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BioCompiler might start life as BioCOBOL

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Update: Matthew has found an even more thorough review paper that discusses computer assisted synthetic biology approaches — it can be found at doi:10.1016/j.copbio.2009.08.007.

The iGEM competition year is running to a close. The teams are headed into November 2010 and have roughly one month left before attending the conference. I’m personally not attending the conference this year — I think the undergraduates will get more out of the experience.

The current year sees our continued efforts to precipitate a dedicated software team — a functioning autonomous unit that will serve to supplement and enhance Waterloo’s impact in the iGEM competition. More importantly, we’re going to do some very interesting science. We’ve had some success talking with other student groups across campus — notably, we should probably talk with the student IEEE/CUBE chapter when we have more work completed. We had involved BIC as well, however, it was early on and we had even less ground to stand upon ( — the primordial software team was mostly interested in BioMortar and BrickLayer at the time — the later project having been taken up by the iGEM Coop students as in Python this year).

This whole BioCompiler business started when Matthew uncovered a nice candidate problem: the compilation of a schematic for behaviour to a fully functioning synthetic biological circuit. Let’s be as precise as we can be here. I mean to say, we will take a description (which could resemble a piece of formal language source code) — and have it compiled into the sequence of BioBricks that will produce the desired behaviour.

This idea has been approached by several groups before — but each time, a different subproblem was considered (this is a reorganization of Matthew’s very nice list here).

  • Synthetic biology programming language: Genetic Engineering of Living Cells (GEC) (Microsoft Research) is a project that hones in on a formal language specification.
  • Synthetic biology computer assisted design (CAD): Berkeley Software (iGEM 2009) created a suite of items — Eugene (formal language for synthetic biology), Spectacles (visualizer integrating parts with their behaviours), Kepler (a dataflow broker). As well, Berkeley is responsible for the award winning Clotho (iGEM 2008 – Best Software Tool) which is a workbench that connects with the parts registry database (amongst other possible resources).
  • Systems biology pathway reaction simulation: Systems Biology Markup Language (SBML), Systems Biology Workbench (SBW) and Jarnac are a set of tools that perform systems biology analysis (which we consider to be an output of synthetic biology). SBML is the formal language, Jarnac is a reaction network simulator (which utilizes JDesigner as a front end) and SBML is a dataflow broker between SBML and Jarnac.
  • BioBrick specific pathway simulation: Minnesota’s Team Comparator (iGEM 2008) created SynBioSS — a tool which estimates the concentration of reactants and products given the appropriate BioBricks on a simulated circuit.

Update — here are a few more items thanks to Matthew Gingerich, George Zarubin and Andre Masella.

  • Molecular biology and bioinformatics analysis: The European Molecular Biology Open Software Suite (EMBOSS) is a toolkit developed by the European Molecular Biology Network (EMBnet) for bioinformatics. This might not be immediately relevant, but it is interesting. EMBOSS is actually relatively complete. More distantly along this vein, there’s also Bioconductor which focuses mostly on microarray analysis and is implemented in R.
  • More synthetic biology computer aided design (CAD): TinkerCell is a GUI-driven piece of software that supports extension with C++ and Python. TinkerCell along with the suite created by Berkeley Software are the two most promising target systems in which to integrate BioCompiler. Finally, there’s GenoCAD which appears to be in an early phase of development — this software looks to emphasize construction with correct syntax and attribute grammars — I’ll have to read more about this.
  • Formal laboratory protocol description: BioCoder is another Microsoft research project — the designed language aims to be both human readable and complete for automation. It reminds me of standard operating procedures (SOP) with greater precision. While BioCoder compiles from protocol to automation, we’ll be compiling to circuitry and protocol. BioCoder will give us some insights about the kinds of protocols that others are thinking of.

There is of course more software, but these are the items that we have become most familiar with — that we like — and that we consider to be standards toward which our own work should strive.

