Intrinsically disordered proteins implicated in paramyxoviral replication machinery

Identification of a Region in the Common Amino-terminal Domain of Hendra Virus P, V, and W Proteins Responsible for Phase Transition and Amyloid Formation

Henipaviruses are BSL-4 zoonotic pathogens responsible in humans for severe encephalitis. Their V protein is a key player in the evasion of the host innate immune response. We previously showed that the Henipavirus V proteins consist of a long intrinsically disordered N-terminal domain (NTD) and a β-enriched C-terminal domain (CTD). These terminals are critical for V binding to DDB1, which is a cellular protein that is a component of the ubiquitin ligase E3 complex, as well as binding to MDA5 and LGP2, which are two host sensors of viral RNA. Here, we serendipitously discovered that the Hendra virus V protein undergoes a liquid-to-hydrogel phase transition and identified the V region responsible for this phenomenon. This region, referred to as PNT3 and encompassing residues 200-310, was further investigated using a combination of biophysical and structural approaches. Congo red binding assays, together with negative-staining transmisison electron microscopy (TEM) studies, show that PNT3 forms amyloid-like fibrils. Fibrillation abilities are dramatically reduced in a rationally designed PNT3 variant in which a stretch of three contiguous tyrosines, falling within an amyloidogenic motif, were replaced by three alanines. Worthy to note, Congo red staining experiments provided hints that these amyloid-like fibrils form not only in vitro but also in cellula after transfection or infection. The present results set the stage for further investigations aimed at assessing the functional role of phase separation and fibrillation by the Henipavirus V proteins.

Disentangling the complexity of low complexity proteins

There are multiple definitions for low complexity regions (LCRs) in protein sequences, with all of them broadly considering LCRs as regions with fewer amino acid types compared to an average composition. Following this view, LCRs can also be defined as regions showing composition bias. In this critical review, we focus on the definition of sequence complexity of LCRs and their connection with structure. We present statistics and methodological approaches that measure low complexity (LC) and related sequence properties. Composition bias is often associated with LC and disorder, but repeats, while compositionally biased, might also induce ordered structures. We illustrate this dichotomy, and more generally the overlaps between different properties related to LCRs, using examples. We argue that statistical measures alone cannot capture all structural aspects of LCRs and recommend the combined usage of a variety of predictive tools and measurements. While the methodologies available to study LCRs are already very advanced, we foresee that a more comprehensive annotation of sequences in the databases will enable the improvement of predictions and a better understanding of the evolution and the connection between structure and function of LCRs. This will require the use of standards for the generation and exchange of data describing all aspects of LCRs.

Short abstract

There are multiple definitions for low complexity regions (LCRs) in protein sequences. In this critical review, we focus on the definition of sequence complexity of LCRs and their connection with structure. We present statistics and methodological approaches that measure low complexity (LC) and related sequence properties. Composition bias is often associated with LC and disorder, but repeats, while compositionally biased, might also induce ordered structures. We illustrate this dichotomy, plus overlaps between different properties related to LCRs, using examples.

Development of TaqMan-based real-time RT-PCR assay based on N gene for the quantitative detection of feline morbillivirus

Background

Morbilliviruses are categorized under the family of Paramyxoviridae and have been associated with severe diseases, such as Peste des petits ruminants, canine distemper and measles with evidence of high morbidity and/or could cause major economic loss in production of livestock animals, such as goats and sheep. Feline morbillivirus (FeMV) is one of the members of Morbilliviruses that has been speculated to cause chronic kidney disease in cats even though a definite relationship is still unclear. To date, FeMV has been detected in several continents, such as Asia (Japan, China, Thailand, Malaysia), Europe (Italy, German, Turkey), Africa (South Africa), and South and North America (Brazil, Unites States). This study aims to develop a TaqMan real-time RT-PCR (qRT-PCR) assay targeting the N gene of FeMV in clinical samples to detect early phase of FeMV infection.

