Trees and Sequence Space

J. Peter Gogarten

University of ConnecticutDept. of Molecular and Cell Biology

Scu lptur e at R

oyal Bot anical G

ardens, Kew

Ways to construct Protein Space

Construction of sequence space from (Eigen et al. 1988) illustrating the construction of a high dimensional sequence space. Each additional sequence position adds another dimension, doubling the diagram for the shorter sequence. Shown is the progression from a single sequence position (line) to a tetramer (hypercube). A four (or twenty) letter code can be accommodated either through allowing four (or twenty) values for each dimension (Rechenberg 1973; Casari et al. 1995), or through additional dimensions (Eigen and Winkler-Oswatitsch 1992).Eigen, M. and R. Winkler-Oswatitsch (1992). Steps Towards Life: A Perspective on Evolution. Oxford; New York, Oxford University Press. Eigen, M., R. Winkler-Oswatitsch and A. Dress (1988). "Statistical geometry in sequence space: a method of quantitative comparative sequence analysis." Proc Natl Acad Sci U S A 85(16): 5913-7 Casari, G., C. Sander and A. Valencia (1995). "A method to predict functional residues in proteins." Nat Struct Biol 2(2): 171-8 Rechenberg, I. (1973). Evolutionsstrategie; Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Stuttgart-Bad Cannstatt, Frommann-Holzboog.

Diversion: From Multidimensional Sequence Space

to Fractals

one symbol -> 1D

coordinate of dimension = pattern length

Two symbols -> Dimension = length of pattern

length 1 = 1D:

Two symbols -> Dimension = length of pattern

length 2 = 2D:

dimensions correspond to positionFor each dimension two possibiities

Note: Here is a possible bifurcation: a larger alphabet could be represented as more choices along the axis of position!

Two symbols -> Dimension = length of pattern

length 3 = 3D:

Two symbols -> Dimension = length of pattern

length 4 = 4D:

aka Hypercube

Two symbols -> Dimension = length of pattern

Three Symbols (the other fork)

Four Symbols:

I.e.: with an alphabet of 4, we have a hypercube (4D) already with a pattern size of 2, provided we stick to a binary pattern in each dimension.

hypercubes at 2 and 4 alphabets

2 character alphabet, pattern size 4

4 character alphabet, pattern size 2

Three Symbols Alphabet suggests fractal representation

3 fractal

enlarge fill in

outer pattern repeats inner pattern= self similar= fractal

3 character alphabet3 pattern fractal

3 character alphapet4 pattern fractal Conjecture:

For n -> infinity, the fractal midght fill a 2D triangle

Note: check Mandelbrot

Same for 4 character alphabet

1 position

2 positions

3 positions

4 character alphabet continued

(with cheating I didn’t actually add beads)

4 positions

4 character alphabet continued

(with cheating I didn’t actually add beads)

5 positions

4 character alphabet continued

(with cheating I didn’t actually add beads)

6 positions

4 character alphabet continued

(with cheating I didn’t actually add beads)

7 positions

Animated GIf 1-12 positions

Protein Space in JalView

Alignment of V F A ATPase ATP binding SU(catalytic and non-catalytic SU)

UPGMA tree of V F A ATPase ATP binding SU with line dropped to partition (and colour) the 4 SU types (VA cat and non cat, F cat and non cat). Note that details of the tree $%#&@.

PCA analysis of V F A ATPase ATP binding SU using colours from the UPGMA tree

Same PCA analysis of V F A ATPase ATP binding SU using colours from the UPGMA tree, but turned slightly. (Giardia A SU selected in grey.)

Same PCA analysis of V F A ATPase ATP binding SU Using colours from the UPGMA tree, but replacing the 1st with the 5th axis. (Eukaryotic A SU selected in grey.)

Same PCA analysis of V F A ATPase ATP binding SU Using colours from the UPGMA tree, but replacing the 1st with the 6th axis. (Eukaryotic B SU selected in grey - forgot rice.)

