How electron tunneling and uphill excitation energy transfer support photochemistry in Halomicronema hongdechloris.

Halomicronema hongdechloris, the first cyanobacterium reported to produce the red-shifted chlorophyll f (Chl f) upon acclimation to far-red light, demonstrates remarkable adaptability to diverse light conditions. The photosystem II (PS II) of this organism undergoes reversible changes in its Chl f content, ranging from practically zero under white-light culture conditions to a Chl f: Chl a ratio of up to 1:8 when exposed to far-red light (FRL) of 720-730 nm for several days. Our ps time- and wavelength-resolved fluorescence data obtained after excitation of living H. hongdechloris cells indicate that the Soret band of a far-red (FR) chlorophyll involved in charge separation absorbs around 470 nm. At 10 K, the fluorescence decay at 715-720 nm is still fast with a time constant of 165 ps indicating an efficient electron tunneling process. There is efficient excitation energy transfer (EET) from 715-720 nm to 745 nm with the latter resulting from FR Chl f, which mainly functions as light-harvesting pigment upon adaptation to FRL. From there, excitation energy reaches the primary donor in the reaction center of PS II with an energetic uphill EET mechanism inducing charge transfer. The fluorescence data are well explained with a secondary donor PD1 represented by a red-shifted Chl a molecule with characteristic fluorescence around 715 nm and a more red-shifted FR Chl f with fluorescence around 725 nm as primary donor at the ChlD1 or PD2 position.

Solution Structures of Two Different FRP-OCP Complexes as Revealed via SEC-SANS.

Photosynthetic organisms have established photoprotective mechanisms in order to dissipate excess light energy into heat, which is commonly known as non-photochemical quenching. Cyanobacteria utilize the orange carotenoid protein (OCP) as a high-light sensor and quencher to regulate the energy flow in the photosynthetic apparatus. Triggered by strong light, OCP undergoes conformational changes to form the active red state (OCPR). In many cyanobacteria, the back conversion of OCP to the dark-adapted state is assisted by the fluorescence recovery protein (FRP). However, the exact molecular events involving OCP and its interaction with FRP remain largely unraveled so far due to their metastability. Here, we use small-angle neutron scattering combined with size exclusion chromatography (SEC-SANS) to unravel the solution structures of FRP-OCP complexes using a compact mutant of OCP lacking the N-terminal extension (∆NTEOCPO) and wild-type FRP. The results are consistent with the simultaneous presence of stable 2:2 and 2:1 FRP-∆NTEOCPO complexes in solution, where the former complex type is observed for the first time. For both complex types, we provide ab initio low-resolution shape reconstructions and compare them to homology models based on available crystal structures. It is likely that both complexes represent intermediate states of the back conversion of OCP to its dark-adapted state in the presence of FRP, which are of transient nature in the photocycle of wild-type OCP. This study demonstrates the large potential of SEC-SANS in revealing the solution structures of protein complexes in polydisperse solutions that would otherwise be averaged, leading to unspecific results.

Intrinsic tryptophan fluorescence quenching by iodine in non-canonical amino acid reveals alteration of the hydrogen bond network in the photoactive orange carotenoid protein.

The Orange Carotenoid Protein (OCP) regulates cyanobacterial photosynthetic activity through photoactivation in intense light. A hydrogen bonding network involving the keto-carotenoid oxygen and Y201 and W288 residues prevents the spontaneous activation of dark-adapted OCP. To investigate the role of the hydrogen bonds in OCP photocycling, we introduced non-canonical amino acids near the keto-carotenoid, particularly iodine at the meta-position of Y201. This modification significantly increased the yield of red OCP photoproducts, albeit with a shorter lifetime. Changes in tryptophan fluorescence during photocycling influenced by the presence of iodine near W288 revealed interactions between Y201 and W288 in the absence of the carotenoid in the C-domain. We propose that upon the relaxation of red states, a ternary complex with the carotenoid is formed. Analysis of spectral signatures and interaction energies indicates that the specific iodo-tyrosine configuration enhances interactions between the carotenoid and W288.

Probing the spectral signatures of orange carotenoid protein by orthogonal translation with aromatic non-canonical amino acids.