Results

A specific assay was developed, since no amplification was observed in viral strains from the same family of Paramyxoviridae, such as canine distemper virus (CDV), Newcastle disease virus (NDV), and measles virus (MeV), and other feline viruses, such as feline coronavirus (FCoV) and feline leukemia virus (FeLV). The lower detection limit of the assay was 1.74 × 10⁴ copies/μL with Cq value of 34.32 ± 0.5 based on the cRNA copy number. The coefficient of variations (CV) values calculated for both intra- and inter-assay were low, ranging from 0.34–0.53% and 1.38–2.03%, respectively. In addition, the clinical sample evaluation using this assay showed a higher detection rate, with 25 (35.2%) clinical samples being FeMV-positive compared to 11 (15.5%) using conventional RT-PCR, proving a more sensitive assay compared to the conventional RT-PCR.

Conclusions

The TaqMan-based real-time RT-PCR assay targeting the N gene described in this study is more sensitive, specific, rapid, and reproducible compared to the conventional RT-PCR assay targeting the N gene, which could be used to detect early infection in cats.

Unique and exclusive peptide signatures directly identify intrinsically disordered proteins from sequences without structural information

Intrinsically disordered proteins are now widely accepted to play crucial roles in biological functions. Identification of signatures of intrinsic disorder is one of the key steps towards building a proper repertoire for their occurrence in proteomes. In this work, systematic computational synthesis of a library of all possible (3368400) dipeptides, tripeptides, tetrapeptides and pentapeptides using the natural 20 amino acids allowed us to identify 36 unique tetrapeptides present exclusively in intrinsically disordered proteins and absent in the complete primary sequence space of naturally occurring structured proteins. Further, out of more than 530000 known naturally occurring primary sequences without any structural information, 1349 sequences contain the above identified unique signatures of intrinsic disorder. These sequences, having cellular functions varying from housekeeping to metabolic to transport, more than double the number of the currently known intrinsically disordered proteins. On similar lines, we report that 26577 pentapeptide signatures exclusive to intrinsically disordered proteins, and absent in naturally occurring structured proteins, identify ∼50% of more than half-a-million curated protein sequences without structural information to be intrinsically disordered. The results reported are a major leap forward in exploring functional manifestations of intrinsically disordered proteins.Communicated by Ramaswamy H. Sarma.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

Bipartite interface of the measles virus phosphoprotein X domain with the large polymerase protein regulates viral polymerase dynamics

Measles virus (MeV) is a highly contagious, re-emerging, major human pathogen. Replication requires a viral RNA-dependent RNA polymerase (RdRP) consisting of the large (L) polymerase protein complexed with the homo-tetrameric phosphoprotein (P). In addition, P mediates interaction with the nucleoprotein (N)-encapsidated viral RNA genome. The nature of the P:L interface and RdRP negotiation of the ribonucleoprotein template are poorly understood. Based on biochemical interface mapping, swapping of the central P tetramerization domain (OD) for yeast GCN4, and functional assays, we demonstrate that the MeV P-to-L interface is bipartite, comprising a coiled-coil microdomain proximal to the OD and an unoccupied face of the triangular prism-shaped C-terminal P X-domain (P-XD), which is distinct from the known P-XD face that binds N-tail. Mixed null-mutant P tetramers regained L-binding competence in a ratio-dependent manner and fully reclaimed bioactivity in minireplicon assays and recombinant MeV, demonstrating that the individual L-binding interface elements are physically and mechanistically distinct. P-XD binding competence to L and N was likewise trans-complementable, which, combined with mathematical modeling, enabled the mechanistic characterization of P through two- and stoichiometrically-controlled three-way complementations. Only one each of the four XDs per P tetramer must be L or N binding-competent for bioactivity, but interaction of the same P-XD with L and N was mutually exclusive, and L binding superseded engaging N. Mixed P tetramers with a single, designated L binding-competent P-XD caused significant RdRP hyperactivity, outlining a model of iterative resolution and reformation of the P-XD:L interface regulating polymerase mobility.