Problems• Jalview’s approach requires an alignment - only

homologous sequences can be depicted in the same space

• Solution: One could use pattern absence / presence as coordinates

muscle alignment

muscle vs clustal

more on alignment programs (statalign, pileup, SAM) here

the same region using tcoffee with default settings

more on alignment programs (statalign, pileup, SAM) here

Sequence editors and viewers

Jalview Homepage, Description Jalview as Java Web Start Application (other JAVA applications are here)

Jalview is easy to install and run. Test file is here (ATPase subunits)(Intro to ATPases: 1bmf in spdbv)(gif of rotation here, movies of the rotation are here and here) (Load all.txt into Jalview,

colour options, mouse use, PID tree,Principle component analysis -> sequence space)More on sequence space here

seaview – phylo_winAnother useful multiple alignment editor is seaview, the companion sequence editor to phylo_win. It runs on PC and most unix flavors, and is the easiest way to get alignments into phylo_win.

Why phylogenetic reconstruction of molecular evolution?

•Systematic classification of organisms. E.g.: •Who were the first angiosperms? (i.e. where are the first angiosperms located relative to present day angiosperms?)•Where in the tree of life is the last common ancestor located?

•Evolution of molecules. E.g.: •domain shuffling, •reassignment of function, •gene duplications, •horizontal gene transfer, •drug targets, •detection of genes that drive evolution of a species/population (e.g. influenca virus, see here for more examples)

Small subunit ribosomal RNA (16S) based tree of life. Carl Woese, George Fox, and many others.

Phylogenetic analysis is an inference of evolutionary relationships between organisms. Phylogenetics tries to answer the question “How did groups of organisms come into existence?”

Those relationships are usually represented by tree-like diagrams.

Note: the assumption of a tree-like process of evolution is controversial!

Steps of the phylogenetic analysis

trees:

an unrooted tree

a branch, a split, or a bipartition sometimes represented as * * * . . . or . . . * * * with sequences in order 1 2 3 A B C

a leaf, or an OTU attached to a terminal branch

#1

#2#3

#B#A

#C

#1 #2 #3 #A #B#C

rooted trees

#1 #2 #3 #A #B

#C

molecular phylogenies are usually scaled with respect to substitutions and not with respect to

time.

What is in a tree?Trees form molecular data are usually calculated as unrooted trees (at least they should be - if they are not this is usually a mistake). To root a tree you either can assume a molecular clock (substitutions occur at a constant rate, again this assumption is usually not warranted and needs to be tested), or you can use an outgroup (i.e. something that you know forms the deepest branch).

For example, to root a phylogeny of birds, you could use the homologous characters from a reptile as outgroup; to find the root in a tree depicting the relations between different human mitochondria, you could use the mitochondria from chimpanzees or from Neanderthals as an outgroup; to root a phylogeny of alpha hemoglobins you could use a beta hemoglobin sequence, or a myoglobin sequence as outgroup.

Trees have a branching pattern (also called the topology), and branch lengths.

Often the branch lengths are ignored in depicting trees (these trees often are referred to as cladograms - note that cladograms should be considered rooted). You can swap branches attached to a node, and in an unrooted you can depict the tree as rooted in any branch you like without changing the tree.

Test:Which of these trees is different?

More tests here

homologyTwo sequences are homologous, if there existed an ancestral molecule in the past that is ancestral to both of the sequences

Types of Homology

Orthologs: “deepest” bifurcation in molecular tree reflects speciation. These are the molecules people interested in the taxonomic classification of organisms want to study.

Paralogs: “deepest” bifurcation in molecular tree reflects gene duplication. The study of paralogs and their distribution in genomes provides clues on the way genomes evolved. Gen and genome duplication have emerged as the most important pathway to molecular innovation, including the evolution of developmental pathways.

Xenologs: gene was obtained by organism through horizontal transfer. The classic example for Xenologs are antibiotic resistance genes, but the history of many other molecules also fits into this category: inteins, selfsplicing introns, transposable elements, ion pumps, other transporters,

Synologs: genes ended up in one organism through fusion of lineages. The paradigm are genes that were transferred into the eukaryotic cell together with the endosymbionts that evolved into mitochondria and plastids (the -logs are often spelled with "ue" like in orthologues)

see Fitch's article in TIG 2000 for more discussion.

