LinearAlifold: Linear-Time Consensus Structure Prediction for RNA Alignments.

Predicting the consensus structure of a set of aligned RNA homologs is a convenient method to find conserved structures in an RNA genome, which has many applications including viral diagnostics and therapeutics. However, the most commonly used tool for this task, RNAalifold, is prohibitively slow for long sequences, due to a cubic scaling with the sequence length, taking over a day on 400 SARS-CoV-2 and SARS-related genomes (∼30,000nt). We present LinearAlifold, a much faster alternative that scales linearly with both the sequence length and the number of sequences, based on our work LinearFold that folds a single RNA in linear time. Our work is orders of magnitude faster than RNAalifold (0.7 hours on the above 400 genomes, or ∼36× speedup) and achieves higher accuracies when compared to a database of known structures. More interestingly, LinearAlifold's prediction on SARS-CoV-2 correlates well with experimentally determined structures, substantially outperforming RNAalifold. Finally, LinearAlifold supports two energy models (Vienna and BL*) and four modes: minimum free energy (MFE), maximum expected accuracy (MEA), ThreshKnot, and stochastic sampling, each of which takes under an hour for hundreds of SARS-CoV variants. Our resource is at: https://github.com/LinearFold/LinearAlifold (code) and http://linearfold.org/linear-alifold (server).

Estimating RNA Secondary Structure Folding Free Energy Changes with efn2.

A number of analyses require estimates of the folding free energy changes of specific RNA secondary structures. These predictions are often based on a set of nearest neighbor parameters that models the folding stability of a RNA secondary structure as the sum of folding stabilities of the structural elements that comprise the secondary structure. In the software suite RNAstructure, the free energy change calculation is implemented in the program efn2. The efn2 program estimates the folding free energy change and the experimental uncertainty in the folding free energy change. It can be run through the graphical user interface for RNAstructure, from the command line, or a web server. This chapter provides detailed protocols for using efn2.

NNDB: An Expanded Database of Nearest Neighbor Parameters for Predicting Stability of Nucleic Acid Secondary Structures.

Nearest neighbor thermodynamic parameters are widely used for RNA and DNA secondary structure prediction and to model thermodynamic ensembles of secondary structures. The Nearest Neighbor Database (NNDB) is a freely available web resource (https://rna.urmc.rochester.edu/NNDB) that provides the functional forms, parameter values, and example calculations. The NNDB provides the 1999 and 2004 set of RNA folding nearest neighbor parameters. We expanded the database to include a set of DNA parameters and a set of RNA parameters that includes m6A in addition to the canonical RNA nucleobases. The site was redesigned using the Quarto open-source publishing system. A downloadable PDF version of the complete resource and downloadable sets of nearest neighbor parameters are available.

Secondary structures that regulate mRNA translation provide insights for ASO-mediated modulation of cardiac hypertrophy.

Translation of upstream open reading frames (uORFs) typically abrogates translation of main (m)ORFs. The molecular mechanism of uORF regulation in cells is not well understood. Here, we data-mined human and mouse heart ribosome profiling analyses and identified a double-stranded RNA (dsRNA) structure within the GATA4 uORF that cooperates with the start codon to augment uORF translation and inhibits mORF translation. A trans-acting RNA helicase DDX3X inhibits the GATA4 uORF-dsRNA activity and modulates the translational balance of uORF and mORF. Antisense oligonucleotides (ASOs) that disrupt this dsRNA structure promote mORF translation, while ASOs that base-pair immediately downstream (i.e., forming a bimolecular double-stranded region) of either the uORF or mORF start codon enhance uORF or mORF translation, respectively. Human cardiomyocytes and mice treated with a uORF-enhancing ASO showed reduced cardiac GATA4 protein levels and increased resistance to cardiomyocyte hypertrophy. We further show the broad utility of uORF-dsRNA- or mORF-targeting ASO to regulate mORF translation for other mRNAs. This work demonstrates that the uORF-dsRNA element regulates the translation of multiple mRNAs as a generalizable translational control mechanism. Moreover, we develop a valuable strategy to alter protein expression and cellular phenotypes by targeting or generating dsRNA downstream of a uORF or mORF start codon.

DNA Structure Design Is Improved Using an Artificially Expanded Alphabet of Base Pairs Including Loop and Mismatch Thermodynamic Parameters.