Two interesting problems arise when we think about these subproblems. First, the programming languages specified (including Eugene from Berkeley’s CAD suite) are exactly what they claim to be. Formal specifications. This is possible because of how concrete they are. They literally document what a synthetic biology circuit is. But this isn’t too different from what humans have been doing in iGEM all along. Second, the synthetic biology items don’t really seem to talk to the systems biology items — whereas we expect that the two — being input and output — to be inextricably linked. I explain my thoughts on the two below.

Why a programming language?

Andre enlightened me to this the other day. Humans invented programming languages to do two things. On an arrow running from the concrete toward the esoteric, we have the practical concern of compressing the amount of code that we want to write while retaining our programs’ expressiveness. This is the origin of macro systems such as COBOL. On an arrow pointing in the reverse — from the cerebral abstract down to the literal — we have the theoretical concern of mathematical beauty, of completeness. This is the origin of such functional languages like Lisp. For humans to have any hope of creating such a Lisp-like language for synthetic biology — we would need to understand all of the reactionary nuances about it, the system with which we tamper — at least inasmuch as a painful heuristic approximation. This is a feat we are no where near completing though footholds are managed with systems biology.

So here we are, BioCOBOL is the first step. A developing simple — though complete macro-like system that is in league in terms of abstraction with the programming language / CAD -like projects we’ve seen thus far. Only, we aim to increase the efficiency of circuit design; so that the programming language is not a literal mapping of the human document — rather, it is an explanation of behaviour. We will abstract it ever so slightly with each iteration of development — departing further and further away from CAD. A subteam headed by Brandon is currently developing the syntax and search algorithms required for the job — Brandon suggests that a weighted traversal of valid circuits should form our algorithmic primitive. My subteam is attempting to characterize as many known circuits in iGEM as possible — analyzing what pieces of input (stimuli: chemical concentrations, gradients, quora, oscillators) may be compressed for their common usage — what function prototypes already exist ( — reacts to an input: promoters) for compression — what the standard outputs are (analogy to printing error messages: GFP-family) etc. — again in the effort to realize what is losslessly compressible. Our software should eventually provide the correct laboratory protocol as well.

In this sense, we are respecting what a compiler is before we even approach more sophisticated compilation: it transforms a document in one language to another.

Incidentally, I should mention that Jordan and George are working on a modelling problem with the lab team — I’m not clear on the specifics, but I take it they want to pull out some differential equations on a set of promoters.

Why do we care that Synthetic Biology logic should talk to Systems Biology logic?

Finally, it is clear that we will eventually want to become even more abstract — even more mathematically complete, even more expressive. While we may never know enough about systems biology to create BioLISP (in our lifetime), we expect there to be sufficient research for us to discover — and perhaps research we can conduct ourselves to come ever closer. Systems biology allows us to think about synthetic biology in terms of reaction concentrations; free energy etc.. It gives the notion of compilation its own ground; the ground we want to cover. Imagine the perfect BioCompiler — stating the a problem to be compiled in terms of the input and output of the system. Let’s be precise here: I mean to say, the products and reactants or behaviour of our circuit. Let us describe what our circuit will do instead of what our circuit is made of. This — the missing link, this compiler — is the logical final step of BioCompiler.

Eddie Ma

October 26th, 2010 at 10:57 am

C# & Bioinformatics: Indexers & Substitution Matrices

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I’ve recently come to appreciate the convenience of C# indexers. What indexers allow you to do is to subscript an object using the familiar bracket notation. I’ve used them for substitution matrices as part of my phylogeny project. Indexers are essentially syntactical sugar that obey the rules of method overloading. I first describe what I think are useful substitution matrix indexers and then a bare bones substitution matrix class (you could use your own). The indexer notation implementation is discussed last, so feel free to skip the preamble if you’re able to deduce what I’m doing.

Note: I’ve only discussed accessors (getters) and not mutators (setters) today.

Some Reasonable Substitution Matrix Indexers

This is the notation you might expect from the indexer notation in C#.