Orange Carotenoid Protein (OCP) is a water-soluble photoreceptor involved in photoprotection of cyanobacteria. The photoactive OCP contains a bound ketocarotenoid cofactor held in a protein matrix with a hydrogen bonding network. We have developed a system to replace essential residues of the photoactive OCP with non-canonical aromatic analogues that produce well-defined chemical or steric changes. Preliminary spectroscopic evaluation of the generated OCP variants demonstrates the potential of this "molecular surgery" to disentangle protein-chromophore interaction networks that are critical for photoreceptor function. In this way, the number and strength of key contacts with non-canonical amino acids could be controlled and manipulated. We have illustrated this principle here by replacing hydrogen bond donating residues with aromatic non-canonical amino acids that alter the state preference of OCP.

Functional interaction of low-homology FRPs from different cyanobacteria with Synechocystis OCP.

Photosynthesis requires a balance between efficient light harvesting and protection against photodamage. The cyanobacterial photoprotection system uniquely relies on the functioning of the photoactive orange carotenoid protein (OCP) that under intense illumination provides fluorescence quenching of the light-harvesting antenna complexes, phycobilisomes. The recently identified fluorescence recovery protein (FRP) binds to the photoactivated OCP and accelerates its relaxation into the basal form, completing the regulatory circle. The molecular mechanism of FRP functioning is largely controversial. Moreover, since the available knowledge has mainly been gained from studying Synechocystis proteins, the cross-species conservation of the FRP mechanism remains unexplored. Besides phylogenetic analysis, we performed a detailed structural-functional analysis of two selected low-homology FRPs by comparing them with Synechocystis FRP (SynFRP). While adopting similar dimeric conformations in solution and preserving binding preferences of SynFRP towards various OCP variants, the low-homology FRPs demonstrated distinct binding stoichiometries and differentially accentuated features of this functional interaction. By providing clues to understand the FRP mechanism universally, our results also establish foundations for upcoming structural investigations necessary to elucidate the FRP-dependent regulatory mechanism.

Interaction of the signaling state analog and the apoprotein form of the orange carotenoid protein with the fluorescence recovery protein.

Photoprotection in cyanobacteria relies on the interplay between the orange carotenoid protein (OCP) and the fluorescence recovery protein (FRP) in a process termed non-photochemical quenching, NPQ. Illumination with blue-green light converts OCP from the basic orange state (OCPO) into the red-shifted, active state (OCPR) that quenches phycobilisome (PBs) fluorescence to avoid excessive energy flow to the photosynthetic reaction centers. Upon binding of FRP, OCPR is converted to OCPO and dissociates from PBs; however, the mode and site of OCPR/FRP interactions remain elusive. Recently, we have introduced the purple OCPW288A mutant as a competent model for the signaling state OCPR (Sluchanko et al., Biochim Biophys Acta 1858:1-11, 2017). Here, we have utilized fluorescence labeling of OCP at its native cysteine residues to generate fluorescent OCP proteins for fluorescence correlation spectroscopy (FCS). Our results show that OCPW288A has a 1.6(±0.4)-fold larger hydrodynamic radius than OCPO, supporting the hypothesis of domain separation upon OCP photoactivation. Whereas the addition of FRP did not change the diffusion behavior of OCPO, a substantial compaction of the OCPW288A mutant and of the OCP apoprotein was observed. These results show that sufficiently stable complexes between FRP and OCPW288A or the OCP apoprotein are formed to be detected by FCS. 1:1 complex formation with a micromolar apparent dissociation constant between OCP apoprotein and FRP was confirmed by size-exclusion chromatography. Beyond the established OCP/FRP interaction underlying NPQ cessation, the OCP apoprotein/FRP interaction suggests a more general role of FRP as a scaffold protein for OCP maturation.

Erratum to: Interaction of the signaling state analog and the apoprotein form of the orange carotenoid protein with the fluorescence recovery protein.

In Fig. 1a in the original article, the amino acid side chains were incorrectly labeled in the structure representation of the orange carotenoid protein (OCP). The corrected figure is printed in this erratum.

The Unique Protein-to-Protein Carotenoid Transfer Mechanism.