We show that in silico design of DNA secondary structures is improved by extending the base pairing alphabet beyond A-T and G-C to include the pair between 2-amino-8-(1'-ß-d-2'-deoxyribofuranosyl)-imidazo-[1,2-a]-1,3,5-triazin-(8H)-4-one and 6-amino-3-(1'-ß-d-2'-deoxyribofuranosyl)-5-nitro-(1H)-pyridin-2-one, abbreviated as P and Z. To obtain the thermodynamic parameters needed to include P-Z pairs in the designs, we performed 47 optical melting experiments and combined the results with previous work to fit free energy and enthalpy nearest neighbor folding parameters for P-Z pairs and G-Z wobble pairs. We find G-Z pairs have stability comparable to that of A-T pairs and should therefore be included as base pairs in structure prediction and design algorithms. Additionally, we extrapolated the set of loop, terminal mismatch, and dangling end parameters to include the P and Z nucleotides. These parameters were incorporated into the RNAstructure software package for secondary structure prediction and analysis. Using the RNAstructure Design program, we solved 99 of the 100 design problems posed by Eterna using the ACGT alphabet or supplementing it with P-Z pairs. Extending the alphabet reduced the propensity of sequences to fold into off-target structures, as evaluated by the normalized ensemble defect (NED). The NED values were improved relative to those from the Eterna example solutions in 91 of 99 cases in which Eterna-player solutions were provided. P-Z-containing designs had average NED values of 0.040, significantly below the 0.074 of standard-DNA-only designs, and inclusion of the P-Z pairs decreased the time needed to converge on a design. This work provides a sample pipeline for inclusion of any expanded alphabet nucleotides into prediction and design workflows.

Genome-Wide DNA Changes Acquired by Candida albicans Caspofungin-Adapted Mutants.

Drugs from the echinocandin (ECN) class are now recommended 'front-line' treatments of infections caused by a prevailing fungal pathogen, C. albicans. However, the increased use of ECNs is associated with a rising resistance to ECNs. As the acquisition of ECN resistance in C. albicans is viewed as a multistep evolution, determining factors that are associated with the decreased ECN susceptibility is of importance. We have recently identified two cohorts of genes that are either up- or downregulated in concert in order to control remodeling of cell wall, an organelle targeted by ECNs, in laboratory mutants with decreased ECN susceptibility. Here, we profiled the global DNA sequence of four of these adapted mutants in search of DNA changes that are associated with decreased ECN susceptibility. We find a limited number of 112 unique mutations representing two alternative mutational pathways. Approximately half of the mutations occurred as hotspots. Approximately half of mutations and hotspots were shared by ECN-adapted mutants despite the mutants arising as independent events and differing in some of their phenotypes, as well as in condition of chromosome 5. A total of 88 mutations are associated with 43 open reading frames (ORFs) and occurred inside of an ORF or within 1 kb of an ORF, predominantly as single-nucleotide substitution. Mutations occurred more often in the 5'-UTR than in the 3'-UTR by a 1.67:1 ratio. A total of 16 mutations mapped to eight genomic features that were not ORFs: Tca4-4 retrotransposon; Tca2-7 retrotransposon; lambda-4a long terminal repeat; mu-Ra long terminal repeat; MRS-7b Major Repeat Sequence; MRS-R Major Repeat Sequence; RB2-5a repeat sequence; and tL (CAA) leucine tRNA. Finally, eight mutations are not associated with any ORF or other genomic feature. Repeated occurrence of single-nucleotide substitutions in non-related drug-adapted mutants strongly indicates that these DNA changes are accompanying drug adaptation and could possibly influence ECN susceptibility, thus serving as factors facilitating evolution of ECN drug resistance due to classical mutations in FKS1.

LinearCoFold and LinearCoPartition: linear-time algorithms for secondary structure prediction of interacting RNA molecules.

