#include <HybridRNA.h>

Inheritance diagram for HybridRNA:

Public Member Functions
	HybridRNA (const char sequence1[], const char sequence2[], const bool IsRNA=true)
	Constructors. More...

	HybridRNA (const char filename1[], const int type1, const char filename2[], const int type2, const bool IsRNA=true)

	HybridRNA (const char filename1[], const int type1, const char filename2[], const int type2, const char *alphabet)

int	AccessFold (const double gamma=0.4, const float percent=50, const int maximumstructures=20, const int window=0, const int maxinternalloopsize=30)

int	FoldBimolecular (const float percent=10, const int maximumstructures=20, const int window=0, const char savefile[]="", const int maxinternalloopsize=30)
	Predict the lowest free energy secondary structure and generate suboptimal structures using a heuristic. More...

int	FoldDuplex (const float percent=40, const int maximumstructures=10, const int window=0, const int maxinternalloopsize=30)
	Predict the lowest free energy secondary structure for two strands that cannot form intramolecular pairs and generate suboptimal structures using a heuristic. More...

int	PartitionFunctionBimolecular (const char savefile[]="")
	Predict the bimolecular partition function for a sequence (with no intramolecular pairs). More...

RNA *	GetRNA1 ()

RNA *	GetRNA2 ()

int	GetErrorCode ()
	Return an error code, where a return of zero is no error. More...

const char *	GetErrorMessage (const int error)
	Return error messages based on code from GetErrorCode and other error codes. More...

bool	GetForbidIntramolecular ()
	Get whether intramolecular pairs are allowed. More...

void	SetForbidIntramolecular (const bool forbid)
	Set whether intramolecular pairs are allowed. More...

void	SetProgress (ProgressHandler &Progress)

void	StopProgress ()

	~HybridRNA ()

Public Member Functions inherited from RNA
	RNA (const char sequence[], const bool IsRNA=true)
	Constructor - user provides a sequence as a c string. More...

	RNA (const char filepathOrSequence[], const RNAInputType fileType, const char *const alphabetName, const bool allowUnknownBases=false, const bool skipThermoTables=false)

	RNA (const char filepathOrSequence[], const RNAInputType fileType, const Thermodynamics *copyThermo)

	RNA (const char filename[], const RNAInputType fileType, const bool IsRNA=true)
	Constructor - user provides a filename for existing file as a c string. More...

	RNA (const bool IsRNA=true)

int	GetErrorCode () const
	Return an error code, where a return of zero is no error. More...

string	GetFullErrorMessage () const

const string	GetErrorDetails () const
	Returns extended details about the last error. (e.g. error messages produced during file read operations that are otherwise lost.) More...

void	SetErrorDetails (const string &details)
	Set extended details about the last error. (e.g. error messages produced during file read operations that are otherwise lost.) More...

void	SetSequenceLabel (const string &label)
	Set the name of the sequence. (This must be called before structure prediction for it to affect the resulting structures.) More...

string	GetErrorMessageString (const int error) const
	Return error messages based on code from GetErrorCode and other error codes. More...

void	ResetError ()

void	EnsureStructureCapcacity (const int minimumStructures)
	Ensure that at a minumum number of structures have been created. More...

int	SpecifyPair (const int i, const int j, const int structurenumber=1)
	Specify a base pair between nucleotides i and j. More...

int	RemovePairs (const int structurenumber=1, bool removeIfLastStructure=true)
	Remove all the current base pairs in a specified structure. More...

int	RemoveBasePair (const int i, const int structurenumber=1)
	Remove a specified pair in a specified structure. More...

double	CalculateFreeEnergy (const int structurenumber=1, const bool UseSimpleMBLoopRules=false)
	Return the predicted Gibb's free energy change for structure # structurenumber, defaulted to 1. More...

double	ExteriorLoopCorrection (const int structurenumber, const bool UseSimpleMBLoopRules, int min_index, int max_index)

int	WriteThermodynamicDetails (const char filename[], const bool UseSimpleMBLoopRules=false)
	Calculate the folding free energy change for all structures and write the details of the calculation to a file. More...

int	FoldSingleStrand (const float percent=20, const int maximumstructures=20, const int window=5, const char savefile[]="", const int maxinternalloopsize=30, bool mfeonly=false, bool simple_iloops=true, bool disablecoax=false)
	Predict the lowest free energy secondary structure and generate suboptimal structures using a heuristic. More...