Orange Carotenoid Protein (OCP) is known as an effector and regulator of cyanobacterial photoprotection. This 35 kDa water-soluble protein provides specific environment for blue-green light absorbing keto-carotenoids, which excitation causes dramatic but fully reversible rearrangements of the OCP structure, including carotenoid translocation and separation of C- and N-terminal domains upon transition from the basic orange to photoactivated red OCP form. Although recent studies greatly improved our understanding of the OCP photocycle and interaction with phycobilisomes and the fluorescence recovery protein, the mechanism of OCP assembly remains unclear. Apparently, this process requires targeted delivery and incorporation of a highly hydrophobic carotenoid molecule into the water-soluble apoprotein of OCP. Recently, we introduced, to our knowledge, a novel carotenoid carrier protein, COCP, which consists of dimerized C-domain(s) of OCP and can combine with the isolated N-domain to form transient OCP-like species. Here, we demonstrate that in vitro COCP efficiently transfers otherwise tightly bound carotenoid to the full-length OCP apoprotein, resulting in formation of photoactive OCP from completely photoinactive species. We accurately analyze the peculiarities of this process that, to the best of our knowledge, appears unique, a previously uncharacterized protein-to-protein carotenoid transfer mechanism. We hypothesize that a similar OCP assembly can occur in vivo, substantiating specific roles of the COCP carotenoid carrier in cyanobacterial photoprotection.

Fluorescent Labeling Preserving OCP Photoactivity Reveals Its Reorganization during the Photocycle.

Orange carotenoid protein (OCP), responsible for the photoprotection of the cyanobacterial photosynthetic apparatus under excessive light conditions, undergoes significant rearrangements upon photoconversion and transits from the stable orange to the signaling red state. This is thought to involve a 12-Å translocation of the carotenoid cofactor and separation of the N- and C-terminal protein domains. Despite clear recent progress, the detailed mechanism of the OCP photoconversion and associated photoprotection remains elusive. Here, we labeled the OCP of Synechocystis with tetramethylrhodamine-maleimide (TMR) and obtained a photoactive OCP-TMR complex, the fluorescence of which was highly sensitive to the protein state, showing unprecedented contrast between the orange and red states and reflecting changes in protein conformation and the distances from TMR to the carotenoid throughout the photocycle. The OCP-TMR complex was sensitive to the light intensity, temperature, and viscosity of the solvent. Based on the observed Förster resonance energy transfer, we determined that upon photoconversion, the distance between TMR (donor) bound to a cysteine in the C-terminal domain and the carotenoid (acceptor) increased by 18 Å, with simultaneous translocation of the carotenoid into the N-terminal domain. Time-resolved fluorescence anisotropy revealed a significant decrease of the OCP rotation rate in the red state, indicating that the light-triggered conversion of the protein is accompanied by an increase of its hydrodynamic radius. Thus, our results support the idea of significant structural rearrangements of OCP, providing, to our knowledge, new insights into the structural rearrangements of OCP throughout the photocycle and a completely novel approach to the study of its photocycle and non-photochemical quenching. We suggest that this approach can be generally applied to other photoactive proteins.

Assembly of photoactive orange carotenoid protein from its domains unravels a carotenoid shuttle mechanism.

The photoswitchable orange carotenoid protein (OCP) is indispensable for cyanobacterial photoprotection by quenching phycobilisome fluorescence upon photoconversion from the orange OCPO to the red OCPR form. Cyanobacterial genomes frequently harbor, besides genes for orange carotenoid proteins (OCPs), several genes encoding homologs of OCP's N- or C-terminal domains (NTD, CTD). Unlike the well-studied NTD homologs, called Red Carotenoid Proteins (RCPs), the role of CTD homologs remains elusive. We show how OCP can be reassembled from its functional domains. Expression of Synechocystis OCP-CTD in carotenoid-producing Escherichia coli yielded violet-colored proteins, which, upon mixing with the RCP-apoprotein, produced an orange-like photoswitchable form that further photoconverted into a species that quenches phycobilisome fluorescence and is spectroscopically indistinguishable from RCP, thus demonstrating a unique carotenoid shuttle mechanism. Spontaneous carotenoid transfer also occurs between canthaxanthin-coordinating OCP-CTD and the OCP apoprotein resulting in formation of photoactive OCP. The OCP-CTD itself is a novel, dimeric carotenoid-binding protein, which can coordinate canthaxanthin and zeaxanthin, effectively quenches singlet oxygen and interacts with the Fluorescence Recovery Protein. These findings assign physiological roles to the multitude of CTD homologs in cyanobacteria and explain the evolutionary process of OCP formation.