Elucidating binding mechanisms and dynamics of intrinsically disordered protein complexes using NMR spectroscopy

Advances in characterizing complexes of intrinsically disordered proteins (IDPs) have led to the discovery of a remarkably diverse interaction landscape that includes folding-upon-binding, highly dynamic complexes, multivalent interactions as well as regulatory switches controlled by post-translational modifications. Nuclear magnetic resonance (NMR) spectroscopy has in recent years made significant contributions to this field by describing the binding mechanisms and mapping conformational dynamics on multiple time scales. Importantly, this progress has been associated with specific methodological developments in NMR, for example in exchange techniques, allowing challenging biological systems to be studied at atomic resolution. In general, the level of dynamics observed in IDP complexes does not correlate with binding affinities, demonstrating the intricate relationship between conformational dynamics and IDP regulatory function.

An ultraweak interaction in the intrinsically disordered replication machinery is essential for measles virus function

Measles virus genome encapsidation is essential for viral replication and is controlled by the intrinsically disordered phosphoprotein (P) maintaining the nucleoprotein in a monomeric form (N) before nucleocapsid assembly. All paramyxoviruses harbor highly disordered amino-terminal domains (PNTD) that are hundreds of amino acids in length and whose function remains unknown. Using nuclear magnetic resonance (NMR) spectroscopy, we describe the structure and dynamics of the 90-kDa N0PNTD complex, comprising 450 disordered amino acids, at atomic resolution. NMR relaxation dispersion reveals the existence of an ultraweak N-interaction motif, hidden within the highly disordered PNTD, that allows PNTD to rapidly associate and dissociate from a specific site on N while tightly bound at the amino terminus, thereby hindering access to the surface of N. Mutation of this linear motif quenches the long-range dynamic coupling between the two interaction sites and completely abolishes viral transcription/replication in cell-based minigenome assays comprising integral viral replication machinery. This description transforms our understanding of intrinsic conformational disorder in paramyxoviral replication. The essential mechanism appears to be conserved across Paramyxoviridae, opening unique new perspectives for drug development against this family of pathogens.

The Unstructured Paramyxovirus Nucleocapsid Protein Tail Domain Modulates Viral Pathogenesis through Regulation of Transcriptase Activity

The paramyxovirus replication machinery comprises the viral large (L) protein and phosphoprotein (P-protein) in addition to the nucleocapsid (N) protein, which encapsidates the single-stranded RNA genome. Common to paramyxovirus N proteins is a C-terminal tail (Ntail). The mechanistic role and relevance for virus replication of the structurally disordered central Ntail section are unknown. Focusing initially on members of the Morbillivirus genus, a series of measles virus (MeV) and canine distemper virus (CDV) N proteins were generated with internal deletions in the unstructured tail section. N proteins with large tail truncations remained bioactive in mono- and polycistronic minireplicon assays and supported efficient replication of recombinant viruses. Bioactivity of Ntail mutants extended to N proteins derived from highly pathogenic Nipah virus. To probe an effect of Ntail truncations on viral pathogenesis, recombinant CDVs were analyzed in a lethal CDV/ferret model of morbillivirus disease. The recombinant viruses displayed different stages of attenuation ranging from ameliorated clinical symptoms to complete survival of infected animals, depending on the molecular nature of the Ntail truncation. Reinfection of surviving animals with pathogenic CDV revealed robust protection against a lethal challenge. The highly attenuated virus was genetically stable after ex vivo passaging and recovery from infected animals. Mechanistically, gradual viral attenuation coincided with stepwise altered viral transcriptase activity in infected cells. These results identify the central Ntail section as a determinant for viral pathogenesis and establish a novel platform to engineer gradual virus attenuation for next-generation paramyxovirus vaccine design.IMPORTANCE Investigating the role of the paramyxovirus N protein tail domain (Ntail) in virus replication, we demonstrated in this study that the structurally disordered central Ntail region is a determinant for viral pathogenesis. We show that internal deletions in this Ntail region of up to 55 amino acids in length are compatible with efficient replication of recombinant viruses in cell culture but result in gradual viral attenuation in a lethal canine distemper virus (CDV)/ferret model. Mechanistically, we demonstrate a role of the intact Ntail region in the regulation of viral transcriptase activity. Recombinant viruses with Ntail truncations induce protective immunity against lethal challenge of ferrets with pathogenic CDV. This identification of the unstructured central Ntail domain as a nonessential paramyxovirus pathogenesis factor establishes a foundation for harnessing Ntail truncations for vaccine engineering against emerging and reemerging members of the paramyxovirus family.

