach allows quantitative assessment of both water and glycerol permeability by monitoring the rate of liposome shrinkage or swelling in response to osmotic gradients . The significantly higher permeability of AQP3-containing proteoliposomes compared to empty control liposomes provides direct evidence of proper protein folding and functionality .
Inhibition Studies:
Confirming the sensitivity of reconstituted AQP3 to known inhibitors provides further validation of proper functional conformation. Two established inhibitors can be used:
Phloretin: Strongly inhibits glycerol permeability through AQP3
HgCl₂ (mercuric chloride): Blocks water transport through interaction with cysteine residues in the AQP3 channel
A properly folded, functional AQP3 will show significant reduction in transport activities when exposed to these inhibitors at appropriate concentrations .
Cell-Based Functional Assays:
For AQP3 expressed in mammalian cell systems, functionality can be assessed through:
Cell volume regulation studies using hypotonic or hypertonic challenges
Glycerol uptake assays using radiolabeled glycerol
Fluorescence-based transport assays using volume-sensitive dyes
These complementary approaches provide robust validation of recombinant AQP3 functionality across different experimental contexts.
Incorporating recombinant AQP3 into artificial membrane systems requires careful consideration of lipid composition, protein-to-lipid ratios, and reconstitution protocols:
Liposome Reconstitution:
The most common approach involves reconstituting purified AQP3 into preformed liposomes through a detergent-mediated process . A typical protocol includes:
Preparation of unilamellar liposomes from a defined lipid mixture (often phosphatidylcholine and phosphatidylserine)
Solubilization of liposomes with a mild detergent (e.g., n-octyl-β-D-glucopyranoside or Triton X-100)
Addition of purified AQP3 at a protein-to-lipid ratio of 1:50 to 1:200 (w/w)
Controlled detergent removal using bio-beads, dialysis, or gel filtration
Quality control by dynamic light scattering to assess proteoliposome size distribution
Planar Lipid Bilayer Systems:
For electrophysiological studies, AQP3 can be incorporated into planar lipid bilayers by:
Forming stable lipid bilayers across apertures in supporting materials
Adding detergent-solubilized AQP3 directly to the chamber
Facilitating insertion through osmotic or electrical gradients
Polymeric Membrane Incorporation:
For biomimetic applications, AQP3 can be integrated into block copolymer membranes that offer greater mechanical stability than lipid systems. The incorporation typically involves:
Preparation of polymer vesicles (polymersomes)
Addition of purified AQP3 in appropriate detergent
Detergent removal through dialysis or biobeads
Confirmation of incorporation through freeze-fracture electron microscopy or functional assays
Successful reconstitution can be verified by measuring the enhanced water and glycerol permeability of the resulting proteoliposomes compared to protein-free controls using stopped-flow spectroscopy .
Several targeted modifications can enhance the stability of recombinant AQP3 while preserving its transport functionality:
Terminal Tag Optimization:
While tags are essential for purification, their positioning and composition can significantly impact stability:
C-terminal tags (such as C-Myc/DDK) generally cause less disruption to AQP3 folding and function than N-terminal modifications
Smaller tags (His₆) typically interfere less with protein structure than larger fusion partners
Incorporating flexible linker sequences between the AQP3 protein and tags can reduce steric hindrance and improve stability
Cysteine Modifications:
Strategic modification of surface-exposed cysteine residues can enhance stability:
Converting reactive cysteines to serines can prevent inappropriate disulfide formation during expression and purification
Retaining critical cysteines involved in mercury sensitivity is important for maintaining characteristic inhibition profiles
Terminal Truncations:
Selective removal of disordered terminal regions can improve expression and stability:
Trimming flexible N- or C-terminal sequences that are not essential for channel formation or regulation
Preserving regions involved in oligomerization and trafficking
Buffer Optimization:
Beyond standard storage conditions, specialized buffer additives can further enhance stability:
Addition of glycerol (10-20%) as both a stabilizer and potential substrate
Inclusion of specific lipids that associate with AQP3 in its native environment
Selected amino acids (arginine, glutamate) that can prevent aggregation through weak interactions with protein surfaces
These modifications should be evaluated through comparative functional assays to ensure that stability enhancements do not compromise the essential transport properties of AQP3 .
