Luciferase is a generic term for a class of enzymes¹ that produce bioluminescence² in nature. The name is derived from the Latin word lucifer — meaning "lightbearer" — which in turn is derived from the Latin words for "light" (lux) and "to bring or carry" (ferre). One well-known example is a luciferase of the Photinini³ firefly Photinus pyralis.

In luminescent⁴ reactions, light is produced by the reduction-oxidation⁵ of a luciferin⁶ (a pigment) and adenosine triphosphate⁷ (ATP). The rate⁸ of this reaction between luciferin⁹ and oxygen is extremely slow unless it is catalyzed¹⁰ by luciferase, often facilitated by the presence of calcium¹¹ ions (similar to muscle contraction¹²). The reaction mechanism¹³ occurs in two steps:

luciferin + ATP → luciferyl adenylate + PP_i¹⁴

luciferyl adenylate + O₂ → oxyluciferin¹⁵ + AMP¹⁶ + light

Light is produced because the reaction forms oxyluciferin in an electronically excited state. The reaction releases a photon of light as oxyluciferin goes back to the ground state. This reaction is very efficient: almost all energy is converted into light. By comparison, an incandescent lamp loses nearly 90% of its power in the form of heat.

Luciferins and luciferases are produced in different forms by different animal species. In addition to fireflies, some species of fungi (Omphalotus olearius), insects, fish, molluscs and algae such as Noctiluca scintillans (milky seas effect¹⁷) are known to produce light by luciferase. Some species even have multiple luciferases that can produce different colors of light using the same luciferin.

But the most diabolical of all must be Oceanobacillus caeni¹⁸: a Gram-positive, rod-shaped, spore-forming bacterium that was isolated from the activated sludge of a wastewater treatment system in South Korea. Her luciferase (KPH78743¹⁹) contains a peptide²⁰ ASP–GLU–VAL–ILE–LEU:

MKLSILDQSP ISKGKTPKDA LEASIELAKL TDELGYHRYW VAEHHDLGGL ASPAPDILLG IIGSQTEQIR
IGSGAVLLPN YSPYHIAERY NELATLYPNR VDLGLGRAPG GSAEVSIALA GNFLEKVRMY PKLVDEVILF
LHQDFPSDHM YAKVSATPVP KTPPVPWLLG TSNKSAKLAI EKRLPFVFGH FMSNEDGPSI VKEYMKNVLN
GKSNVIVTVS AICAETTEEA EEIAMSNYLW KILQDKGEGK EGVPSIEEAK AYPYSLEEKE RIERMKQNQI
VGNPSQVREQ LENLQSEYEV DELMIVTITH SYEARKKSYQ LLAEEFCLA

Assignment

In biology, a sequence motif is a peptide (a part of a protein) that is widespread in many different proteins. The repetitive nature usually relates to a biological function²¹ of a macromolecule containing the motif. The search for motifs is often complicated by the fact that small variations occur, so repetitions are not necessarily identical.

To represent all possible variations of a motif, the protein database PROSITE²² uses a pattern that consists of one or more units separated by dashes (-), for example [AC]-x-V-x-{ED}. Each unit describes which letters may occur at a particular position in the motif. There are four different notations for units:

• an uppercase letter (e.g. V) denotes that only this letter may occur at this position

• the lowercase letter x denotes that any letter may occur at this position

• one or more uppercase letters enclosed in square brackets (e.g. [AC]) denotes that one of these letters should occur at this position

• one or more uppercase letters enclosed in curly brackets (e.g. {ED}) denotes that none of these letters may occur at this position

The same uppercase letter may occur multiple times between a pair of square or curly brackets, but this doesn't change the pattern. Since each unit corresponds to a single position in a motif, the length of a motif that matches a pattern always equals the number of units in the pattern.

For example, the five-unit pattern [DJINN]-x-V-x-{SATAN} matches five-letter motifs whose first letter is a D, I, J or N, whose second and fourth letters can be any letter, whose third letter is a V, and whose fifth letter is no A, N, S or T. This pattern for example matches the motif DEVIL.

Your task:

• Write a function unit that takes a string $$u$$ (str). If the string $$u$$ does not describe a pattern with a single unit (see the four possible notations for units used by PROSITE), an AssertionError must be raised with the message invalid pattern. Otherwise the function must return a string (str) with all the uppercase letters in the alphabet that match unit $$u$$. Those letters must be listed in alphabetic order and there must be no duplicates.

• Write a function expand that takes a pattern $$p$$ (str). The function must return a list (list) containing for each unit in pattern $$p$$ a string (str) with all uppercase letters in the alphabet that match the unit. Those letters must be listed in alphabetic order and there must be no duplicates.

• Write a function ismotif that takes two arguments: i) a pattern $$p$$ (str) and ii) a string $$m$$ (str). The function must return a Boolean value (bool) that indicates if string $$m$$ matches pattern $$p$$. Pattern matching should make no distinction between uppercase and lowercase letters in string $$m$$. We also stress once more that a string by definition does not match a pattern whose number of units differs from the length of the string.

• Write a function motifs that takes two arguments: i) a pattern $$p$$ (str) and ii) a string $$s$$ (str). The function must return a set (set) containing all motifs in $$s$$. A motif is a sequence of letters in $$s$$ that matches pattern $$p$$. In the set, each motif is represented as a tuple (tuple) with two elements: i) the position (int) of the motif's first letter in string $$s$$ and ii) a string (str) with the letters of the motif. Pattern matching should make no distinction between uppercase and lowercase letters in string $$s$$. The positions of the characters in a string are numbered from left to right, starting from zero.

If the first argument passed these functions is no string (str) representing a valid pattern, an AssertionError must be raised with the message invalid pattern.

Example

>>> unit('V')
'V'
>>> unit('x')
'ABCDEFGHIJKLMNOPQRSTUVWXYZ'
>>> unit('[DJINN]')
'DIJN'
>>> unit('{SATAN}')
'BCDEFGHIJKLMOPQRUVWXYZ'
>>> unit('abc')
Traceback (most recent call last):
AssertionError: invalid pattern

>>> expand('[DJINN]-x-V-x-{SATAN}')
['DIJN', 'ABCDEFGHIJKLMNOPQRSTUVWXYZ', 'V', 'ABCDEFGHIJKLMNOPQRSTUVWXYZ', 'BCDEFGHIJKLMOPQRUVWXYZ']

>>> ismotif('[DJINN]-x-V-x-{SATAN}', 'DEVIL')
True
>>> ismotif('[DJINN]-x-V-x-{SATAN}', 'dive')
False
>>> ismotif('[DJINN]-x-V-x-{SATAN}', 'SATAN')
False

>>> motifs('[DJINN]-x-V-x-{SATAN}', 'GNFLEKVRMYPKLVDEVILFLHQDFPSDHMYAKVSATPVPKTPPVPWLLGTSNKSAKLAI')
{(14, 'DEVIL')}
>>> motifs('[DIL]-x-{AEIOU}-[AEIOU]-x-x-[ORS]', 'fanhymkkcllnpwsdetailslmmipiedqcwwffvluciferrhaqcnhgqdyytspmhinfernodkwcfiyveagp')
{(15, 'details'), (37, 'lucifer'), (61, 'inferno')}