How order and disorder within paramyxoviral nucleoproteins and phosphoproteins orchestrate the molecular interplay of transcription and replication

In this review, we summarize computational and experimental data gathered so far showing that structural disorder is abundant within paramyxoviral nucleoproteins (N) and phosphoproteins (P). In particular, we focus on measles, Nipah, and Hendra viruses and highlight both commonalities and differences with respect to the closely related Sendai virus. The molecular mechanisms that control the disorder-to-order transition undergone by the intrinsically disordered C-terminal domain (NTAIL) of their N proteins upon binding to the C-terminal X domain (XD) of the homologous P proteins are described in detail. By having a significant residual disorder, NTAIL-XD complexes are illustrative examples of "fuzziness", whose possible functional significance is discussed. Finally, the relevance of N-P interactions as promising targets for innovative antiviral approaches is underscored, and the functional advantages of structural disorder for paramyxoviruses are pinpointed.

Quarterly intrinsic disorder digest (April-May-June, 2014)

This is the 6^th issue of the Digested Disorder series that continues to use only 2 criteria for inclusion of a paper to this digest: The publication date (a paper should be published within the covered time frame) and the topic (a paper should be dedicated to any aspect of protein intrinsic disorder). The current digest issue covers papers published during the second quarter of 2014; i.e., during the period of April, May, and June of 2014. Similar to previous issues, the papers are grouped hierarchically by topics they cover, and for each of the included papers a short description is given on its major findings.

The structurally disordered paramyxovirus nucleocapsid protein tail domain is a regulator of the mRNA transcription gradient

The paramyxovirus RNA-dependent RNA-polymerase (RdRp) complex loads onto the nucleocapsid protein (N)-encapsidated viral N:RNA genome for RNA synthesis. Binding of the RdRp of measles virus (MeV), a paramyxovirus archetype, is mediated through interaction with a molecular recognition element (MoRE) located near the end of the carboxyl-terminal Ntail domain. The structurally disordered central Ntail section is thought to add positional flexibility to MoRE, but the functional importance of this Ntail region for RNA polymerization is unclear. To address this question, we dissected functional elements of Ntail by relocating MoRE into the RNA-encapsidating Ncore domain. Linker-scanning mutagenesis identified a microdomain in Ncore that tolerates insertions. MoRE relocated to Ncore supported efficient interaction with N, MoRE-deficient Ntails had a dominant-negative effect on bioactivity that was alleviated by insertion of MoRE into Ncore, and recombinant MeV encoding N with relocated MoRE grew efficiently and remained capable of mRNA editing. MoRE in Ncore also restored viability of a recombinant lacking the disordered central Ntail section, but this recombinant was temperature-sensitive, with reduced RdRp loading efficiency and a flattened transcription gradient. These results demonstrate that virus replication requires high-affinity RdRp binding sites in N:RNA, but productive RdRp binding is independent of positional flexibility of MoRE and cis-acting elements in Ntail. Rather, the disordered central Ntail section independent of the presence of MoRE in Ntail steepens the paramyxovirus transcription gradient by promoting RdRp loading and preventing the formation of nonproductive polycistronic viral mRNAs. Disordered Ntails may have evolved as a regulatory element to adjust paramyxovirus gene expression.