int	GenerateAllSuboptimalStructures (const float percent=5, const double deltaG=0.6)
	Predict the lowest free energy secondary structure and generate all suboptimal structures. More...

int	MaximizeExpectedAccuracy (const double maxPercent=20, const int maxStructures=20, const int window=1, const double gamma=1.0)
	Predict the structure with maximum expected accuracy and suboptimal structures. More...

int	PartitionFunction (const char savefile[]="", double temperature=-10.0, bool disablecoax=false, bool restoreSHAPE=true)
	Predict the partition function for a sequence. More...

int	Rsample (const vector< double > &experimentalRestraints, RsampleData &refdata, const int randomSeed=0, const char savefile[]="", const double cparam=0.5, const double offset=1.10, const int numsamples=10000)

int	PredictProbablePairs (const float probability=0)
	Predict structures containing highly probable pairs. More...

int	ProbKnot (int iterations=1, int MinHelixLength=1, double threshold=0)
	Predict maximum expected accuracy structures that contain pseudoknots from either a sequence or a partition function save file. More...

int	ProbKnotFromSample (int iterations=1, int MinHelixLength=1, double threshold=0)
	Predict maximum expected accuracy structures that contain pseudoknots from a file containing ensemble of structures. More...

int	ReFoldSingleStrand (const float percent=20, const int maximumstructures=20, const int window=5)
	Re-predict the lowest free energy secondary structure and generate suboptimal structures using a heuristic. More...

int	Stochastic (const int structures=1000, const int seed=1)
	Sample structures from the Boltzman ensemable. More...

int	ForceDoubleStranded (const int i)
	Force a nucleotide to be double stranded (base paired). More...

int	ForceFMNCleavage (const int i)
	Indicate a nucleotide that is accessible to FMN cleavage (a U in GU pair). More...

int	ForceMaximumPairingDistance (const int distance)
	Force a maximum distance between apired nucleotides. More...

int	ForceModification (const int i)
	Force modification for a nucleotide. More...

int	ForcePair (const int i, const int j)
	Force a pair between two nucleotides. More...

int	ForceProhibitPair (const int i, const int j)
	Prohibit a pair between two nucleotides. More...

int	ForceSingleStranded (const int i)
	Force a nucleotide to be single stranded. More...

int	GetForcedDoubleStranded (const int constraintnumber)
	Return a nucleotide that is forced double stranded. More...

int	GetForcedFMNCleavage (const int constraintnumber)
	Return a nucleotide that is accessible to FMN cleavage. More...

int	GetForcedModification (const int constraintnumber)
	Return a nucleotide that is accessible to modification. More...

int	GetForcedPair (const int constraintnumber, const bool fiveprime)
	Return a nucleotide in a forced pair. More...

int	GetForcedProhibitedPair (const int constraintnumber, const bool fiveprime)
	Return a nucleotide in a prohibited pair. More...

int	GetForcedSingleStranded (const int constraintnumber)
	Return a nucleotide that is forced single stranded. More...

int	GetMaximumPairingDistance ()
	Return the maximum pairing distance. More...

int	GetNumberOfForcedDoubleStranded ()
	Return the number of nucletides forced to be paired. More...

int	GetNumberOfForcedFMNCleavages ()
	Return the number of nucleotides accessible to FMN cleavage. More...

int	GetNumberOfForcedModifications ()
	Return the number of nucleotides accessible to chemical modification. More...

int	GetNumberOfForcedPairs ()
	Return the number of forced base pairs. More...

int	GetNumberOfForcedProhibitedPairs ()
	Return the number of prohibited base pairs. More...

int	GetNumberOfForcedSingleStranded ()
	Return the number of nucleotides that are not allowed to pair. More...

int	ReadConstraints (const char filename[])
	Read a set of folding constraints to disk in a plain text file. More...

int	ReadSHAPE (const char filename[], const double slope, const double intercept, RestraintType modifier=RESTRAINT_SHAPE, const bool IsPseudoEnergy=true)
	Read SHAPE data from disk. More...

int	ReadSHAPE (const char filename[], const double dsSlope, const double dsIntercept, const double ssSlope, const double ssIntercept, RestraintType modifier=RESTRAINT_SHAPE)
	Read SHAPE data from disk including single-stranded SHAPE pseudo free energys. More...

