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| 12 | <DIV ALIGN=RIGHT> |
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| 13 | version 3.6 |
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| 14 | </DIV> |
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| 15 | <P> |
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| 16 | <DIV ALIGN=CENTER> |
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| 17 | <H1>PROTDIST -- Program to compute distance matrix<BR> |
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| 18 | from protein sequences</H1> |
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| 19 | </DIV> |
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| 20 | <P> |
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| 21 | © Copyright 1993, 2000-2002 by the University of Washington. Permission |
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| 22 | is granted to copy |
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| 23 | this document provided that no fee is charged for it and that this copyright |
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| 24 | notice is not removed. |
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| 25 | <P> |
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| 26 | This program uses protein sequences to compute a distance matrix, under |
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| 27 | four different models of amino acid replacement. It can also |
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| 28 | compute a table of similarity between the amino acid sequences. |
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| 29 | The distance for each |
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| 30 | pair of species estimates the total branch length between the two species, and |
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| 31 | can be used in the distance matrix programs FITCH, KITSCH or NEIGHBOR. This |
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| 32 | is an alternative to use of the sequence data itself in the |
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| 33 | parsimony program PROTPARS. |
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| 34 | <P> |
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| 35 | The program reads in protein sequences and writes an output file containing |
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| 36 | the distance matrix or similarity table. The four models of amino acid |
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| 37 | substitution are |
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| 38 | one which is based on the Jones, Taylor and Thornton (1992) model of |
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| 39 | amino acid change, one based on the PAM matrixes of Margaret Dayhoff, one due to |
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| 40 | Kimura (1983) which approximates it based simply on the fraction of |
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| 41 | similar amino acids, and one based on a model in which the amino acids are |
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| 42 | divided up into groups, with change occurring based on the genetic code |
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| 43 | but with greater difficulty of changing between groups. The program correctly |
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| 44 | takes into account a variety of sequence ambiguities. |
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| 45 | <P> |
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| 46 | The four methods are: |
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| 47 | <P> |
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| 48 | (1) The Dayhoff PAM matrix. This uses Dayhoff's PAM 001 matrix from |
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| 49 | Dayhoff (1979), page 348. The PAM model is an empirical one that |
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| 50 | scales probabilities of change from one amino acid to another in |
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| 51 | terms of a unit which is an expected 1% change between two amino acid |
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| 52 | sequences. The PAM 001 matrix is used to make a transition probability |
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| 53 | matrix which allows prediction of the probability of changing from any |
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| 54 | one amino acid to any other, and also predicts equilibrium amino acid |
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| 55 | composition. The program assumes that these probabilities are correct |
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| 56 | and bases its computations of distance on them. The distance that is |
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| 57 | computed is scaled in units of expected fraction of amino acids |
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| 58 | changed. This is a unit of 100 PAM's. |
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| 59 | <P> |
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| 60 | (2) The Jones-Taylor-Thornton model. This is similar to the Dayhoff |
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| 61 | PAM model, except that it is based on a recounting of the number of |
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| 62 | observed changes in amino acids by Jones, Taylor, and Thornton (1992). |
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| 63 | They used a much larger sample of protein sequences than did Dayhoff. |
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| 64 | The distance is scaled in units of the expected fraction of amino acids |
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| 65 | changed (100 PAM's). Because its sample is so much larger this |
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| 66 | model is to be preferred over the original Dayhoff PAM model. It |
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| 67 | is the default model in this program. |
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| 68 | <P> |
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| 69 | (3) Kimura's distance. This is a rough-and-ready distance formula for |
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| 70 | approximating PAM distance by simply measuring the fraction of amino |
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| 71 | acids, p, that differs between two sequences and computing the |
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| 72 | distance as (Kimura, 1983) |
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| 73 | <P> |
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| 74 | D = - log<SUB>e</SUB> ( 1 - p - 0.2 p<SUP>2</SUP> ). |
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| 75 | <P> |
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| 76 | This is very quick to do but has some obvious limitations. It does not |
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| 77 | take into account which amino acids differ or to what amino acids |
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| 78 | they change, so some information is lost. The units of the distance |
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| 79 | measure are fraction of amino acids differing, as also in the case of |
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| 80 | the PAM distance. If the fraction of amino acids differing gets larger |
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| 81 | than 0.8541 the distance becomes infinite. |
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| 82 | <P> |
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| 83 | (4) The Categories distance. This is my own concoction. I imagined |
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| 84 | a nucleotide sequence changing according to Kimura's 2-parameter model, |
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| 85 | with the exception that some changes of amino acids are less likely than |
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| 86 | others. The amino acids are grouped into a series of categories. Any |
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| 87 | base change that does not change which category the amino acid is in is |
