Bacterial Gene Finding and Glimmer(also Archaeal and viral gene finding)

Arthur L. Delcher and Steven SalzbergCenter for Bioinformatics and Computational Biology

University of Maryland

Outline• A (very) brief overview of microbial gene-finding

– Codon composition methods– GeneMark: Markov models

• Glimmer1 & 2– Interpolated Markov Model (IMM)– Interpolated Context Model (ICM)

• Glimmer3– Reducing false positives– Improving coding initiation site predictions– Running Glimmer3

Step One• Find open reading frames (ORFs).

…TAGAAAAATGGCTCTTTAGATAAATTTCATGAAAAATATTGA…

Stopcodon

Stopcodon

Step One• Find open reading frames (ORFs).

• But ORFs generally overlap …

…TAGAAAAATGGCTCTTTAGATAAATTTCATGAAAAATATTGA…

Stopcodon

Stopcodon

…ATCTTTTTACCGAGAAATCTATTTAAAGTACTTTTTATAACT…

ShiftedStop

Stopcodon

Reversestrand

Campylobacter jejuni RM1221 30.3%GC

All ORFs on both strands shown- color indicates reading frame

Longest ORFs likely to be protein-coding genes

Note the low GC content

Campylobacter jejuni RM1221 30.3%GC

Purple lines are the predicted genes

Purple ORFs show annotated (“true”) genes

Campylobacter jejuni RM1221 30.3%GC

Mycobacterium smegmatis MC2 67.4%GC

Note what happens in a high-GC genome

Campylobacter jejuni RM1221 30.3%GC

Mycobacterium smegmatis MC2 67.4%GC

Purple lines show annotated genes

The Problem

• Need to decide which orfs are genes.– Then figure out the coding start sites

• Can do homology searches but that won’t find novel genes– Besides, there are errors in the databases

• Generally can assume that there are some known genes to use as training set.– Or just find the obvious ones

Codon Composition

• Find patterns of nucleotides in known coding regions (assumed to be available).– Nucleotide distribution at 3 codon positions– Hexamers– GC-skew

• (G-C)/(G+C) computed in windows of size N– Amino-acid composition

• Use these to decide which orfs are genes.– Prefer longer orfs– Must deal with overlaps

Bacterial Replication

Early replication

Theta structure

Termination of Replication

E. coli

B. subtilis

Borrelia burgdorferi (Lyme disease pathogen)

GC-skew plot

Codon Composition

Nucleotide variation at codon position:Campylobacter jejuni

  Codon Position

  1 2 3

a 36% 36% 36%

c 13% 17% 9%

g 30% 14% 10%

t 21% 33% 44%

Mycobacterium smegmatis

  Codon Position

  1 2 3

a 19% 23% 6%

c 27% 28% 48%

g 42% 20% 39%

t 12% 28% 7%

Codon-Composition Gene Finders• ZCURVE

– Guo, Ou & Zhang, NAR 31, 2003– Based on nucleotide and di-nucleotide frequency in

codons– Uses Z-transform and Fisher linear discriminant

• MED– Ouyang, Zhu, Wang & She, JBCB 2(2) 2004– Based on amino-acid frequencies– Uses nearest-neighbor classification on entropies

Probabilistic Methods

• Create models that have a probability of generating any given sequence.

• Train the models using examples of the types of sequences to generate.

• The “score” of an orf is the probability of the model generating it.– Can also use a negative model (i.e., a model of non-

orfs) and make the score be the ratio of the probabilities (i.e., the odds) of the two models.

– Use logs to avoid underflow

Fixed-Order Markov Models

• k th-order Markov model bases the probability of an event on the preceding k events.

• Example: With a 3rd-order model the probability of this sequence:

would be:

{Context

(G | CTA) (A | TAG) (T | AGA)P P P⋅ ⋅L L

}Context

CTAGATL L

Target

Target

Fixed-Order Markov Models

• Advantages:– Easy to train. Count frequencies of (k+1)-mers in

training data.– Easy to compute probability of sequence.

• Disadvantages:– Many (k+1)-mers may be undersampled in training

data.– Models data as fixed-length chunks.

TargetFixed-LengthContext

GeneMark

• Borodovsky & McIninch, Comp. Chem 17, 1993.