int	ReadDMS (const char filename[], const bool bynt=false)

int	ReadDSO (const char filename[])
	Read double strand offset data from disk. More...

int	ReadSSO (const char filename[])
	Read single strand offset data from disk. More...

int	ReadExperimentalPairBonus (const char filename[], double const experimentalOffset, double const experimentalScaling)
	Read experimental pair bonuses from disk. More...

void	RemoveConstraints ()
	Remove all folding constraints. More...

void	SetConstraints (vector< int > ss)

int	SetExtrinsic (int i, int j, double k)
	Add extrinsic restraints for partition function calculations. More...

int	WriteConstraints (const char filename[])
	Write the current set of folding constraints to disk in a plain text file. More...

int	AddComment (const char comment[], const int structurenumber=1)
	Add a comment associated with a structure. More...

int	WriteCt (const char filename[], bool append=false, CTCommentProvider &commentProvider=CTComments::Energy) const
	Write a ct file of the structures. More...

int	WriteDotBracket (const char filename[], const int structurenumber=-1, const DotBracketFormat format=DBN_FMT_MULTI_TITLE, CTCommentProvider &commentProvider=CTComments::Energy) const
	Write dot-bracket file of structures. More...

int	BreakPseudoknot (const bool minimum_energy=true, const int structurenumber=0, const bool useFastMethod=true)
	Break any pseudoknots that might be in a structure. More...

bool	ContainsPseudoknot (const int structurenumber)
	Report if there are any pseudoknots in a structure. More...

double	GetEnsembleEnergy ()
	Get the ensemble folding free energy change. More...

double	GetEnsembleDefect (const int structurenumber=1, const int start=0, const int end=0)
	Get the ensemble defect of a secondary structure. More...

double	GetFreeEnergy (const int structurenumber)
	Get the folding free energy change for a predicted structure. More...

int	GetPair (const int i, const int structurenumber=1)
	Get the nucleotide to which the specified nucleotide is paired. More...

double	GetPairEnergy (const int i, const int j)
	Get the lowest folding free energy possible for a structure containing pair i-j. More...

double	GetPairProbability (const int i, const int j)
	Get a base pair probability. More...

int	GetPairProbabilities (double *arr, const int size)

int	GetStructureNumber () const
	Get the total number of specified or predicted structures. More...

int	DetermineDrawingCoordinates (const int height, const int width, const int structurenumber=1)
	Determine the coordinates for drawing a secondary structure. More...

std::string	GetCommentString (const int structurenumber=1)
	Provide the comment from the ct file as a string. More...

int	GetNucleotideXCoordinate (const int i)
	Get the X coordinate for nucleotide i for drawing a structure. More...

int	GetNucleotideYCoordinate (const int i)
	Get the Y coordinate for nucleotide i for drawing a structure. More...

int	GetLabelXCoordinate (const int i)
	Get the X coordinate for placing the nucleotide index label specified by i. More...

int	GetLabelYCoordinate (const int i)
	Get the Y coordinate for placing the nucleotide index label specified by i. More...

char	GetNucleotide (const int i)

int	GetSequenceLength () const
	Get the total length of the sequence. More...

const char *	GetSequence () const

std::string	GetSequence (size_t start, size_t length=std::string::npos) const

bool	GetBackboneType () const
	Get the backbone type. More...

double	GetVprimeQ (const int i, const int j)

double	GetW (const int i, const int j)

structure *	GetStructure ()

void	SetProgress (ProgressHandler &Progress)

void	StopProgress ()

ProgressHandler *	GetProgress ()

	~RNA ()
	Destructor. More...

void	CopyThermo (Thermodynamics &copy)
	Copy thermodynamic parameters from an instance of an RNA class. More...