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| 88 | allowed, but if an amino acid changes category this is allowed only a |
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| 89 | certain fraction of the time. The fraction is called the "ease" and |
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| 90 | there is a parameter for it, which is 1.0 when all changes are allowed |
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| 91 | and near 0.0 when changes between categories are nearly impossible. |
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| 92 | <P> |
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| 93 | In this option I have allowed the user to select the Transition/Transversion |
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| 94 | ratio, which of several genetic codes to use, and which categorization |
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| 95 | of amino acids to use. There are three of them, a somewhat random sample: |
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| 96 | <P> |
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| 97 | <DL COMPACT> |
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| 98 | <DT>(a)</DT> <DD>The George-Hunt-Barker (1988) classification of amino acids,</DD> |
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| 99 | <DT>(b)</DT> <DD>A classification provided by my colleague Ben Hall when I asked him for one,</DD> |
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| 100 | <DT>(c)</DT> <DD>One I found in an old "baby biochemistry" book (Conn and Stumpf, 1963), |
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| 101 | which contains most of the biochemistry I was ever taught, and all that I ever |
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| 102 | learned.</DD> |
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| 103 | </DL> |
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| 104 | <P> |
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| 105 | Interestingly enough, all of them are consisten with the same linear |
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| 106 | ordering of amino acids, which they divide up in different ways. For the |
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| 107 | Categories model I have set as default the George/Hunt/Barker classification |
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| 108 | with the "ease" parameter set to 0.457 which is approximately the value |
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| 109 | implied by the empirical rates in the Dayhoff PAM matrix. |
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| 110 | <P> |
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| 111 | The method uses, as I have noted, Kimura's (1980) 2-parameter model of DNA |
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| 112 | change. The Kimura "2-parameter" model allows |
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| 113 | for a difference between transition and transversion rates. Its transition |
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| 114 | probability matrix for a short interval of time is: |
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| 115 | <P> |
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| 116 | <PRE> |
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| 117 | To: A G C T |
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| 118 | --------------------------------- |
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| 119 | A | 1-a-2b a b b |
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| 120 | From: G | a 1-a-2b b b |
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| 121 | C | b b 1-a-2b a |
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| 122 | T | b b a 1-a-2b |
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| 123 | </PRE> |
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| 124 | <P> |
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| 125 | where <EM>a</EM> is <EM>u dt</EM>, the product of the rate of transitions per unit time and <EM>dt</EM> |
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| 126 | is the length <EM>dt</EM> of the time interval, and <EM>b</EM> is <EM>v dt</EM>, the product of half the |
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| 127 | rate of transversions (i.e., the rate of a specific transversion) |
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| 128 | and the length dt of the time interval. |
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| 129 | <P> |
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| 130 | Each distance that is calculated is an estimate, from that particular pair of |
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| 131 | species, of the divergence time between those two species. The Kimura |
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| 132 | distance is straightforward to compute. The other two are considerably |
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| 133 | slower, and they look at all positions, and find that distance which |
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| 134 | makes the likelihood highest. This likelihood is in effect the length of |
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| 135 | the internal branch in a two-species tree that connects these two |
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| 136 | species. Its likelihood is just the product, under the model, of the |
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| 137 | probabilities of each position having the (one or) two amino acids that |
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| 138 | are actually found. This is fairly slow to compute. |
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| 139 | <P> |
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| 140 | The computation proceeds from an eigenanalysis (spectral decomposition) |
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| 141 | of the transition probability matrix. In the case of the PAM 001 matrix |
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| 142 | the eigenvalues and eigenvectors are precomputed and are hard-coded |
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| 143 | into the program in over 400 statements. In the case of the Categories |
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| 144 | model the program computes the eigenvalues and eigenvectors itself, which |
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| 145 | will add a delay. But the delay is independent of the number of species |
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| 146 | as the calculation is done only once, at the outset. |
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| 147 | <P> |
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| 148 | The actual algorithm for estimating the distance is in both cases a |
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| 149 | bisection algorithm which tries to find the point at which the derivative |
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| 150 | os the likelihood is zero. Some of the kinds of ambiguous amino acids |
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| 151 | like "glx" are correctly taken into account. However, gaps are treated |
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| 152 | as if they are unkown nucleotides, which means those positions get dropped |
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| 153 | from that particular comparison. However, they are not dropped from the |
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| 154 | whole analysis. You need not eliminate regions containing gaps, as long |
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| 155 | as you are reasonably sure of the alignment there. |
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| 156 | <P> |
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| 157 | Note that there is an |
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| 158 | assumption that we are looking at all positions, including those |
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| 159 | that have not changed at all. It is important not to restrict attention |
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| 160 | to some positions based on whether or not they have changed; doing that |