• Uses 5th-order Markov model.• Model is 3-periodic, i.e., a separate model for

each nucleotide position in the codon.• DNA region gets 7 scores: 6 reading frames &

non-coding―high score wins.• Lukashin & Borodovsky, Nucl. Acids Res. 26,

1998 is the HMM version.

Interpolated Markov Models (IMM)

• Introduced in Glimmer 1.0Salzberg, Delcher, Kasif & White, NAR 26, 1998.

• Probability of the target position depends on a variable number of previous positions (sometimes 2 bases, sometimes 3, 4, etc.)

• How many is determined by the specific context.• E.g., for context ggtta the next position might

depend on previous 3 bases tta .

But for context catta all 5 bases might be used.

ggtta

Real IMMs

• Model has additional probabilities, λ, that determine which parts of the context to use.

• E.g., the probability of g occurring after context atca is:

(atca) (g | atca) (1 (atca))[ (tca) (g | tca) (1 (tca))[ (ca) (g | ca) (1 (ca))[ (a) (g | a) (1 (a)) (g)]]]

PP

PP

P

λλ λλ λλ λλ

+ −+ −+ −+ −

Real IMMs• Result is a linear combination of different

Markov orders:

where

• Can view this as interpolating the results of different-order models.

• The probability of a sequence is still the probability of the bases in the sequence.

4 3 2

1 0

(g | atca) (g | tca) (g | ca)(g | a) (g)

b P b P b Pb P b P+ +

+ +

0 1 2 3 4 1b b b b b+ + + + =

Real IMMs

• Problem: How to determine the λ’s (or equivalently the bj’s)?

• Traditionally done with EM algorithm using cross-validation (deleted estimation).– Slow– Hard to understand results– Overtraining can be a problem

• We will cover EM later as part of HMMs

Glimmer IMM

• Glimmer assumes:– Longer context is always better– Only reason not to use it is undersampling in training

data.

• If sequence occurs frequently enough in training data, use it, i.e.,

• Otherwise, use frequency and χ2 significance to set λ.

• Interpolation is always between only 2 adjacent model lengths.

1λ =

More Precisely• Suppose context of length k+1 occurs a times, a<400,

with target distribution D1; and context of length k occurs ≥400 times, with target distribution D2

• Let p be the χ2 probability that D1 differs from D2

• Then the interpolated distribution will be:

1 21400 400

pa paD D⎛ ⎞ ⎛ ⎞+ −⎜ ⎟ ⎜ ⎟

⎝ ⎠ ⎝ ⎠

This formula computes the probability of a base B at any position in a sequence, given the context preceding that position

This formula is repeatedly invoked for all positions in an ORF

IMMs vs Fixed-Order Models• Performance

– IMM generally should do at least as well as a fixed-order model.

– Some risk of overtraining.

• IMM result can be stored and used like a fixed-order model.

• IMM will be somewhat slower to train and will use more memory.

TargetVariable-LengthContext

Interpolated Context Model (ICM)

• Introduced in Glimmer 2.0 Delcher, Harmon, et al., Nucl. Acids Res. 27, 1999.

• Doesn’t require adjacent bases in the window preceding the target position.

• Choose set of positions that are most informative about the target position.

TargetVariable-PositionContext

ICM• For all windows compare distribution at each context position

with target position

• Choose position with max mutual information

( , )( ; ) ( , ) log

( ) ( )x y

p x yI X Y p x y

p x p y=∑∑

Compare

ICM

• Continue for windows with fixed base at chosen positions

• Recurse until too few training windows– Result is a tree—depth is # of context positions used