Comparative functional analysis between recombinant and native AQP3 reveals important similarities and differences that researchers should consider:
Water Permeability:
Properly folded recombinant AQP3 demonstrates water transport capabilities comparable to native AQP3 when reconstituted into proteoliposomes . Both exhibit:
High osmotic water permeability coefficients (Pf values)
Similar temperature dependence (activation energy)
Glycerol Transport:
Recombinant AQP3 maintains the distinctive glycerol transport function of native AQP3, with some system-dependent variations:
HEK293T-expressed AQP3 typically shows glycerol permeability very close to native levels
Cell-free produced AQP3 may exhibit slightly different kinetics depending on reconstitution conditions
Both recombinant forms demonstrate the expected inhibition by phloretin
Oligomeric State:
Native AQP3 functions as a tetramer, and recombinant preparations should maintain this quaternary structure:
Properly prepared recombinant AQP3 forms tetramers similar to native protein
Size exclusion chromatography and native PAGE can confirm the correct oligomeric state
Functional differences sometimes observed in recombinant preparations may relate to incomplete tetramerization
Post-translational Modifications:
The expression system significantly impacts post-translational modifications:
HEK293T-expressed AQP3 contains mammalian-type glycosylation and phosphorylation patterns similar to native protein
Cell-free or bacterial expression systems lack these modifications, potentially affecting regulatory properties but generally preserving basic transport functions
Reconstitution of AQP3 into artificial membrane systems presents several challenges that can impact experimental outcomes:
Inadequate Detergent Removal:
Residual detergent can create artifacts in permeability measurements by causing leaky proteoliposomes or destabilizing the protein.
Solutions:
Extend bio-bead incubation times or use multiple sequential additions of fresh beads
Implement dialysis against detergent-free buffer with multiple buffer exchanges
Apply size exclusion chromatography as a final polishing step to remove detergent micelles
Quantify residual detergent using colorimetric assays to confirm complete removal
Improper Protein Orientation:
Random insertion of AQP3 into liposomes results in mixed orientations, complicating data interpretation.
Solutions:
Use asymmetric reconstitution protocols that favor unidirectional insertion
Apply protease digestion to selectively remove externally oriented protein domains
Develop orientation-specific antibody labeling to quantify the proportion of correctly oriented channels
Account for bidirectional insertion mathematically when analyzing permeability data
Protein Aggregation During Reconstitution:
AQP3 can aggregate during the transition from detergent micelles to lipid bilayers.
Solutions:
Maintain the protein in suitable detergent (e.g., Brij-98) throughout the process
Include glycerol (5-10%) in reconstitution buffers to stabilize the protein
Perform reconstitution at reduced temperatures (4-15°C) to minimize aggregation
Filter solutions immediately before reconstitution to remove pre-formed aggregates
Suboptimal Lipid Composition:
The lipid environment significantly impacts AQP3 stability and function.
Solutions:
Include cholesterol (10-20 mol%) to enhance membrane organization and protein stability
Use a mixture of phospholipids that mimics the native membrane environment
Avoid highly charged lipids that may interfere with AQP3 folding or function
Systematically test different lipid compositions to identify optimal reconstitution conditions
Addressing these challenges through careful optimization of reconstitution protocols will significantly improve the reliability and reproducibility of functional AQP3 studies .
Distinguishing between water and glycerol transport through AQP3 requires specialized experimental approaches:
Selective Substrate Gradients:
Creating specific osmotic or solute gradients allows selective measurement of different transport activities:
Water-Specific Transport:
Glycerol-Specific Transport:
Differential Inhibition Patterns:
Exploit the differential sensitivity of water and glycerol transport to specific inhibitors:
| Inhibitor | Water Transport Inhibition | Glycerol Transport Inhibition | Working Concentration |
|---|---|---|---|
| Phloretin | Moderate | Strong | 0.5-1.0 mM |
| HgCl₂ | Strong | Moderate | 0.3-1.0 mM |
| CuSO₄ | Moderate | Weak | 1.0-5.0 mM |
| TEA | Weak | Moderate | 1.0-10.0 mM |
By applying these inhibitors selectively, researchers can parse out the relative contributions of each transport pathway .