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| 161 | would bias the distances by making them too large, and that in turn |
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| 162 | would cause the distances |
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| 163 | to misinterpret the meaning of those positions that |
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| 164 | had changed. |
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| 165 | <P> |
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| 166 | The program can now correct distances for unequal rates of change at different |
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| 167 | amino acid positions. This correction, which was introduced for DNA |
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| 168 | sequences by Jin and Nei (1990), assumes that the distribution of rates |
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| 169 | of change among amino acid positions follows a Gamma distribution. The |
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| 170 | user is asked for the value of a parameter that determines the amount of |
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| 171 | variation of rates among amino acid positions. Instead of the more |
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| 172 | widely-known coefficient alpha, PROTDIST uses the coefficient of variation |
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| 173 | (ratio of the standard deviation to the mean) of rates among amino acid |
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| 174 | positions. . So if there is 20% variation in rates, the CV is |
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| 175 | is 0.20. The square of the C.V. is also the reciprocal of the |
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| 176 | better-known "shape parameter", alpha, of the Gamma |
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| 177 | distribution, so in this case the shape parameter alpha = 1/(0.20*0.20) |
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| 178 | = 25. If you want to achieve a particular value of alpha, such as 10, |
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| 179 | you will want to use a CV of 1/sqrt(100) = 1/10 = 0.1. |
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| 180 | <P> |
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| 181 | In addition to the four distance calculations, the program can also |
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| 182 | compute a table of similarities between amino acid sequences. These values |
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| 183 | are the fractions of amino acid positions identical between the sequences. |
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| 184 | The diagonal values are 1.0000. No attempt is made to count similarity |
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| 185 | of nonidentical amino acids, so that no credit is given for having |
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| 186 | (for example) different hydrophobic amino acids at the corresponding |
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| 187 | positions in the two sequences. This option has been requested by many |
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| 188 | users, who need it for descriptive purposes. It is not intended that |
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| 189 | the table be used for inferring the tree. |
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| 190 | <P> |
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| 191 | <H2>INPUT FORMAT AND OPTIONS</H2> |
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| 192 | <P> |
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| 193 | Input is fairly standard, with one addition. As usual the first line of the |
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| 194 | file gives the number of species and the number of sites. There follows the |
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| 195 | character W if the Weights option is being used. |
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| 196 | <P> |
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| 197 | Next come the species data. Each |
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| 198 | sequence starts on a new line, has a ten-character species name |
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| 199 | that must be blank-filled to be of that length, followed immediately |
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| 200 | by the species data in the one-letter code. The sequences must either |
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| 201 | be in the "interleaved" or "sequential" formats |
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| 202 | described in the Molecular Sequence Programs document. The I option |
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| 203 | selects between them. The sequences can have internal |
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| 204 | blanks in the sequence but there must be no extra blanks at the end of the |
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| 205 | terminated line. Note that a blank is not a valid symbol for a deletion. |
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| 206 | <P> |
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| 207 | After that are the lines (if any) containing the information for the |
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| 208 | W option, as described below. |
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| 209 | <P> |
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| 210 | The options are selected using an interactive menu. The menu looks like this: |
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| 211 | <P> |
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| 212 | <TABLE><TR><TD BGCOLOR=white> |
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| 213 | <PRE> |
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| 214 | |
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| 215 | Protein distance algorithm, version 3.6a3 |
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| 216 | |
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| 217 | Settings for this run: |
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| 218 | P Use JTT, PAM, Kimura or categories model? Jones-Taylor-Thornton matrix |
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| 219 | G Gamma distribution of rates among positions? No |
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| 220 | C One category of substitution rates? Yes |
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| 221 | W Use weights for positions? No |
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| 222 | M Analyze multiple data sets? No |
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| 223 | I Input sequences interleaved? Yes |
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| 224 | 0 Terminal type (IBM PC, ANSI)? (none) |
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| 225 | 1 Print out the data at start of run No |
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| 226 | 2 Print indications of progress of run Yes |
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| 227 | |
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| 228 | Are these settings correct? (type Y or the letter for one to change) |
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| 229 | </PRE> |
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| 230 | </TD></TR></TABLE> |
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| 231 | <P> |
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| 232 | The user either types "Y" (followed, of course, by a carriage-return) |
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| 233 | if the settings shown are to be accepted, or the letter or digit corresponding |
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| 234 | to an option that is to be changed. |
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| 235 | <P> |
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| 236 | The G option chooses Gamma distributed rates of evolution across amino |
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| 237 | acid psoitions. The program will pronmpt you for the Coefficient of Variation |
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| 238 | of rates. As is noted above, thi is 1/sqrt(alpha) if alpha is the more |