Many RNAs function through RNA-RNA interactions. Fast and reliable RNA structure prediction with consideration of RNA-RNA interaction is useful, however, existing tools are either too simplistic or too slow. To address this issue, we present LinearCoFold, which approximates the complete minimum free energy structure of two strands in linear time, and LinearCoPartition, which approximates the cofolding partition function and base pairing probabilities in linear time. LinearCoFold and LinearCoPartition are orders of magnitude faster than RNAcofold. For example, on a sequence pair with combined length of 26,190 nt, LinearCoFold is 86.8× faster than RNAcofold MFE mode, and LinearCoPartition is 642.3× faster than RNAcofold partition function mode. Surprisingly, LinearCoFold and LinearCoPartition's predictions have higher PPV and sensitivity of intermolecular base pairs. Furthermore, we apply LinearCoFold to predict the RNA-RNA interaction between SARS-CoV-2 genomic RNA (gRNA) and human U4 small nuclear RNA (snRNA), which has been experimentally studied, and observe that LinearCoFold's prediction correlates better with the wet lab results than RNAcofold's.

Secondary structures that regulate mRNA translation provide insights for ASO-mediated modulation of cardiac hypertrophy.

Translation of upstream open reading frames (uORFs) typically abrogates translation of main (m)ORFs. The molecular mechanism of uORF regulation in cells is not well understood. Here, we identified a double-stranded RNA (dsRNA) structure residing within the GATA4 uORF that augments uORF translation and inhibits mORF translation. Antisense oligonucleotides (ASOs) that disrupt this dsRNA structure promote mORF translation, while ASOs that base-pair immediately downstream (i.e., forming a bimolecular double-stranded region) of either the uORF or mORF start codon enhance uORF or mORF translation, respectively. Human cardiomyocytes and mice treated with a uORF-enhancing ASO showed reduced cardiac GATA4 protein levels and increased resistance to cardiomyocyte hypertrophy. We further show the general utility of uORF-dsRNA- or mORF- targeting ASO to regulate mORF translation for other mRNAs. Our work demonstrates a regulatory paradigm that controls translational efficiency and a useful strategy to alter protein expression and cellular phenotypes by targeting or generating dsRNA downstream of a uORF or mORF start codon. Bullet points for discoveries: dsRNA within GATA4 uORF activates uORF translation and inhibits mORF translation. ASOs that target the dsRNA can either inhibit or enhance GATA4 mORF translation. ASOs can be used to impede hypertrophy in human cardiomyocytes and mouse hearts.uORF- and mORF-targeting ASOs can be used to control translation of multiple mRNAs.

RNA Secondary Structure Analysis Using RNAstructure.

RNAstructure is a user-friendly program for the prediction and analysis of RNA secondary structure. It is available as a web server, a program with a graphical user interface, or a set of command line tools. The programs are available for Microsoft Windows, macOS, or Linux. This article provides protocols for prediction of RNA secondary structure (using the web server, the graphical user interface, or the command line) and high-affinity oligonucleotide binding sites to a structured RNA target (using the graphical user interface). © 2023 Wiley Periodicals LLC. Basic Protocol 1: Predicting RNA secondary structure using the RNAstructure web server Alternate Protocol 1: Predicting secondary structure and base pair probabilities using the RNAstructure graphical user interface Alternate Protocol 2: Predicting secondary structure and base pair probabilities using the RNAstructure command line interface Basic Protocol 2: Predicting binding affinities of oligonucleotides complementary to an RNA target using OligoWalk.

RNA design via structure-aware multifrontier ensemble optimization.

MOTIVATION: RNA design is the search for a sequence or set of sequences that will fold to desired structure, also known as the inverse problem of RNA folding. However, the sequences designed by existing algorithms often suffer from low ensemble stability, which worsens for long sequence design. Additionally, for many methods only a small number of sequences satisfying the MFE criterion can be found by each run of design. These drawbacks limit their use cases. RESULTS: We propose an innovative optimization paradigm, SAMFEO, which optimizes ensemble objectives (equilibrium probability or ensemble defect) by iterative search and yields a very large number of successfully designed RNA sequences as byproducts. We develop a search method which leverages structure level and ensemble level information at different stages of the optimization: initialization, sampling, mutation, and updating. Our work, while being less complicated than others, is the first algorithm that is able to design thousands of RNA sequences for the puzzles from the Eterna100 benchmark. In addition, our algorithm solves the most Eterna100 puzzles among all the general optimization based methods in our study. The only baseline solving more puzzles than our work is dependent on handcrafted heuristics designed for a specific folding model. Surprisingly, our approach shows superiority on designing long sequences for structures adapted from the database of 16S Ribosomal RNAs. AVAILABILITY AND IMPLEMENTATION: Our source code and data used in this article is available at https://github.com/shanry/SAMFEO.