Lipid composition and properties affect protein-mediated carotenoid uptake efficiency from membranes.

Carotenoids are pigments of diverse functions ranging from coloration over light-harvesting to photoprotection. Yet, the number of carotenoid-binding proteins, which mobilize these pigments in physiological media, is limited, and the mechanisms of carotenoid mobilization are still not well understood. The same applies for the determinants of carotenoid uptake from membranes into carotenoproteins, especially regarding the dependence on the chemical properties of membrane lipids. Here, we investigate xanthophyll uptake capacity and kinetics of a paradigmatic carotenoid-binding protein, the homolog of the Orange Carotenoid Protein's C-terminal domain from Anabaena sp. PCC 7120 (AnaCTDH), using liposomes formed from defined lipid species and loaded with canthaxanthin (CAN) and echinenone (ECN), respectively. Phospholipids with different chain length and degree of saturation were investigated. The composition of carotenoid-loaded liposomes directly affected the incorporation yield and storage ratio of CAN and ECN as well as the rate of carotenoid uptake by AnaCTDH. Generally, saturated PC lipids were identified as unsuitable, and a high phase transition temperature of the lipids negatively affected the carotenoid incorporation and storage yield. For efficient carotenoid transfer, the velocity increases with increasing chain length or membrane thickness. An average transfer yield of 93 % and 43 % were obtained for the formation of AnaCTDH(CAN) and AnaCTDH(ECN) holoproteins, respectively. In summary, the most suitable lipids for the formation of AnaCTDH(CAN/ECN) holoproteins by carotenoid transfer from artificial liposomes are phosphatidylcholine (18:1) and phosphatidylglycerol (14:0). Thus, these two lipids provide the best conditions for further investigation of lipid-protein interaction and the carotenoid uptake process.

Elements of the C-terminal tail of a C-terminal domain homolog of the Orange Carotenoid Protein determining xanthophyll uptake from liposomes.

Carotenoids perform multifaceted roles in life ranging from coloration over light harvesting to photoprotection. The Orange Carotenoid Protein (OCP), a light-driven photoswitch involved in cyanobacterial photoprotection, accommodates a ketocarotenoid vital for its function. OCP extracts its ketocarotenoid directly from membranes, or accepts it from homologs of its C-terminal domain (CTDH). The CTDH from Anabaena (AnaCTDH) was shown to be important for carotenoid transfer and delivery from/to membranes. The C-terminal tail of AnaCTDH is a critical structural element likely serving as a gatekeeper and facilitator of carotenoid uptake from membranes. We investigated the impact of amino acid substitutions within the AnaCTDH-CTT on echinenone and canthaxanthin uptake from DOPC and DMPG liposomes. The transfer rate was uniformly reduced for substitutions of Arg-137 and Arg-138 to Gln or Ala, and depended on the lipid type, indicating a weaker interaction particularly with the lipid head group. Our results further suggest that Glu-132 has a membrane-anchoring effect on the PC lipids, specifically at the choline motif as inferred from the strongly different effects of the CTT variants on the extraction from the two liposome types. The substitution of Pro-130 by Gly suggests that the CTT is perpendicular to both the membrane and the main AnaCTDH protein during carotenoid extraction. Finally, the simultaneous mutation of Leu-133, Leu-134 and Leu-136 for alanines showed that the hydrophobicity of the CTT is crucial for carotenoid uptake. Since some substitutions accelerated carotenoid transfer into AnaCTDH while others slowed it down, carotenoprotein properties can be engineered toward the requirements of applications.

Raman Vibrational Signatures of Excited States of Echinenone in the Orange Carotenoid Protein (OCP) and Implications for its Photoactivation Mechanism.