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| 239 | familiar "shape coefficient" of the Gamma distribution. If the G option |
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| 240 | is not selected, the program defaults to having no variation of rates |
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| 241 | among sites. |
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| 242 | <P> |
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| 243 | The options M and 0 are the usual ones. They are described in the |
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| 244 | main documentation file of this package. Option I is the same as in |
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| 245 | other molecular sequence programs and is described in the documentation file |
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| 246 | for the sequence programs. |
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| 247 | <P> |
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| 248 | The P option selects one of the four distance methods, or the |
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| 249 | similarity table. It toggles among these |
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| 250 | five methods. The default method, if none is specified, is the |
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| 251 | Jones-Taylor-Thornton model. If the Categories distance is selected |
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| 252 | another menu option, T, will appear allowing the user |
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| 253 | to supply the Transition/Transversion ratio that should be assumed |
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| 254 | at the underlying DNA level, and another one, C, which allows the |
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| 255 | user to select among various nuclear and mitochondrial genetic codes.i |
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| 256 | The transition/transversion ratio can be any number from 0.5 upwards. |
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| 257 | <P> |
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| 258 | The W (Weights) option is invoked in the usual way, with only weights 0 |
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| 259 | and 1 allowed. It selects a set of sites to be analyzed, ignoring the |
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| 260 | others. The sites selected are those with weight 1. If the W option is |
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| 261 | not invoked, all sites are analyzed. |
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| 262 | <P> |
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| 263 | <H2>OUTPUT FORMAT</H2> |
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| 264 | <P> |
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| 265 | As the |
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| 266 | distances are computed, the program prints on your screen or terminal |
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| 267 | the names of the species in turn, |
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| 268 | followed by one dot (".") for each other species for which the distance to |
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| 269 | that species has been computed. Thus if there are ten species, the first |
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| 270 | species name is printed out, followed by one dot, then on the next line |
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| 271 | the next species name is printed out followed by two dots, then the |
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| 272 | next followed by three dots, and so on. The pattern of dots should form |
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| 273 | a triangle. When the distance matrix has been written out to the output |
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| 274 | file, the user is notified of that. |
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| 275 | <P> |
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| 276 | The output file contains on its first line the number of species. The |
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| 277 | distance matrix is then printed in standard |
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| 278 | form, with each species starting on a new line with the species name, followed |
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| 279 | by the distances to the species in order. These continue onto a new line |
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| 280 | after every nine distances. The distance matrix is square |
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| 281 | with zero distances on the diagonal. In general the format of the distance |
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| 282 | matrix is such that it can serve as input to any of the distance matrix |
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| 283 | programs. |
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| 284 | <P> |
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| 285 | If the similarity table is selected, the table that is produced is not |
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| 286 | in a format that can be used as input to the distance matrix programs. |
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| 287 | it has a heading, and the species names are also put at the tops of the |
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| 288 | columns of the table (or rather, the first 8 characters of each species |
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| 289 | name is there, the other two characters omitted to save space). There |
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| 290 | is not an option to put the table into a format that can be read by |
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| 291 | the distance matrix programs, nor is there one to make it into a table |
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| 292 | of fractions of difference by subtracting the similarity values from 1. |
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| 293 | This is done deliberately to make it more difficult for the use to |
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| 294 | use these values to construct trees. The similarity values are |
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| 295 | not corrected for multiple changes, and their use to construct trees |
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| 296 | (even after converting them to fractions of difference) would be |
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| 297 | wrong, as it would lead to severe conflict between the distant |
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| 298 | pairs of sequences and the close pairs of sequences. |
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| 299 | <P> |
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| 300 | If the option to print out the data is selected, the output file will |
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| 301 | precede the data by more complete information on the input and the menu |
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| 302 | selections. The output file begins by giving the number of species and the |
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| 303 | number of characters, and the identity of the distance measure that is |
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| 304 | being used. |
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| 305 | <P> |
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| 306 | In the Categories model of substitution, |
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| 307 | the distances printed out are scaled in terms of expected numbers of |
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| 308 | substitutions, counting both transitions and transversions but not |
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| 309 | replacements of a base by itself, and scaled so that the average rate of |
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| 310 | change is set to 1.0. For the Dayhoff PAM and Kimura models the |