DNA Structure Design Is Improved Using an Artificially Expanded Alphabet of Base Pairs Including Loop and Mismatch Thermodynamic Parameters.

We show that in silico design of DNA secondary structures is improved by extending the base pairing alphabet beyond A-T and G-C to include the pair between 2-amino-8-(1'-ß-D-2'-deoxyribofuranosyl)-imidazo-[1,2- a ]-1,3,5-triazin-(8 H )-4-one and 6-amino-3-(1'-ß-D-2'-deoxyribofuranosyl)-5-nitro-(1 H )-pyridin-2-one, simply P and Z. To obtain the thermodynamic parameters needed to include P-Z pairs in the designs, we performed 47 optical melting experiments and combined the results with previous work to fit a new set of free energy and enthalpy nearest neighbor folding parameters for P-Z pairs and G-Z wobble pairs. We find that G-Z pairs have stability comparable to A-T pairs and therefore should be considered quantitatively by structure prediction and design algorithms. Additionally, we extrapolated the set of loop, terminal mismatch, and dangling end parameters to include P and Z nucleotides. These parameters were incorporated into the RNAstructure software package for secondary structure prediction and analysis. Using the RNAstructure Design program, we solved 99 of the 100 design problems posed by Eterna using the ACGT alphabet or supplementing with P-Z pairs. Extending the alphabet reduced the propensity of sequences to fold into off-target structures, as evaluated by the normalized ensemble defect (NED). The NED values were improved relative to those from the Eterna example solutions in 91 of 99 cases where Eterna-player solutions were provided. P-Z-containing designs had average NED values of 0.040, significantly below the 0.074 of standard-DNA-only designs, and inclusion of the P-Z pairs decreased the time needed to converge on a design. This work provides a sample pipeline for inclusion of any expanded alphabet nucleotides into prediction and design workflows.

Algorithm for optimized mRNA design improves stability and immunogenicity.

Messenger RNA (mRNA) vaccines are being used to combat the spread of COVID-19 (refs. 1-3), but they still exhibit critical limitations caused by mRNA instability and degradation, which are major obstacles for the storage, distribution and efficacy of the vaccine products4. Increasing secondary structure lengthens mRNA half-life, which, together with optimal codons, improves protein expression5. Therefore, a principled mRNA design algorithm must optimize both structural stability and codon usage. However, owing to synonymous codons, the mRNA design space is prohibitively large-for example, there are around 2.4 × 10632 candidate mRNA sequences for the SARS-CoV-2 spike protein. This poses insurmountable computational challenges. Here we provide a simple and unexpected solution using the classical concept of lattice parsing in computational linguistics, where finding the optimal mRNA sequence is analogous to identifying the most likely sentence among similar-sounding alternatives6. Our algorithm LinearDesign finds an optimal mRNA design for the spike protein in just 11 minutes, and can concurrently optimize stability and codon usage. LinearDesign substantially improves mRNA half-life and protein expression, and profoundly increases antibody titre by up to 128 times in mice compared to the codon-optimization benchmark on mRNA vaccines for COVID-19 and varicella-zoster virus. This result reveals the great potential of principled mRNA design and enables the exploration of previously unreachable but highly stable and efficient designs. Our work is a timely tool for vaccines and other mRNA-based medicines encoding therapeutic proteins such as monoclonal antibodies and anti-cancer drugs7,8.

In vivo secondary structural analysis of Influenza A virus genomic RNA.

Influenza A virus (IAV) is a respiratory virus that causes epidemics and pandemics. Knowledge of IAV RNA secondary structure in vivo is crucial for a better understanding of virus biology. Moreover, it is a fundament for the development of new RNA-targeting antivirals. Chemical RNA mapping using selective 2'-hydroxyl acylation analyzed by primer extension (SHAPE) coupled with Mutational Profiling (MaP) allows for the thorough examination of secondary structures in low-abundance RNAs in their biological context. So far, the method has been used for analyzing the RNA secondary structures of several viruses including SARS-CoV-2 in virio and in cellulo. Here, we used SHAPE-MaP and dimethyl sulfate mutational profiling with sequencing (DMS-MaPseq) for genome-wide secondary structure analysis of viral RNA (vRNA) of the pandemic influenza A/California/04/2009 (H1N1) strain in both in virio and in cellulo environments. Experimental data allowed the prediction of the secondary structures of all eight vRNA segments in virio and, for the first time, the structures of vRNA5, 7, and 8 in cellulo. We conducted a comprehensive structural analysis of the proposed vRNA structures to reveal the motifs predicted with the highest accuracy. We also performed a base-pairs conservation analysis of the predicted vRNA structures and revealed many highly conserved vRNA motifs among the IAVs. The structural motifs presented herein are potential candidates for new IAV antiviral strategies.