• Then same interpolation as IMM, between node and parent in tree

Compare

Sample ICM Modelver = 2.00 len = 12 depth = 7 periodicity = 3 nodes = 21845 0 ---|---|---|*-? 0.0260 0.225 0.240 0.358 0.177 1 ---|---|---|a*? 0.0769 0.243 0.165 0.501 0.092 2 ---|---|---|c*? 0.0243 0.237 0.294 0.264 0.205 3 ---|---|---|g*? 0.0597 0.219 0.240 0.407 0.134 4 ---|---|---|t*? 0.0277 0.209 0.245 0.291 0.256 5 ---|---|--*|aa? 0.0051 0.320 0.202 0.478 0.000 6 ---|---|--*|ac? 0.0046 0.195 0.118 0.541 0.146 7 ---|---|--*|ag? 0.0101 0.180 0.207 0.613 0.000 8 ---|---|*--|at? 0.0037 0.236 0.147 0.400 0.217 9 ---|---|--*|ca? 0.0019 0.199 0.246 0.303 0.253 10 ---|---|--*|cc? 0.0090 0.297 0.189 0.308 0.207 11 ---|---|--*|cg? 0.0035 0.180 0.406 0.267 0.148 12 ---|---|--*|ct? 0.0083 0.279 0.327 0.189 0.206 13 ---|---|--*|ga? 0.0057 0.277 0.326 0.397 0.000 14 ---|---|--*|gc? 0.0057 0.233 0.158 0.473 0.136 15 ---|---|--*|gg? 0.0056 0.119 0.252 0.417 0.213 16 ---|---|--*|gt? 0.0096 0.207 0.232 0.359 0.203 17 ---|---|--*|ta? 0.0034 0.205 0.170 0.400 0.224 18 ---|---|--*|tc? 0.0062 0.179 0.238 0.290 0.293 19 ---|---|--*|tg? 0.0052 0.183 0.338 0.323 0.156 20 ---|---|-*-|tt? 0.0076 0.244 0.244 0.194 0.318 21 ---|---|-*a|aa? 0.0035 0.376 0.199 0.425 0.000 22 ---|---|-*c|aa? 0.0037 0.313 0.197 0.490 0.000 23 ---|---|-*g|aa? 0.0052 0.283 0.199 0.517 0.000 24 ---|--*|--t|aa? 0.0060 0.259 0.231 0.510 0.000 25 ---|---|-*a|ac? 0.0031 0.176 0.138 0.519 0.166

ICM

• ICM’s not just for modeling genes• Can use to model any set of training

sequences– Doesn’t even need to be DNA

• Have used recently to finding contaminant sequences in shotgun sequencing projects.– Used a non-periodic (i.e., homogeneous) model

Fixed-Length Sequences and ICMs

• Array of ICM’s―a different one for each position in fixed-length sequence.

• Can model fixed regions around transcription start sites or splice sites.

• Positions in region can be permuted.

Overlapping Orfs• Glimmer1 & 2 used rules.• For overlapping orfs A and B, the overlap region AB is

scored separately:– If AB scores higher in A’s reading frame, and A is longer than B,

then reject B.– If AB scores higher in B’s reading frame, and B is longer than A,

then reject A.– Otherwise, output both A and B with a “suspicious” tag.

• Also try to move start site to eliminate overlaps.

• Leads to high false-positive rate, especially in high-GC genomes.

Glimmer 2.0 Overlap Comments

OrfID Start End Frame Len Score Comments 2 499 1689 [+1 L=1191 r=-1.151] [ShadowedBy #3] 3 1977 418 [-1 L=1560 r=-1.317] [Contains #2] [LowScoreBy #4 L=257 S=0] 4 1721 2611 [+2 L= 891 r=-1.156] [OlapWith #3 L=257 S=99] 5 2624 3775 [+2 L=1152 r=-1.184] 7 3775 4356 [+1 L= 582 r=-1.223] [DelayedBy #5 L=216] 8 4501 6615 [+1 L=2115 r=-1.181] [OlapWith #9 L=2103 S=99] 9 6633 4513 [-1 L=2121 r=-1.365] [LowScoreBy #8 L=2103 S=0] 10 6648 9173 [+3 L=2526 r=-1.155] 11 9229 10008 [+1 L= 780 r=-1.217] 12 10411 11208 [+1 L= 798 r=-1.192] 13 11215 12243 [+1 L=1029 r=-1.165] [ShorterThan #15 L=865 S=99] 15 12827 11379 [-3 L=1449 r=-1.295] [LowScoreBy #13 L=865 S=0] [LowScoreBy #16 16 12243 13298 [+3 L=1056 r=-1.228] [OlapWith #15 L=585 S=99] [DelayedBy #13 L= 17 13298 14137 [+2 L= 840 r=-1.161] 18 15143 14133 [-3 L=1011 r=-1.230] 19 15193 15519 [+1 L= 327 r=-1.284] 20 15519 17249 [+3 L=1731 r=-1.175] 21 17249 19015 [+2 L=1767 r=-1.266] [DelayedBy #20 L=1263] 23 19052 41620 [+2 L=22569 r=-1.144] 25 42693 41692 [-1 L=1002 r=-1.200] [ShadowedBy #26] 26 41623 43065 [+1 L=1443 r=-1.401] [Contains #25] [LowScoreBy #27 L=167 S=0] 27 42899 43351 [+2 L= 453 r=-1.261] [ShorterThan #26 L=167 S=99] 28 43351 44685 [+1 L=1335 r=-1.169] 29 45223 45747 [+1 L= 525 r=-1.153] 30 45261 44695 [-1 L= 567 r=-1.298] [DelayedBy #29 L=363] 31 46261 45857 [-2 L= 405 r=-1.275] 32 46701 46420 [-1 L= 282 r=-1.273] 33 46752 47543 [+3 L= 792 r=-1.178]