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| 311 | distance are scaled in terms of the expected numbers of amino acid |
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| 312 | substitutions per site. Of course, when a branch is twice as |
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| 313 | long this does not mean that there will be twice as much net change expected |
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| 314 | along it, since some of the changes may occur in the same site and overlie or |
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| 315 | even reverse each |
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| 316 | other. The branch lengths estimates here are in terms of the expected |
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| 317 | underlying numbers of changes. That means that a branch of length 0.26 |
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| 318 | is 26 times as long as one which would show a 1% difference between |
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| 319 | the protein (or nucleotide) sequences at the beginning and end of the |
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| 320 | branch. But we |
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| 321 | would not expect the sequences at the beginning and end of the branch to be |
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| 322 | 26% different, as there would be some overlaying of changes. |
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| 323 | <P> |
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| 324 | One problem that can arise is that two or more of the species can be so |
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| 325 | dissimilar that the distance between them would have to be infinite, as |
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| 326 | the likelihood rises indefinitely as the estimated divergence time |
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| 327 | increases. For example, with the Kimura model, if the two sequences |
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| 328 | differ in 85.41% or more of their positions then the estimate of divergence |
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| 329 | time would be infinite. Since there is no way to represent an infinite |
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| 330 | distance in the output file, the program regards this as an error, issues a |
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| 331 | warning message indicating which pair of species are causing the problem, and |
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| 332 | computes a distance of -1.0. |
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| 333 | <P> |
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| 334 | <H2>PROGRAM CONSTANTS</H2> |
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| 335 | <P> |
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| 336 | The constants that are available to be changed by the user at the beginning |
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| 337 | of the program include |
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| 338 | "namelength", the length of species names in |
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| 339 | characters, and "epsilon", a parameter which controls the accuracy of the |
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| 340 | results of the iterations which estimate the distances. Making "epsilon" |
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| 341 | smaller will increase run times but result in more decimal places of |
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| 342 | accuracy. This should not be necessary. |
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| 343 | <P> |
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| 344 | The program spends most of its time doing real arithmetic. Any software or |
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| 345 | hardware changes that speed up that arithmetic will speed it up by a nearly |
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| 346 | proportional amount. |
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| 347 | <P> |
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| 348 | <HR> |
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| 349 | <P> |
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| 350 | <H3>TEST DATA SET</H3> |
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| 351 | <P> |
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| 352 | (Note that although these may look like DNA sequences, they are being |
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| 353 | treated as protein sequences consisting entirely of alanine, cystine, |
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| 354 | glycine, and threonine). |
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| 355 | <P> |
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| 356 | <TABLE><TR><TD BGCOLOR=white> |
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| 357 | <PRE> |
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| 358 | 5 13 |
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| 359 | Alpha AACGTGGCCACAT |
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| 360 | Beta AAGGTCGCCACAC |
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| 361 | Gamma CAGTTCGCCACAA |
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| 362 | Delta GAGATTTCCGCCT |
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| 363 | Epsilon GAGATCTCCGCCC |
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| 364 | </PRE> |
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| 365 | </TD></TR></TABLE> |
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| 366 | <P> |
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| 367 | <HR> |
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| 368 | <P> |
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| 369 | <H3>CONTENTS OF OUTPUT FILE (with all numerical options on )</H3> |
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| 370 | <P> |
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| 371 | (Note that when the numerical options are not on, the output file produced is |
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| 372 | in the correct format to be used as an input file in the distance matrix |
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| 373 | programs). |
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| 374 | <P> |
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| 375 | <TABLE><TR><TD BGCOLOR=white> |
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| 376 | <PRE> |
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| 377 | |
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| 378 | Jones-Taylor-Thornton model distance |
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| 379 | |
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| 380 | Name Sequences |
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| 381 | ---- --------- |
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| 382 | |
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| 383 | Alpha AACGTGGCCA CAT |
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| 384 | Beta ..G..C.... ..C |
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| 385 | Gamma C.GT.C.... ..A |
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| 386 | Delta G.GA.TT..G .C. |
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| 387 | Epsilon G.GA.CT..G .CC |
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| 388 | |
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| 389 | |
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| 390 | |
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| 391 | Alpha 0.0000 0.3304 0.6257 1.0320 1.3541 |
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| 392 | Beta 0.3304 0.0000 0.3756 1.0963 0.6776 |
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| 393 | Gamma 0.6257 0.3756 0.0000 0.9758 0.8616 |
|---|
| 394 | Delta 1.0320 1.0963 0.9758 0.0000 0.2267 |
|---|
| 395 | Epsilon 1.3541 0.6776 0.8616 0.2267 0.0000 |
|---|
| 396 | </PRE> |
|---|
| 397 | </TD></TR></TABLE> |
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| 398 | </BODY> |
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| 399 | </HTML> |
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