The Disordered Region of the HCV Protein NS5A: Conformational Dynamics, SH3 Binding, and Phosphorylation

Intrinsically disordered proteins (IDPs) perform their physiological role without possessing a well-defined three-dimensional structure. Still, residual structure and conformational dynamics of IDPs are crucial for the mechanisms underlying their functions. For example, regions of transient secondary structure are often involved in molecular recognition, with the structure being stabilized (or not) upon binding. Long-range interactions, on the other hand, determine the hydrodynamic radius of the IDP, and thus the distance over which the protein can catch binding partners via so-called fly-casting mechanisms. The modulation of long-range interactions also presents a convenient way of fine-tuning the protein's interaction network, by making binding sites more or less accessible. Here we studied, mainly by nuclear magnetic resonance spectroscopy, residual secondary structure and long-range interactions in nonstructural protein 5A (NS5A) from hepatitis C virus (HCV), a typical viral IDP with multiple functions during the viral life cycle. NS5A comprises an N-terminal folded domain, followed by a large (∼250-residue) disordered C-terminal part. Comparing nuclear magnetic resonance spectra of full-length NS5A with those of a protein construct composed of only the C-terminal residues 191-447 (NS5A-D2D3) allowed us to conclude that there is no significant interaction between the globular and disordered parts of NS5A. NS5A-D2D3, despite its overall high flexibility, shows a large extent of local residual (α-helical and β-turn) structure, as well as a network of electrostatic long-range interactions. Furthermore, we could demonstrate that these long-range interactions become modulated upon binding to the host protein Bin1, as well as after NS5A phosphorylation by CK2. As the charged peptide regions involved in these interactions are well conserved among the different HCV genotypes, these transient long-range interactions may be important for some of the functions of NS5A over the course of the HCV life cycle.

Multi-Timescale Dynamics in Intrinsically Disordered Proteins from NMR Relaxation and Molecular Simulation

Intrinsically disordered proteins (IDPs) access highly diverse ensembles of conformations in their functional states. Although this conformational plasticity is essential to their function, little is known about the dynamics underlying interconversion between accessible states. Nuclear magnetic resonance (NMR) relaxation rates contain a wealth of information about the time scales and amplitudes of motion in IDPs, but the highly dynamic nature of IDPs complicates their interpretation. We present a novel framework in which a series of molecular dynamics (MD) simulations are used in combination with experimental (15)N relaxation measurements to characterize the ensemble of dynamic processes contributing to the observed rates. By accounting for the distinct dynamic averaging present in the different conformational states sampled by the equilibrium ensemble, we are able to accurately describe both dynamic time scales and local and global conformational sampling. The method is robust, systematically improving agreement with independent experimental relaxation data, irrespective of the actively targeted rates, and suggesting interdependence of motions occurring on time scales varying over 3 orders of magnitude.

Self-Assembly of Measles Virus Nucleocapsid-like Particles: Kinetics and RNA Sequence Dependence

Measles virus RNA genomes are packaged into helical nucleocapsids (NCs), comprising thousands of nucleo‐proteins (N) that bind the entire genome. N‐RNA provides the template for replication and transcription by the viral polymerase and is a promising target for viral inhibition. Elucidation of mechanisms regulating this process has been severely hampered by the inability to controllably assemble NCs. Here, we demonstrate self‐organization of N into NC‐like particles in vitro upon addition of RNA, providing a simple and versatile tool for investigating assembly. Real‐time NMR and fluorescence spectroscopy reveals biphasic assembly kinetics. Remarkably, assembly depends strongly on the RNA‐sequence, with the genomic 5′ end and poly‐Adenine sequences assembling efficiently, while sequences such as poly‐Uracil are incompetent for NC formation. This observation has important consequences for understanding the assembly process.