In this study, the vibrational characteristics of optically excited echinenone in various solvents and the Orange Carotenoid Protein (OCP) in red and orange states are systematically investigated through steady-state and time-resolved spectroscopy techniques. Time-resolved experiments, employing both Transient Absorption (TA) and Femtosecond Stimulated Raman Spectroscopy (FSRS), reveal different states in the OCP photoactivation process. The time-resolved studies indicate vibrational signatures of exited states positioned above the S1 state during the initial 140 fs of carotenoid evolution in OCP, an absence of a vibrational signature for the relaxed S1 state of echinenone in OCP, and more robust signatures of a highly excited ground state (GS) in OCP. Differences in S1 state vibration population signatures between OCP and solvents are attributed to distinct conformations of echinenone in OCP and hydrogen bonds at the keto group forming a short-lived intramolecular charge transfer (ICT) state. The vibrational dynamics of the hot GS in OCP show a more pronounced red shift of ground state CC vibration compared to echinenone in solvents, thus suggesting an unusually hot form of GS. The study proposes a hypothesis for the photoactivation mechanism of OCP, emphasizing the high level of vibrational excitation in longitudinal stretching modes as a driving force. In conclusion, the comparison of vibrational signatures reveals unique dynamics of energy dissipation in OCP, providing insights into the photoactivation mechanism and highlighting the impact of the protein environment on carotenoid behavior. The study underscores the importance of vibrational analysis in understanding the intricate processes involved in early phase OCP photoactivation.

Light-Induced Conformational Flexibility of the Orange Carotenoid Protein Studied by Quasielastic Neutron Scattering with In Situ Illumination.

The orange carotenoid protein plays a vital role in the photoprotection of cyanobacteria and exhibits a significant structural change upon photoactivation. A rarely considered aspect is the importance of internal protein dynamics in facilitating the structural transition to the active state. In this study, we use quasielastic neutron scattering under (in situ) blue light illumination for the first time to directly probe the protein dynamics of the orange carotenoid protein in the dark-adapted and active states. This shows that the localized internal dynamics of amino acid residues is significantly enhanced upon photoactivation. This is attributed to the photoinduced structural changes exposing larger areas of the protein surface to the solvent, thus resulting in a higher degree of motional freedom. However, the flexibility of the W288A mutant assumed to mimic the active state structure is found to be different, thus highlighting the importance of in situ experiments.

Stages of OCP-FRP Interactions in the Regulation of Photoprotection in Cyanobacteria, Part 2: Small-Angle Neutron Scattering with Partial Deuteration.

We used small-angle neutron scattering partially coupled with size-exclusion chromatography to unravel the solution structures of two variants of the Orange Carotenoid Protein (OCP) lacking the N-terminal extension (OCP-ΔNTE) and its complex formation with the Fluorescence Recovery Protein (FRP). The dark-adapted, orange form OCP-ΔNTEO is fully photoswitchable and preferentially binds the pigment echinenone. Its complex with FRP consists of a monomeric OCP component, which closely resembles the compact structure expected for the OCP ground state, OCPO. In contrast, the pink form OCP-ΔNTEP, preferentially binding the pigment canthaxanthin, is mostly nonswitchable. The pink OCP form appears to occur as a dimer and is characterized by a separation of the N- and C-terminal domains, with the canthaxanthin embedded only into the N-terminal domain. Therefore, OCP-ΔNTEP can be viewed as a prototypical model system for the active, spectrally red-shifted state of OCP, OCPR. The dimeric structure of OCP-ΔNTEP is retained in its complex with FRP. Small-angle neutron scattering using partially deuterated OCP-FRP complexes reveals that FRP undergoes significant structural changes upon complex formation with OCP. The observed structures are assigned to individual intermediates of the OCP photocycle in the presence of FRP.

Parameterization of a single H-bond in Orange Carotenoid Protein by atomic mutation reveals principles of evolutionary design of complex chemical photosystems.

Introduction: Dissecting the intricate networks of covalent and non-covalent interactions that stabilize complex protein structures is notoriously difficult and requires subtle atomic-level exchanges to precisely affect local chemical functionality. The function of the Orange Carotenoid Protein (OCP), a light-driven photoswitch involved in cyanobacterial photoprotection, depends strongly on two H-bonds between the 4-ketolated xanthophyll cofactor and two highly conserved residues in the C-terminal domain (Trp288 and Tyr201). Method: By orthogonal translation, we replaced Trp288 in Synechocystis OCP with 3-benzothienyl-L-alanine (BTA), thereby exchanging the imino nitrogen for a sulphur atom. Results: Although the high-resolution (1.8 Å) crystal structure of the fully photoactive OCP-W288_BTA protein showed perfect isomorphism to the native structure, the spectroscopic and kinetic properties changed distinctly. We accurately parameterized the effects of the absence of a single H-bond on the spectroscopic and thermodynamic properties of OCP photoconversion and reveal general principles underlying the design of photoreceptors by natural evolution. Discussion: Such "molecular surgery" is superior over trial-and-error methods in hypothesis-driven research of complex chemical systems.