Temperature Dependence Analysis:
Water and glycerol transport through AQP3 exhibit different activation energies (Ea):
Water transport: Typically lower Ea (3-6 kcal/mol)
Glycerol transport: Higher Ea (10-15 kcal/mol)
Measuring transport rates at multiple temperatures (typically 10°C, 20°C, and 30°C) and constructing Arrhenius plots allows calculation of activation energies, providing another means to differentiate between transport mechanisms.
Direct Substrate Tracking:
For definitive differentiation:
Use isotopically labeled glycerol (³H-glycerol) to directly track glycerol movement
Combine with water transport measurements using D₂O or fluorescent volume indicators
This approach provides unambiguous distinction between the two transport pathways
These complementary approaches enable comprehensive characterization of the dual functionality of recombinant AQP3 .
Ensuring the proper folding and functionality of recombinant AQP3 requires a multi-faceted quality control approach:
Biochemical Assessment:
SDS-PAGE Analysis: Evaluate protein purity and apparent molecular weight (31.4 kDa for monomeric AQP3)
Native PAGE: Confirm correct oligomeric state (tetramer formation)
Western Blotting: Verify identity using specific anti-AQP3 antibodies or tag-specific antibodies
Circular Dichroism (CD): Assess secondary structure content, particularly alpha-helical content characteristic of properly folded aquaporins
Structural Integrity:
Size Exclusion Chromatography (SEC): Monitor homogeneity and detect aggregation or degradation
Thermal Shift Assays: Measure protein stability through melting temperature (Tm) determination
Limited Proteolysis: Properly folded AQP3 shows characteristic resistance to proteolytic cleavage
Fluorescence Spectroscopy: Intrinsic tryptophan fluorescence can indicate proper tertiary structure
Functional Validation:
Proteoliposome Water Permeability: Confirm significantly higher water transport rates compared to control liposomes
Glycerol Transport Assays: Verify characteristic glycerol permeability
Inhibitor Sensitivity: Test responsiveness to known AQP3 inhibitors (phloretin for glycerol transport, HgCl₂ for water transport)
pH Sensitivity Profile: Assess functional activity across a range of pH values (5.0-9.0)
Advanced Structural Analysis:
Negative Stain Electron Microscopy: Visualize protein particles to confirm appropriate size and shape
Cryo-EM Analysis: For higher-resolution structural confirmation when sufficient quantities are available
Mass Spectrometry: Verify intact mass and detect potential post-translational modifications
A comprehensive quality control workflow incorporating multiple orthogonal methods provides confidence in the structural and functional integrity of recombinant AQP3 preparations for downstream experimental applications .
Maximizing yield and functionality of cell-free expressed AQP3 requires strategic optimization of multiple parameters:
Reaction Component Optimization:
Extract Preparation: Enhance extract preparation by including additional chaperones or modifying cell growth conditions before extract preparation
DNA Template Design: Optimize codon usage for cell-free expression and include appropriate regulatory elements
Reaction Buffer Composition: Adjust magnesium and potassium concentrations, which critically influence translation efficiency
Energy Regeneration System: Implement enhanced ATP regeneration systems to extend reaction duration
Membrane Protein-Specific Adaptations:
Detergent Selection: While Brij-98 has proven effective for AQP3, systematic screening of detergent type and concentration can further improve yields
Lipid Supplementation: Addition of specific lipids (phosphatidylcholine, cholesterol) during synthesis can enhance co-translational folding
Molecular Chaperones: Supplement reactions with chaperones (DnaK/DnaJ/GrpE, GroEL/GroES) to improve folding efficiency
Disulfide Bond Formation: For proteins requiring disulfide bonds, include oxidized/reduced glutathione pairs
Reaction Format Optimization:
Continuous Exchange Cell-Free (CECF) System: Implement dialysis-based formats that remove inhibitory byproducts and replenish substrates
Temperature Cycling: Apply temperature cycles between optimal translation (30°C) and folding (15-20°C) temperatures
Reaction Scale: Optimize volumes from micro-scale screening to preparative production scales
Reaction Duration: Extend productive synthesis through feeding strategies or continuous exchange
Post-Translational Processing:
Purification Strategy Integration: Design cell-free reactions compatible with downstream purification by including appropriate detergents
One-Step Procedures: Develop approaches that combine synthesis and incorporation into nanodiscs or liposomes
Quality Assessment: Implement real-time monitoring of synthesis using fluorescent reporters
By systematically optimizing these parameters, researchers can achieve milligram-scale production of functional AQP3, representing a significant improvement over traditional expression systems that typically yield lower quantities . The cell-free approach provides unprecedented flexibility for rapid production of variants for structure-function studies.