CD28-Selective Inhibition Prolongs Non-Human Primate Kidney Transplant Survival.

Costimulation blockade using belatacept results in improved renal function after kidney transplant as well as decreased likelihood of death/graft loss and reduced cardiovascular risk; however, higher rates and grades of acute rejection have prevented its widespread clinical adoption. Treatment with belatacept blocks both positive (CD28) and negative (CTLA-4) T cell signaling. CD28-selective therapies may offer improved potency by blocking CD28-mediated costimulation while leaving CTLA-4 mediated coinhibitory signals intact. Here we test a novel domain antibody directed at CD28 (anti-CD28 dAb (BMS-931699)) in a non-human primate kidney transplant model. Sixteen macaques underwent native nephrectomy and received life-sustaining renal allotransplantation from an MHC-mismatched donor. Animals were treated with belatacept alone, anti-CD28 dAb alone, or anti-CD28 dAb plus clinically relevant maintenance (MMF, Steroids) and induction therapy with either anti-IL-2R or T cell depletion. Treatment with anti-CD28 dAb extended survival compared to belatacept monotherapy (MST 187 vs. 29 days, p=0.07). The combination of anti-CD28 dAb and conventional immunosuppression further prolonged survival to MST ∼270 days. Animals maintained protective immunity with no significant infectious issues. These data demonstrate CD28-directed therapy is a safe and effective next-generation costimulatory blockade strategy with a demonstrated survival benefit and presumed advantage over belatacept by maintaining intact CTLA-4 coinhibitory signaling.

Generation and Functional Analysis of Defective Viral Genomes during SARS-CoV-2 Infection.

Defective viral genomes (DVGs) have been identified in many RNA viruses as a major factor influencing antiviral immune response and viral pathogenesis. However, the generation and function of DVGs in SARS-CoV-2 infection are less known. In this study, we elucidated DVG generation in SARS-CoV-2 and its relationship with host antiviral immune response. We observed DVGs ubiquitously from transcriptome sequencing (RNA-seq) data sets of in vitro infections and autopsy lung tissues of COVID-19 patients. Four genomic hot spots were identified for DVG recombination, and RNA secondary structures were suggested to mediate DVG formation. Functionally, bulk and single-cell RNA-seq analysis indicated the interferon (IFN) stimulation of SARS-CoV-2 DVGs. We further applied our criteria to the next-generation sequencing (NGS) data set from a published cohort study and observed a significantly higher amount and frequency of DVG in symptomatic patients than those in asymptomatic patients. Finally, we observed exceptionally diverse DVG populations in one immunosuppressive patient up to 140 days after the first positive test of COVID-19, suggesting for the first time an association between DVGs and persistent viral infections in SARS-CoV-2. Together, our findings strongly suggest a critical role of DVGs in modulating host IFN responses and symptom development, calling for further inquiry into the mechanisms of DVG generation and into how DVGs modulate host responses and infection outcome during SARS-CoV-2 infection. IMPORTANCE Defective viral genomes (DVGs) are generated ubiquitously in many RNA viruses, including SARS-CoV-2. Their interference activity to full-length viruses and IFN stimulation provide the potential for them to be used in novel antiviral therapies and vaccine development. SARS-CoV-2 DVGs are generated through the recombination of two discontinuous genomic fragments by viral polymerase complex, and this recombination is also one of the major mechanisms for the emergence of new coronaviruses. Focusing on the generation and function of SARS-CoV-2 DVGs, these studies identify new hot spots for nonhomologous recombination and strongly suggest that the secondary structures within viral genomes mediate the recombination. Furthermore, these studies provide the first evidence for IFN stimulation activity of de novo DVGs during natural SARS-CoV-2 infection. These findings set up the foundation for further mechanism studies of SARS-CoV-2 recombination and provide evidence to harness the immunostimulatory potential of DVGs in the development of a vaccine and antivirals for SARS-CoV-2.

