BJ Kullback

BJ Strait

C Chiarabelli

C Papadimitriou

CE Shannon

CR Munteanu

D De Lucrezia

G Evangelista

M Jacob

O Weiss

PL Luisi

TG Dewey

The UniProt Consortium

SpringerPlus

English

Grzegorz Szoniec

Maciej J Ogorzalek

Crossref

SHORT REPORT Open AccessEntropy of never born protein sequencesGrzegorz Szoniec* and Maciej J OgorzalekAbstractBackground: A Never Born protein is a theoretical protein which does not occur in nature. The reason why someproteins were selected and some were not during evolution is not known. We applied information theory to findsimilarities and differences in information content in Never Born and natural proteins.Findings: Both block and relative entropies are similar what means that both protein kinds contain stronglyrandom sequences.An artificially generated Never Born protein sequence is closely as random as a natural one.Conclusions: Information theory approach suggests that protein selection during evolution was rather random/non-deterministic.Natural proteins have no noticeable unique features in information theory sense.Keywords: Never born protein, Block entropy, Relative entropy, Kullback-Leibler divergence, Origin of lifeIntroductionExisting and known proteins are only a small subset of allpossible sequences. Why were only some proteins selectedduring evolution? The reason is not known but two pos-sible ways are considered: deterministic and random. Toinvestigate theoretical sequences of amino acids a termNever Born Protein was introduced (Chiarabelli et al.2006). Since 2006 only a few papers about them have beenpublished. The most significant research has shown that20% of them fold (i.e. reach stable and functional 3Dstructure) in laboratory conditions (Chiarabelli et al. 2006)and a tool for generating sequences with no similarity tonatural proteins has been developed – Random Blast(Evangelista et al. 2007). The high folding ratio has beenpositively surprising and has abated opinion that existingproteins are the only stable and folding sequences. Sur-prisingly, as 1 out of 5 absolutely randomly generated pro-teins was a possibly useful one for living organisms. Theauthors did not expect so high percentage, furthermoretheir results came with doubts about correctness of theirapproach/methodology. Up to now this has been the mostimportant discovery in Never Born protein science.The question about proteins origin is still open. Thereare papers that proved natural and synthetic (random)proteins are not different (Jacob 1969; Luisi 2003) oronly slightly different from each other(Weiss et al.2000), there are also papers that proved these twogroups of proteins are significantly different and pro-tein selection during evolution was a driven process(Munteanu et al. 2008; De Lucrezia et al. 2012). The re-sults depend on methodology (which is not discussed herebecause of limited scope of this report) neverthelessanother open question is which approach should be con-sidered as more correct and reliable than others.Information theory (Shannon 1948) is applied to almostany branch of science. Information quantities i.e. Shannonentropy H (Shannon 1948) and Kullback–Leibler diver-gence (or relative entropy) DKL (Kullback & Leibler 1951)are defined asH ¼  ∑ipilog pið Þ ð1ÞDKL P Qk Þ ¼ ∑ipilog pi=qið Þð ð2ÞWhere P and Q are probability densities, P = {pi} andQ = {qi}. Shannon entropy is a measure of uncertainty inan outcome with probability pi and relative entropy is ameasure of similarity between two probability densities(it is not a true metric i.e. DKL(P||Q) is not equal to DKL(Q||P) except when P =Q).In protein science, information properties of naturalproteins were comprehensively studied (Strait & Dewey* Correspondence: myszonie@cyf-kr.edu.plInformation Technology Department, Faculty of Physics, Astronomy andApplied Computer Science, Jagiellonian University, 4 Reymonta Street,Cracow 30-059, Polanda SpringerOpen Journal© 2013 Szoniec and Ogorzałek; licensee Springer. This is an Open Access article distributed under the terms of the CreativeCommons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.Szoniec and Ogorzalek SpringerPlus 2013, 2:200http://www.springerplus.com/content/2/1/2001996) and further intensively developed e.g. (Dewey 1996).In this short report we apply some of those ideas to NeverBorn proteins and we show that protein picking duringevolution is closer to be a