Public Member Functions inherited from Thermodynamics
	Thermodynamics (const bool isRNA=true, const char *const alphabetName=NULL, const double temperature=310.15)

	Thermodynamics (const Thermodynamics &copyThermo)

int	SetTemperature (double temperature)
	Set the temperature of folding in K. More...

double	GetTemperature () const

string	GetAlphabetName () const
	Get the name of the extended alphabet for which thermodynamic parameters should be loaded. More...

int	ReadThermodynamic (const char directory=NULL, const char alphabet=NULL, const double temperature=-1.0)
	Function to read the thermodynamic parameters. More...

int	ReloadDataTables (const double new_temperature=-1.0)

bool	VerifyThermodynamic ()
	Force the datatables to be read if they haven't already. Return true if the tables were already loaded or if the attempt to (re)open them succeded. More...

datatable *	GetDatatable ()

datatable *	GetEnthalpyTable (const char *alphabet=NULL)

void	ClearEnergies ()
	Clear the currently loaded energy datatable and release its resources. More...

void	ClearEnthalpies ()
	Clear the currently loaded enthalpy datatable and release its resources. More...

bool	GetEnergyRead () const
	Return whether this instance of Thermodynamics has the paremters populated (either from disk or from another Thermodynamics class). More...

bool	IsAlphabetRead () const

	~Thermodynamics ()

Private Member Functions
void	commonconstructor (const char fileNameOrsequence1[], const int fileType1, const char fileNameOrsequence2[], const int fileType2)

void	SetupBimolecular ()

Private Attributes
bool	forbidunimolecular

TwoRNA *	sequences

Additional Inherited Members
Static Public Member Functions inherited from RNA
static const char *	GetErrorMessage (const int error)
	Return error messages based on code from GetErrorCode and other error codes. More...

Public Attributes inherited from Thermodynamics
bool	isrna

Protected Member Functions inherited from RNA
int	FileReader (const char filename[], const RNAInputType fileType)

void	init (const char *sequenceOrFileName, const RNAInputType fileType, const bool allowUnknownBases=false, const bool skipThermoTables=false)

Protected Member Functions inherited from Thermodynamics
virtual void	CopyThermo (const Thermodynamics &copy)
	Copy thermodynamic parameters from an instance of Thermodynamics class. More...

Protected Attributes inherited from RNA
int	ErrorCode

ProgressHandler *	progress

PFPRECISION *	w5

PFPRECISION *	w3

PFPRECISION **	wca

pfdatatable *	pfdata

DynProgArray< PFPRECISION > *	w

DynProgArray< PFPRECISION > *	v

DynProgArray< PFPRECISION > *	wmb

DynProgArray< PFPRECISION > *	wl

DynProgArray< PFPRECISION > *	wmbl

DynProgArray< PFPRECISION > *	wcoax

DynProgArray< PFPRECISION > *	wlc

PFPRECISION	Q

Protected Attributes inherited from Thermodynamics
datatable *	data

datatable *	enthalpy

bool	copied

double	nominal_temperature

string	nominal_alphabetName

bool	skipThermoTables

Detailed Description

HybridRNA Class.

The HybridRNA class provides an entry point for all the bimolecular structure prediction routines of RNAstructure. The class is inherited from the RNA class and contains an instance of TwoRNA, which itself contains two instances to the class RNA.

Constructor & Destructor Documentation

◆ HybridRNA() [1/3]

HybridRNA::HybridRNA	(	const char	sequence1[],
		const char	sequence2[],
		const bool	IsRNA = `true`
	)

Constructors.

The two constuctors are available to reach the TwoRNA constructors, from which this class is built. Please see the TwoRNA constructor entries for documentation.

◆ HybridRNA() [2/3]

HybridRNA::HybridRNA	(	const char	filename1[],
		const int	type1,
		const char	filename2[],
		const int	type2,
		const bool	IsRNA = `true`
	)

◆ HybridRNA() [3/3]

HybridRNA::HybridRNA	(	const char	filename1[],
		const int	type1,
		const char	filename2[],
		const int	type2,
		const char *	alphabet
	)

◆ ~HybridRNA()

HybridRNA::~HybridRNA ( )

Member Function Documentation

◆ AccessFold()

int HybridRNA::AccessFold	(	const double	gamma = `0.4`,
		const float	percent = `50`,
		const int	maximumstructures = `20`,
		const int	window = `0`,
		const int	maxinternalloopsize = `30`
	)

Predict the lowest free energy secondary structure for two interacting strands and generate suboptimal structures. This method does not allow intramolecular pairs. It considers accessibility with a heuristic that uses the partition function. If the temperature has not been specified using the RNA base class SetTemperature and no free energies have been calculated, the thermodynamic parameters have not been read and therefore they will be read by this function call. The parameter files should be located in the directory specified by the environment variable $DATAPATH of the pwd. In case of error, the function returns a non-zero that can be parsed by GetErrorMessage() or GetErrorMessageString().