A riboswitch separated from its ribosome-binding site still regulates translation.

Riboswitches regulate downstream gene expression by binding cellular metabolites. Regulation of translation initiation by riboswitches is posited to occur by metabolite-mediated sequestration of the Shine-Dalgarno sequence (SDS), causing bypass by the ribosome. Recently, we solved a co-crystal structure of a prequeuosine1-sensing riboswitch from Carnobacterium antarcticum that binds two metabolites in a single pocket. The structure revealed that the second nucleotide within the gene-regulatory SDS, G34, engages in a crystal contact, obscuring the molecular basis of gene regulation. Here, we report a co-crystal structure wherein C10 pairs with G34. However, molecular dynamics simulations reveal quick dissolution of the pair, which fails to reform. Functional and chemical probing assays inside live bacterial cells corroborate the dispensability of the C10-G34 pair in gene regulation, leading to the hypothesis that the compact pseudoknot fold is sufficient for translation attenuation. Remarkably, the C. antarcticum aptamer retained significant gene-regulatory activity when uncoupled from the SDS using unstructured spacers up to 10 nucleotides away from the riboswitch-akin to steric-blocking employed by sRNAs. Accordingly, our work reveals that the RNA fold regulates translation without SDS sequestration, expanding known riboswitch-mediated gene-regulatory mechanisms. The results infer that riboswitches exist wherein the SDS is not embedded inside a stable fold.

Linear-Time Algorithms for RNA Structure Prediction.

RNA secondary structure prediction is widely used to understand RNA function. Existing dynamic programming-based algorithms, both the classical minimum free energy (MFE) methods and partition function methods, suffer from a major limitation: their runtimes scale cubically with the RNA length, and this slowness limits their use in genome-wide applications. Inspired by incremental parsing for context-free grammars in computational linguistics, we designed linear-time heuristic algorithms, LinearFold and LinearPartition, to approximate the MFE structure, partition function and base pairing probabilities. These programs are orders of magnitude faster than Vienna RNAfold and CONTRAfold on long sequences. More interestingly, LinearFold and LinearPartition lead to more accurate predictions on the longest sequence families for which the structures are well established (16S and 23S Ribosomal RNAs), as well as improved accuracies for long-range base pairs (500 + nucleotides apart). This chapter provides protocols for using LinearFold and LinearPartition for secondary structure prediction.

LazySampling and LinearSampling: fast stochastic sampling of RNA secondary structure with applications to SARS-CoV-2.

Many RNAs fold into multiple structures at equilibrium, and there is a need to sample these structures according to their probabilities in the ensemble. The conventional sampling algorithm suffers from two limitations: (i) the sampling phase is slow due to many repeated calculations; and (ii) the end-to-end runtime scales cubically with the sequence length. These issues make it difficult to be applied to long RNAs, such as the full genomes of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). To address these problems, we devise a new sampling algorithm, LazySampling, which eliminates redundant work via on-demand caching. Based on LazySampling, we further derive LinearSampling, an end-to-end linear time sampling algorithm. Benchmarking on nine diverse RNA families, the sampled structures from LinearSampling correlate better with the well-established secondary structures than Vienna RNAsubopt and RNAplfold. More importantly, LinearSampling is orders of magnitude faster than standard tools, being 428× faster (72 s versus 8.6 h) than RNAsubopt on the full genome of SARS-CoV-2 (29 903 nt). The resulting sample landscape correlates well with the experimentally guided secondary structure models, and is closer to the alternative conformations revealed by experimentally driven analysis. Finally, LinearSampling finds 23 regions of 15 nt with high accessibilities in the SARS-CoV-2 genome, which are potential targets for COVID-19 diagnostics and therapeutics.

Isothermal Titration Calorimetry Analysis of a Cooperative Riboswitch Using an Interdependent-Sites Binding Model.

Isothermal titration calorimetry (ITC) is a powerful biophysical tool to characterize energetic profiles of biomacromolecular interactions without any alteration of the underlying chemical structures. In this protocol, we describe procedures for performing, analyzing, and interpreting ITC data obtained from a cooperative riboswitch-ligand interaction.