Glimmer3

• Uses a dynamic programming algorithm to choose the highest-scoring set of orfs and start sites.

• Not quite an HMM– Allows small overlaps between genes

• “small” is user-defined– Scores of genes are not necessarily probabilities.– Score includes component for likelihood of start

site

Reverse Scoring

• In Glimmer3 orfs are scored from 3’ end to 5’ end, i.e., from stop codon back toward start codon.

• Helps find the start site.– The start should appear near the peak of the

cumulative score in this direction.– Keeps the context part of the model entirely in the

coding portion of gene, which it was trained on.

Reverse Scoring

Finding Start Sites

• Can specify a position weight matrix (PWM) for the ribosome binding site.

• Used to boost the scoreof potential start sites that have a match.

• Would like to try:– A fixed-length ICM model of start sites.– A decision-tree model of start sites.– Hard to get enough reliable data.

• Glimmer2 had a hybridization-energy calculation with 16sRNA tail sequence that didn’t work well.

Glimmer3 vs. Glimmer2

Table 3. Probability models trained on the output of the long-orfs program. Predictions compared to genes with annotated function.

Table 4. Probability models trained on the output of the long-orfs program. Predictions compared to all annotated genes.

Other Glimmer3 Features• Can specify any set of start or stop codons

– Including by NCBI translation table #• Can specify list of “guaranteed” genes

– Or just orfs and let Glimmer choose the starts• Can specify genome regions to avoid

– Guarantee no prediction will overlap these regions– Useful for RNA genes (tRNAs, rRNAs)

• Output more meaningful orf scores.• Allow genes to extend beyond end of sequence

– important for annotation of incomplete genomes

Glimmer3 Output ----- Start ----- --- Length ---- -------------- Scores ------------ ID Frame of Orf of Gene Stop of Orf of Gene Raw Frame +1 +2 +3 -1 -2 -3 NC ... ... ... ... ... ... ... ... -2 10516 10459 10337 177 120 1.14 0 - - 99 - 0 - 0 -3 10787 10781 10629 156 150 -10.69 0 - - 99 - - 0 0 -3 11132 11120 11004 126 114 -13.54 0 - - 99 - - 0 0 -2 12058 12055 11936 120 117 -2.25 0 - - 99 - 0 - 0 -3 12437 12371 12249 186 120 -13.68 0 - - 99 0 - 0 00007 +3 8109 8142 12632 4521 4488 16.05 99 - - 99 - - - 00008 -2 12763 12724 12545 216 177 4.17 99 - - - - 99 - 0 +1 12850 12877 12996 144 117 -16.13 0 0 - 99 - - - 0 -2 13165 13036 12905 258 129 -1.31 0 - - 99 - 0 - 0 -3 13649 13634 13473 174 159 -7.11 0 - - 99 - 0 0 0 -2 13675 13663 13256 417 405 2.83 0 - - 99 - 0 - 0 -2 13972 13972 13850 120 120 4.25 0 - - 99 - 0 - 00009 +3 12633 12642 14087 1452 1443 15.20 99 - - 99 - - - 0 +1 14194 14323 14454 258 129 1.62 0 0 - - - - 99 00010 -3 14669 14663 14088 579 573 13.36 99 - - - - - 99 0 +1 14482 14548 14673 189 123 3.07 0 0 - - - - 99 0 +2 14570 14642 14806 234 162 -4.35 0 - 0 - - - - 990011 -2 14947 14935 14696 249 237 16.17 99 - - 0 - 99 - 00012 +3 14655 14718 14954 297 234 3.06 99 - - 99 - - - 0 -2 15115 15100 14975 138 123 -7.02 0 - - - - 0 - 99 +1 15004 15070 15288 282 216 -2.46 0 0 - - - - 99 0 +1 15364 15475 15594 228 117 -5.48 0 0 - - - - 99 00013 -3 15701 15671 15000 699 669 13.07 99 - - - - - 99 0 +3 15531 15591 15728 195 135 -8.84 0 - - 0 - - - 99 +1 15631 15649 15762 129 111 -0.69 3 3 - - - - - 96 -2 15922 15898 15719 201 177 -0.41 6 - - - - 6 - 93 -2 16561 16561 16307 252 252 1.73 0 - - 99 - 0 - 0 -2 16741 16711 16562 177 147 1.72 0 - - 99 - 0 - 0