•Branches, splits, bipartitions•In a rooted tree: clades•Mono-, Para-, polyphyletic groups, cladists and a natural taxonomy

Terminology

The term cladogram refers to a strictly bifurcating diagram, where each clade is defined by a common ancestor that only gives rise to members of this clade. I.e., a clade is monophyletic (derived from one ancestor) as opposed to polyphyletic (derived from many ancestors). (note you need to know where the root is!)

A clade is recognized and defined by shared derived characters (= synapomorphies). Shared primitive characters (= sympleisiomorphies , aternativie spelling is symplesiomorphies) do not define a clade. (see in class example drawing ala Hennig).

To use these terms you need to have polarized characters; for most molecular characters you don't know which state is primitive and which is derived (exceptions:....).

The Coral of Life (Darwin)

Coalescence – the

process of tracing

lineages backwards

in time to their

common ancestors.

Every two extant

lineages coalesce

to their most recent

common ancestor.

Eventually, all

lineages coalesce

to the cenancestor.

t/2(Kingman, 1982)

Illustration is from J. Felsenstein, “Inferring Phylogenies”, Sinauer, 2003

Coalescence of ORGANISMAL and MOLECULAR Lineages

•20 lineages

•One extinction and one speciation event per generation

•One horizontal transfer event once in 5 generations (I.e., speciation events)

RED: organismal lineages (no HGT)BLUE: molecular lineages (with HGT)GRAY: extinct lineages

•20 lineages

•One extinction and one speciation event per generation

•One horizontal transfer event once in 5 generations (I.e., speciation events)

RED: organismal lineages (no HGT)BLUE: molecular lineages (with HGT)GRAY: extinct lineages

RESULTS:

•Most recent common ancestors are different for organismal and molecular phylogenies

•Different coalescence times

•Long coalescence time for the last two lineages

RESULTS:

•Most recent common ancestors are different for organismal and molecular phylogenies

•Different coalescence times

•Long coalescence time for the last two lineages

Time

Adam and Eve never met

Albrecht Dürer, The Fall of Man, 1504

MitochondrialEve

Y chromosomeAdam

Lived approximately

50,000 years ago

Lived 166,000-249,000

years ago

Thomson, R. et al. (2000) Proc Natl Acad Sci U S A 97, 7360-5

Underhill, P.A. et al. (2000) Nat Genet 26, 358-61

Cann, R.L. et al. (1987) Nature 325, 31-6

Vigilant, L. et al. (1991) Science 253, 1503-7

The same is true for ancestral rRNAs, EF, ATPases!

EX

TA

NT

LIN

EA

GE

S F

OR

TH

E S

IMU

LAT

ION

S O

F 5

0 LI

NE

AG

ES

Modified from Zhaxybayeva and Gogarten (2004), TIGs 20, 182-187

green: organismal lineages ; red: molecular lineages (with gene transfer)

Lineages Through Time Plot

10 simulations of organismal evolution assuming a constant number of species (200) throughout the simulation; 1 speciation and 1 extinction per time step. (green O)

25 gene histories simulated for each organismal history assuming 1 HGT per 10 speciation events (red x)

log

(n

umb

er o

f su

rviv

ing

line

age

s)

Bacterial 16SrRNA based phylogeny (from P. D. Schloss and J. Handelsman, Microbiology and Molecular Biology Reviews,

December 2004.)

The deviation from the “long branches at the base” pattern could be due to • under sampling• an actual radiation

• due to an invention that was not transferred• following a mass extinction

More Terminology

Related terms: autapomorphy = a derived character that is only present in one group; an autapomorphic character does not tell us anything about the relationship of the group that has this character ot other groups.

homoplasy = a derived character that was derived twice independently (convergent evolution). Note that the characters in question might still be homologous (e.g. a position in a sequence alignment, frontlimbs turned into wings in birds and bats).

paraphyletic = a taxonomic group that is defined by a common ancestor, however, the common ancestor of this group also has decendants that do not belong to this taxonomic group. Many systematists despise paraphyletic groups (and consider them to be polyphyletic). Examples for paraphyletic groups are reptiles and protists. Many consider the archaea to be paraphyletic as well.

holophyletic = same as above, but the common ancestor gave rise only to members of the group.