Parameters

gamma	is a scaling factor that weights accessibility. The defaults is 0.4
percent	is the maximum % difference in free energy in suboptimal structures from the lowest free energy structure. The default is 50.
maximumstructures	is the maximum number of suboptimal structures to generate. The fefault is 20.
window	is a parameter that specifies how different the suboptimal structures should be from each other (0=no restriction and larger integers require structures to be more different). The default is 0.
maxinternalloopsize	is the maximum number of unpaired nucleotides in bulge and internal loops. This is used to accelerate the prediction speed. The default is 30.

Returns: An int that indicates an error code (0 = no error, 5 = error reading thermodynamic parameter files, 14 = traceback error).

◆ commonconstructor()

void HybridRNA::commonconstructor	(	const char	fileNameOrsequence1[],
		const int	fileType1,
		const char	fileNameOrsequence2[],
		const int	fileType2
	)

private

◆ FoldBimolecular()

int HybridRNA::FoldBimolecular	(	const float	percent = `10`,
		const int	maximumstructures = `20`,
		const int	window = `0`,
		const char	savefile[] = `""`,
		const int	maxinternalloopsize = `30`
	)

Predict the lowest free energy secondary structure and generate suboptimal structures using a heuristic.

This function predicts the lowest free energy structure and suboptimal structures. If the temperature has not been specified using the RNA base class SetTemperature and no free energies have been calculated, the thermodynamic parameters have not been read and therefore they will be read by this function call. The parameter files should be located in the directory specified by the environment variable $DATAPATH of the pwd. In case of error, the function returns a non-zero that can be parsed by GetErrorMessage() or GetErrorMessageString().

Parameters

percent	is the maximum % difference in free energy in suboptimal structures from the lowest free energy structure. The default is 10.
maximumstructures	is the maximum number of suboptimal structures to generate. The defaults is 20.
window	is a parameter that specifies how different the suboptimal structures should be from each other (0=no restriction and larger integers require structures to be more different). The default is 0.
savefile	is c string containing a file path and name for a savefile (.sav)that can be used to generate energy dot plots and to refold the secondary structure using different suboptimal structure parameters. The default is "", which results in no save file written.
maxinternalloopsize	is the maximum number of unpaired nucleotides in bulge and internal loops. This is used to accelerate the prediction speed. The default is 30.

Returns: An int that indicates an error code (0 = no error, 5 = error reading thermodynamic parameter files, 14 = traceback error).

◆ FoldDuplex()

int HybridRNA::FoldDuplex	(	const float	percent = `40`,
		const int	maximumstructures = `10`,
		const int	window = `0`,
		const int	maxinternalloopsize = `30`
	)

Predict the lowest free energy secondary structure for two strands that cannot form intramolecular pairs and generate suboptimal structures using a heuristic.

This function predicts the lowest free energy bimolecular structure and suboptimal structures. This function does not allow any folding constraints. If the temperature has not been specified using SetTemperature and no free energies have been calculated, the thermodynamic parameters have not been read and therefore they will be read by this function call. The parameter files should be located in the directory specified by the environment variable $DATAPATH of the pwd. In case of error, the function returns a non-zero that can be parsed by GetErrorMessage() or GetErrorMessageString().

Parameters

percent	is the maximum % difference in free energy in suboptimal structures from the lowest free energy structure. The default is 40.
maximumstructures	is the maximum number of suboptimal structures to generate. The default is 10.
window	is a parameter that specifies how different the suboptimal structures should be from each other (0=no restriction and larger integers require structures to be more different). The default is 0.
maxinternalloopsize	is the maximum number of unpaired nucleotides in bulge and internal loops. This is used to accelerate the prediction speed. The default is 30.

Returns: An int that indicates an error code (0 = no error, 5 = error reading thermodynamic parameter files, 14 = traceback error).

◆ GetErrorCode()

int HybridRNA::GetErrorCode ( )

Return an error code, where a return of zero is no error.

This function returns and error flag that is generated during construction by RNA(const char &filename, const int type, const bool IsRNA=true) or from CalculateFreeEnergy(). An error of zero is always no error. Other codes are errors and a c-string can be fetched for the error with GetErrorMessage().