Intrinsic Disorder to Order Transitions in the Scaffold Phosphoprotein P from the Respiratory Syncytial Virus RNA Polymerase Complex

Intrinsic disorder is at the center of biochemical regulation and is particularly overrepresented among the often multifunctional viral proteins. Replication and transcription of the respiratory syncytial virus (RSV) relies on a RNA polymerase complex with a phosphoprotein cofactor P as the structural scaffold, which consists of a four-helix bundle tetramerization domain flanked by two domains predicted to be intrinsically disordered. Because intrinsic disorder cannot be reduced to a defined atomic structure, we tackled the experimental dissection of the disorder-order transitions of P by a domain fragmentation approach. P remains as a tetramer above 70 °C but shows a pronounced reversible secondary structure transition between 10 and 60 °C. While the N-terminal module behaves as a random coil-like IDP in a manner independent of tetramerization, the isolated C-terminal module displays a cooperative and reversible metastable transition. When linked to the tetramerization domain, the C-terminal module becomes markedly more structured and stable, with strong ANS binding. Therefore, the tertiary structure in the C-terminal module is not compact, conferring "late" molten globule-like IDP properties, stabilized by interactions favored by tetramerization. The presence of a folded structure highly sensitive to temperature, reversibly and almost instantly formed and broken, suggests a temperature sensing activity. The marginal stability allows for exposure of protein binding sites, offering a thermodynamic and kinetic fine-tuning in order-disorder transitions, essential for the assembly and function of the RSV RNA polymerase complex.

A protein with simultaneous capsid scaffolding and dsRNA-binding activities enhances the birnavirus capsid mechanical stability

Viral capsids are metastable structures that perform many essential processes; they also act as robust cages during the extracellular phase. Viruses can use multifunctional proteins to optimize resources (e.g., VP3 in avian infectious bursal disease virus, IBDV). The IBDV genome is organized as ribonucleoproteins (RNP) of dsRNA with VP3, which also acts as a scaffold during capsid assembly. We characterized mechanical properties of IBDV populations with different RNP content (ranging from none to four RNP). The IBDV population with the greatest RNP number (and best fitness) showed greatest capsid rigidity. When bound to dsRNA, VP3 reinforces virus stiffness. These contacts involve interactions with capsid structural subunits that differ from the initial interactions during capsid assembly. Our results suggest that RNP dimers are the basic stabilization units of the virion, provide better understanding of multifunctional proteins, and highlight the duality of RNP as capsid-stabilizing and genetic information platforms.

Structural disorder within paramyxoviral nucleoproteins

In this review I summarize available data pointing to the abundance of structural disorder within the nucleoprotein (N) from three paramyxoviruses, namely the measles (MeV), Nipah (NiV) and Hendra (HeV) viruses. I provide a detailed description of the molecular mechanisms that govern the disorder-to-order transition that the intrinsically disordered C-terminal domain (NTAIL) of their N proteins undergoes upon binding to the C-terminal X domain (XD) of the homologous phosphoproteins. I also show that a significant flexibility persists within NTAIL-XD complexes, which makes them illustrative examples of "fuzziness". Finally, I discuss the functional implications of structural disorder for viral transcription and replication in light of the promiscuity of disordered regions and of the considerable reach they confer to the components of the replicative machinery.

Visualizing the molecular recognition trajectory of an intrinsically disordered protein using multinuclear relaxation dispersion NMR

Despite playing important roles throughout biology, molecular recognition mechanisms in intrinsically disordered proteins remain poorly understood. We present a combination of (1)H(N), (13)C', and (15)N relaxation dispersion NMR, measured at multiple titration points, to map the interaction between the disordered domain of Sendai virus nucleoprotein (NT) and the C-terminal domain of the phosphoprotein (PX). Interaction with PX funnels the free-state equilibrium of NT by stabilizing one of the previously identified helical substates present in the prerecognition ensemble in a nonspecific and dynamic encounter complex on the surface of PX. This helix then locates into the binding site at a rate coincident with intrinsic breathing motions of the helical groove on the surface of PX. The binding kinetics of complex formation are thus regulated by the intrinsic free-state conformational dynamics of both proteins. This approach, providing high-resolution structural and kinetic information about a complex folding and binding interaction trajectory, can be applied to a number of experimental systems to provide a general framework for understanding conformational disorder in biomolecular function.