Finding Initial Training Set• Glimmer1 & 2 have program long-orfs• It finds orfs longer than min-length that do not overlap

other such orfs.– Current version automatically finds min-length.

• Works OK for low- to medium-GC genomes• Terrible for high-GC genomes

– Up to half the orfs can be wrong.– Uses first possible start site―even if orf is correct much of

sequence isn’t.

• Can use codon composition information in Glimmer3 version (similar to MED).

Running Glimmer3

#1 Find long, non-overlapping orfs to use as a training setlong-orfs --no_header -t 1.0 tpall.1con tp.longorfs

#2 Extract the training sequences from the genome fileextract --nostop tpall.1con tp.longorfs > tp.train

#3 Build the icm from the training sequencesbuild-icm -r tp.icm < tp.train

#4 Run first Glimmerglimmer3 -o50 -g110 -t30 tpall.1con tp.icm tp.run1

#5 Get training coordinates from first predictionstail +2 tp.run1.predict > tp.coords

#6 Create a position weight matrix (PWM) from the regions# upstream of the start locations in tp.coordsupstream-coords.awk 25 0 tp.coords | extract tpall.1con - > tp.upstreamelph tp.upstream LEN=6 | get-motif-counts.awk > tp.motif

#7 Determine the distribution of start-codon usage in tp.coordsset startuse = `start-codon-distrib --3comma tpall.1con tp.coords`

#8 Run second Glimmerglimmer3 -o50 -g110 -t30 -b tp.motif -P $startuse tpall.1con tp.icm tp

A novel application of Glimmer• P. didemni is a

photosynthetic microbe that lives as an endosymbiont in the sea squirt > patella

• P. didemni can only be cultured in L. patella cells

L. patella (sea squirt)

A novel application of Glimmer• Generated 82,337 shotgun reads• Bacterial genome 5 Mb• Host genome estimated at 160 Mb• Depth of coverage therefore much greater for

bacterial contigs• Singleton reads primarily belong to host

A novel application of Glimmer• Create training sets by classifying reads from

scaffolds > 10kb as bacterial– 36,920 reads

• Reads where both read and mate were singletons were treated as sea squirt– 21,276 reads

• 21,141 reads unclassified

A novel application of Glimmer• Train a non-periodic IMM on both sets of data• 2 IMMs created• Then classify reads using the ratio of scores from

the two IMMs• In a 5-fold cross-validation, classification

accuracy was– 98.9% on P. didemni reads– 99.9% on L. patella reads

A novel application of Glimmer• Finally, re-assemble using ONLY bacterial reads• Original assembly:

– 65 scaffolds of 20 Kb or longer– total scaffold length 5.74 Mb

• Improved assembly:– 58 scaffolds of 20 Kb or longer– total scaffold length 5.84 Mb

Acknowledgements

Art DelcherSteven Salzberg

Owen White (TIGR)Simon Kasif (Boston U.)Doug Harmon (Loyola College)

Kirsten BratkeEdwin Powers (Johns Hopkins U.)Dan Haft (TIGR)Bill Nelson (TIGR)