Fortuitously compatible protein surfaces primed allosteric control in cyanobacterial photoprotection.

Highly specific interactions between proteins are a fundamental prerequisite for life, but how they evolve remains an unsolved problem. In particular, interactions between initially unrelated proteins require that they evolve matching surfaces. It is unclear whether such surface compatibilities can only be built by selection in small incremental steps, or whether they can also emerge fortuitously. Here, we used molecular phylogenetics, ancestral sequence reconstruction and biophysical characterization of resurrected proteins to retrace the evolution of an allosteric interaction between two proteins that act in the cyanobacterial photoprotection system. We show that this interaction between the orange carotenoid protein (OCP) and its unrelated regulator, the fluorescence recovery protein (FRP), evolved when a precursor of FRP was horizontally acquired by cyanobacteria. FRP's precursors could already interact with and regulate OCP even before these proteins first encountered each other in an ancestral cyanobacterium. The OCP-FRP interaction exploits an ancient dimer interface in OCP, which also predates the recruitment of FRP into the photoprotection system. Together, our work shows how evolution can fashion complex regulatory systems easily out of pre-existing components.

Stages of OCP-FRP Interactions in the Regulation of Photoprotection in Cyanobacteria, Part 1: Time-Resolved Spectroscopy.

Most cyanobacteria utilize a water-soluble Orange Carotenoid Protein (OCP) to protect their light-harvesting complexes from photodamage. The Fluorescence Recovery Protein (FRP) is used to restore photosynthetic activity by inactivating OCP via dynamic OCP-FRP interactions, a multistage process that remains underexplored. In this work, applying time-resolved spectroscopy, we demonstrate that the interaction of FRP with the photoactivated OCP begins early in the photocycle. Interacting with the compact OCP state, FRP completely prevents the possibility of OCP domain separation and formation of the signaling state capable of interacting with the antenna. The structural element that prevents FRP binding and formation of the complex is the short α-helix at the beginning of the N-terminal domain of OCP, which masks the primary site in the C-terminal domain of OCP. We determined the rate of opening of this site and show that it remains exposed long after the relaxation of the red OCP states. Observations of the OCP transitions on the ms time scale revealed that the relaxation of the orange photocycle intermediates is accompanied by an increase in the interaction of the carotenoid keto group with the hydrogen bond donor tyrosine-201. Our data refine the current model of photoinduced OCP transitions and the interaction of its intermediates with FRP.

Engineering the photoactive orange carotenoid protein with redox-controllable structural dynamics and photoprotective function.

Photosynthesis requires various photoprotective mechanisms for survival of organisms in high light. In cyanobacteria exposed to high light, the Orange Carotenoid Protein (OCP) is reversibly photoswitched from the orange (OCPO) to the red (OCPR) form, the latter binds to the antenna (phycobilisomes, PBs) and quenches its overexcitation. OCPR accumulation implicates restructuring of a compact dark-adapted OCPO state including detachment of the N-terminal extension (NTE) and separation of protein domains, which is reversed by interaction with the Fluorescence Recovery Protein (FRP). OCP phototransformation supposedly occurs via an intermediate characterized by an OCPR-like absorption spectrum and an OCPO-like protein structure, but the hierarchy of steps remains debatable. Here, we devise and analyze an OCP variant with the NTE trapped on the C-terminal domain (CTD) via an engineered disulfide bridge (OCPCC). NTE trapping preserves OCP photocycling within the compact protein structure but precludes functional interaction with PBs and especially FRP, which is completely restored upon reduction of the disulfide bridge. Non-interacting with the dark-adapted oxidized OCPCC, FRP binds reduced OCPCC nearly as efficiently as OCPO devoid of the NTE, suggesting that the low-affinity FRP binding to OCPO is realized via NTE displacement. The low efficiency of excitation energy transfer in complexes between PBs and oxidized OCPCC indicates that OCPCC binds to PBs in an orientation suboptimal for quenching PBs fluorescence. Our approach supports the presence of the OCPR-like intermediate in the OCP photocycle and shows effective uncoupling of spectral changes from functional OCP photoactivation, enabling redox control of its structural dynamics and function.