random/non-deterministicprocess. Our approach is strictly theoretical as (Strait &Dewey 1996).Methods and resultsNatural proteins were randomly picked from UniProtdatabase (The UniProt Consortium 2012). Never BornProteins were generated with Random Blast tool (in bothcases the number of sequences is 1250, in total around400,000 amino acids, sequences lengths vary from 61 toaround 1700 amino acids). Shannon entropies were cal-culated not only for every amino acid but also for blocks(block entropy (Papadimitriou et al. 2010)) of lengthfrom 2 to 20. Block entropy was calculated identicallylike Shannon entropy but probabilities refered to aminoacid subsequences (blocks) of a specific length. Probabi-lities were normalized over occurrences in all sequences(the data and the scripts are available at http://www.cyfronet.pl/~myszonie/ent). The results are presented inFigure 1 and Table 1.ConclusionsThe plot (Figure 1) proves that the values of entropy forboth groups of proteins are very close. It means that un-certainty or in other words a number of possible aminoacid combinations, is almost the same. This indicatesthat natural protein sequences are random like NeverBorn Protein sequences. Moreover, relative entropyvalues show that encoding a natural protein sequenceusing probability density of Never Born Proteins requiresonly a small excess of information (and vice versa). Sum-ming up the inferences, protein selection during evolu-tion is – in an information theory approach - closer tobe a random process than deterministic one what is in-line with (Jacob 1969; Jacob 2003; Weiss et al. 2000).There is still a doubt wheter that small difference doesnot play a key role.Competing interestsThe authors declare that they have no competing interests.Authors’ contributionsGS designed and carried out the research and drafted the manuscript. MJOsupervised the research. Both authors read and approved the final manuscript.AcknowledgementsThe author would like to acknowledge Dr. Marcin Krol (JagiellonianUniversity, Poland) for the discussion and Prof. Fabio Polticelli (Roma TreUniversity, Italy) for the Random Blast binaries.Received: 20 December 2012 Accepted: 15 March 2013Published: 30 April 2013ReferencesChiarabelli C et al (2006) On the folding frequency in a totally random library ofde novo proteins obtained by phage display. Chem Biodiver 3:840–859De Lucrezia D et al (2012) Do natural proteins differ from random sequencespolypeptides? Natural vs. random proteins classification using anevolutionary neural network. PLoS One 7:e36634Dewey TG (1996) Algorithmic complexity of a protein. Phys Rev E 54:R39–R41Evangelista G et al (2007) Randomblast a tool to generate random never bornprotein sequences. Bio-Algorithms and Med-Systems 5:27–31Jacob M (1969) On symmetry and function of biological systems. In: Engstrom A,Strondberg B (eds) Wiley Interscience, New YorkKullback BJ, Leibler RA (1951) On information and sufficiency. Ann Math Statist22:79–86Luisi PL (2003) Contingency and determinism. Phil Trans R Soc A 361:1141–1147Munteanu CR et al (2008) Natural/random protein classification models based onstar network topological indices. J Theor Biol 254:775–783Papadimitriou C et al (2010) Entropy analysis of natural language written texts.Physica A 389:3260–3266Shannon CE (1948) A mathematical theory of communication. Bell Labs Techn J27:379–423Strait BJ, Dewey TG (1996) The Shannon information entropy of proteinsequences. Biophys J 71:148–155The UniProt Consortium (2012) Reorganizing the protein space at the UniversalProtein Resource (UniProt). Nucleic Acids Res 40:D71–D75Weiss O et al (2000) Information content of protein sequences. J Math Biol206:379–386doi:10.1186/2193-1801-2-200Cite this article as: Szoniec and Ogorzalek: Entropy of never bornprotein sequences. SpringerPlus 2013 2:200.Figure 1 Block entropies Hn (in bits) vs. block lengths n ofnever born (blue) and natural (purple) proteins.Table 1 Relative entropies between never born andnatural proteinsDKL(PNBP||QNP) DKL(PNP||QNBP)0.1554 0.1307Szoniec and Ogorzalek SpringerPlus 2013, 2:200 Page 2 of 2http://www.springerplus.com/content/2/1/200

Entropy of never born protein sequences

https://springerplus.springeropen.com/track/pdf/10.1186/2193-1801-2-200?site=springerplus.springeropen.com

Entropy of never born protein sequences

Abstract

Similar works

Full text

Available Versions

Crossref