Recombinant AQP3's unique water and glycerol transport properties make it valuable for several biomimetic applications:
Water Purification Membranes:
Incorporation of recombinant AQP3 into synthetic membranes can create highly efficient water filtration systems with dual functionality:
The water channel activity provides high water permeability while maintaining selectivity against ions and contaminants
The glycerol permeability allows controlled passage of specific beneficial solutes while rejecting others
Implementation approaches include:
Incorporation into block copolymer membranes that offer greater mechanical stability than lipid systems
Development of mixed-matrix membranes containing AQP3-proteoliposomes embedded in polymer supports
Creation of biomimetic membranes with oriented AQP3 channels for maximum efficiency
Controlled Release Systems:
AQP3's dual permeability can be exploited in drug delivery applications:
Design of vesicular systems that selectively release water-soluble or glycerol-soluble therapeutic agents
Development of responsive delivery systems where transport can be modulated by pH or inhibitors
Creation of compartmentalized reaction systems with controlled solute exchange
Biosensing Platforms:
Functional reconstitution of AQP3 enables development of novel sensing technologies:
Detection systems for glycerol and related compounds based on AQP3 transport activity
Osmotic pressure sensors utilizing the water permeability properties
Label-free detection platforms based on changes in AQP3 function upon binding of inhibitors or modulators
These biomimetic applications leverage the functional characteristics of recombinant AQP3 to address challenges in separation technology, controlled delivery, and sensing systems . The cell-free production approach enables scaling to quantities needed for these applications.
Recombinant AQP3 serves as a crucial tool for investigating the molecular mechanisms underlying skin hydration and wound healing processes:
Skin Hydration Studies:
AQP3 functions as a glycerol transporter in skin and plays a vital role in regulating stratum corneum (SC) and epidermal glycerol content . Recombinant AQP3 enables:
In vitro reconstitution experiments to quantify water and glycerol transport rates under controlled conditions
Structure-function studies to identify domains critical for glycerol transport in skin cells
Development of skin-relevant model systems to test hypothesized mechanisms of hydration maintenance
Wound Healing Investigations:
AQP3 is directly involved in wound healing processes , and recombinant protein studies help elucidate:
The role of glycerol transport in supporting cell migration during wound repair
Water channel function in maintaining proper osmotic balance during the inflammatory phase
Potential interactions between AQP3 and other proteins involved in wound healing cascades
Tissue Engineering Applications:
Recombinant AQP3 contributes to advanced skin tissue engineering through:
Development of hydrating matrices incorporating functional AQP3 for improved moisture retention
Creation of wound dressings with controlled water and glycerol delivery capabilities
Engineering of skin substitutes with enhanced barrier function through regulated water transport
Pharmacological Intervention Development:
Using recombinant AQP3 as a screening platform enables:
Identification of novel compounds that modulate AQP3 activity for dermatological applications
Testing of formulations designed to optimize skin hydration through AQP3-mediated mechanisms
Development of interventions for conditions characterized by impaired skin barrier function
These applications highlight how recombinant AQP3 serves as both a research tool for mechanistic understanding and a potential therapeutic target for skin conditions related to hydration and wound healing .