Returns: An integer that provides the error code.

◆ GetErrorMessage()

const char * HybridRNA::GetErrorMessage ( const int error )

Return error messages based on code from GetErrorCode and other error codes.

0 = no error <100 = Error to be fetched from RNA base class. 100-999 = Error associated with bimolecular folding, to be handled here. >=1000 = Errors for underlying sequence, get message from TwoRNA base class.

Parameters

error is the integer error code provided by GetErrorCode().

Returns: A pointer to a c string that provides an error message or from other functions that return integer error codes.

◆ GetForbidIntramolecular()

bool HybridRNA::GetForbidIntramolecular ( )

Get whether intramolecular pairs are allowed.

Returns: A bool that indicates whether intramolecular pairs are forbidden (true = forbidden, false = not).

◆ GetRNA1()

RNA * HybridRNA::GetRNA1 ( )

Access the underlying RNA class from an instance of TwoRNA. This is provided for use with two sequence methods. Generally, there is no need for end users to use this function.

Returns: A pointer to the underlying RNA class for sequence 1.

◆ GetRNA2()

RNA * HybridRNA::GetRNA2 ( )

Access the underlying RNA class from an instance of TwoRNA. This is provided for use with two sequence methods. Generally, there is no need for end users to use this function.

Returns: A pointer to the underlying RNA class for sequence 2.

◆ PartitionFunctionBimolecular()

int HybridRNA::PartitionFunctionBimolecular ( const char savefile[] = "" )

Predict the bimolecular partition function for a sequence (with no intramolecular pairs).

This function must be called to predict base pair probabilities, perform stochastic traceback, or for maximizing expected accuracy. This predicts the partition function without intramolecular pairs. If the temperature has not been specified using SetTemperature and no free energies have been calculated, the thermodynamic parameters have not been read and therefore they will be read by this function call. The parameter files should be located in the directory specified by the environment variable $DATAPATH of the pwd. In case of error, the function returns a non-zero that can be parsed by GetErrorMessage() or GetErrorMessageString().

Parameters

savefile is a c string that contains the path and filename for creating a save file. This defaults to "", which indicates no file is to be written.

Returns: An int that indicates an error code (0 = no error, 5 = error reading thermodynamic parameter files).

◆ SetForbidIntramolecular()

void HybridRNA::SetForbidIntramolecular ( const bool forbid )

Set whether intramolecular pairs are allowed.

If true is passed to this function, intramolecular pairs will be forbidden in FoldBimolecular.

Parameters

forbid is a bool that indicates whether intramolecular pairs are forbid.

◆ SetProgress()

void HybridRNA::SetProgress ( ProgressHandler & Progress )

Provide a TProgressDialog for following calculation progress. A TProgressDialog class has a public function void update(int percent) that indicates the progress of a long calculation.

Parameters

Progress is a TProgressDialog class.

◆ SetupBimolecular()

void HybridRNA::SetupBimolecular ( )

private

◆ StopProgress()

void HybridRNA::StopProgress ( )

Provide a means to stop using a TProgressDialog. StopProgress tells the RNA class to no longer follow progress. This should be called if the TProgressDialog is deleted, so that this class does not make reference to it.

Member Data Documentation

◆ forbidunimolecular

bool HybridRNA::forbidunimolecular

private

◆ sequences

TwoRNA* HybridRNA::sequences

private

The documentation for this class was generated from the following files:

RNA_class/HybridRNA.h
RNA_class/HybridRNA.cpp

Public Member Functions

Private Member Functions

Private Attributes

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ HybridRNA() [1/3]

◆ HybridRNA() [2/3]

◆ HybridRNA() [3/3]

◆ ~HybridRNA()

Member Function Documentation

◆ AccessFold()

◆ commonconstructor()

◆ FoldBimolecular()

◆ FoldDuplex()

◆ GetErrorCode()

◆ GetErrorMessage()

◆ GetForbidIntramolecular()

◆ GetRNA1()

◆ GetRNA2()

◆ PartitionFunctionBimolecular()

◆ SetForbidIntramolecular()

◆ SetProgress()

◆ SetupBimolecular()

◆ StopProgress()

Member Data Documentation

◆ forbidunimolecular

◆ sequences