Strategic mutations in recombinant AQP3 offer powerful tools for dissecting the molecular basis of its dual permeability to water and glycerol:
Selectivity Filter Modifications:
The AQP3 pore contains a distinctive selectivity region that determines which molecules can pass through the channel:
Mutations of key aromatic residues (phenylalanine, tyrosine) in the selectivity filter can alter the glycerol/water permeability ratio
Conversion of specific residues to mimic those found in water-selective aquaporins can reduce glycerol permeability
Introduction of charged residues at strategic positions can modify electrostatic interactions with passing solutes
Pore Size Determinants:
The dimensions of the AQP3 channel critically influence its transport properties:
Mutations that alter pore diameter through substitution with larger or smaller amino acids
Modifications to constriction regions that serve as "checkpoints" for molecular passage
Engineering of the extracellular and cytoplasmic vestibules that influence substrate entry
Functional Domain Analysis:
Systematic mutation of different protein regions reveals their contributions to channel function:
NPA motif variations that affect water orientation and hydrogen bonding during transport
Transmembrane domain modifications that influence channel stability and conformational dynamics
Loop region alterations that may impact channel gating or regulation
Comparative Mutational Analysis:
A particularly valuable approach involves creating chimeric constructs:
Hybrid proteins containing segments from water-selective aquaporins (AQP1) and aquaglyceroporins (AQP3)
Systematic exchange of domains between different aquaglyceroporins (AQP3, AQP7, AQP9)
Introduction of sequence variations observed in different species to identify evolutionarily conserved functional elements
The cell-free expression system is particularly advantageous for mutational studies as it allows rapid production and functional testing of multiple variants . These studies not only advance fundamental understanding of channel selectivity but also guide design of AQP3 variants with enhanced or modified properties for biotechnological applications.
Comprehensive evaluation of AQP3 inhibitors requires multi-faceted approaches that assess both binding interactions and functional consequences:
Functional Transport Assays:
The gold standard for inhibitor assessment involves direct measurement of transport activity:
Stopped-Flow Light Scattering: Measures real-time changes in proteoliposome volume during water or glycerol transport, allowing precise determination of inhibition kinetics and IC₅₀ values
Radioactive Tracer Flux: Quantifies movement of labeled substrates (³H-glycerol) in the presence of inhibitors
Fluorescence-Based Assays: Utilizes volume-sensitive dyes to monitor transport inhibition in real-time
Binding Characterization:
Understanding the molecular interactions between inhibitors and AQP3:
Isothermal Titration Calorimetry (ITC): Provides direct measurement of binding thermodynamics
Surface Plasmon Resonance (SPR): Offers real-time analysis of binding kinetics and affinity
Microscale Thermophoresis (MST): Detects subtle changes in protein movement upon inhibitor binding
Structural Analysis:
Techniques that provide insight into inhibitor binding sites and mechanisms:
Hydrogen-Deuterium Exchange Mass Spectrometry (HDX-MS): Identifies regions of AQP3 protected by inhibitor binding
Computational Docking and Molecular Dynamics: Predicts binding modes and conformational changes
X-ray Crystallography or Cryo-EM (for stable complexes): Provides direct visualization of inhibitor-protein interactions
Comparative Inhibition Profiles:
A comprehensive inhibitor assessment should evaluate:
| Parameter | Methodology | Key Information |
|---|---|---|
| Potency | Dose-response curves | IC₅₀ and Hill coefficient |
| Selectivity | Testing against multiple AQPs | Specificity for AQP3 vs. other aquaporins |
| Mode of Inhibition | Kinetic analysis | Competitive, non-competitive, or mixed inhibition |
| Reversibility | Washout experiments | Persistence of inhibition after inhibitor removal |
| pH/Temperature Dependency | Assays under varying conditions | Robustness of inhibition across conditions |
The combination of these techniques provides a comprehensive profile of potential AQP3 inhibitors, guiding further development of compounds with improved potency, selectivity, and pharmacological properties . Such inhibitors serve as valuable research tools and potential therapeutic agents for conditions involving dysregulated AQP3 function.