// Let there be a class called SubMatrix which contains data from BLOSUM62.

var  sm = new SubMatrix( ... );
     // I'll assume you already have some constructors.

int  index_of_proline = sm['P'];
     // Returns the row or column that corresponds to proline, 14.

char token_at_three = sm[3];
     // Returns the amino acid at position three, aspartate.

int  score_proline_to_aspartate = sm['P', 'D'];
     // Returns the score for a mutation from proline to aspartate, -1.

int  score_aspartate_to_proline = sm[3, 14];
     // Returns the score for a mutation from aspartate to proline, -1.

An Example Bare Bones Substitution Matrix Class

Let’s say you’ve loaded up the BLOSUM62 and are representing it internally in some 2D array…

// We've keying the rows and columns in the order given by BLOSUM62:
// ARNDCQEGHILKMFPSTWYVBZX* (24 rows, columns)

int[,] imatrix;

For convenience, let’s say you’ll also keep a dictionary to map at which array position one finds each amino acid…

// Keys = amino acid letters, Values = row or column index

Dictionary<char, int> indexOfAA;

Finally, we’ll put these two elements into a class and assume that you’ve already written your own constructors that will take care of the above two items — either from accepting arrays and strings as arguments or by reading from raw files. If this isn’t true and you need more help, feel free to leave a comment and I’ll extend this bare bones example.

// Bare bones class ...
public partial class SubMatrix {

    // Properties ...
    private int[,] imatrix;
    private Dictionary<char, int> indexOfAA;

    // Automatic Properties ...
    public int Width { // Returns number of rows of the matrix.
        get {
            return imatrix.GetLength(0);
        }
    }

    // Constructors ...
    ...
}

I’ve added the automatic property “Width” above — automatic properties are C# members that provide encapsulation: a public face to some arbitrary backend data — you’ve been using these all along when you’ve called “List.Count” or “Array.Length“.

Substitution Matrix Indexer Implementation

You can implement the example substitution matrix indexers as follows. Notice the use of the “this” keyword and square[] brackets[] to specify[] arguments[].

//And finally ...
public partial class SubMatrix {

    // Indexers ...
    // Give me the row or column index where I can find the token "aa".
    public int this[char aa] {
        get {
            return this.indexOfAA[aa];
        }
    }
    // Give me the amino acid at the row or column index "index".
    public char this[int index] {
        get {
            return this.key[index];
        }
    }
    // Give me the score for mutating token "row" to token "column".
    public double this[char row, char column] {
        get {
            return this.imatrix[this.indexOfAA[row], this.indexOfAA[column]];
        }
    }
    // Give me the score for mutating token at index "row" to index "column".
    public double this[int row, int column] {
        get {
            return this.imatrix[row, column];
        }
    }
}

Similar constructs are available in Python and Ruby but not Java. I’ll likely cover those later as well as how to set values too.

Eddie Ma

September 1st, 2010 at 11:15 am

C# & Bioinformatics: Align Strings to Edit Strings

without comments

This post follows roughly from the e-strings (R. Edgar, 2004) topic that I posted about here. The previous source code was listed in Ruby and JS, but this time I’ve used C#.

In this post, I discuss alignment strings (a-strings), then why and how to convert them into edit strings (e-strings). Incidentally, I can’t seem to recover where I first saw alignment strings so tell me if you know.

Alignment strings

When you perform a pairwise sequence alignment, the transformation that you perform on the two sequences is finite. You can record precisely where insertions, deletions and substitutions (or matches) are made. This is useful if you want to retain the original sequences, or later on build a multiple sequence alignment while keeping the history of modifications. There’s a datastructure I’ve seen described called alignment strings, and in it you basically list out the characters ‘I’, ‘D’ and ‘M’ to describe the pairwise alignment.

Consider the example two protein subsequences below.

gi|115372949: GQAGDIRRLQSFNFQTYFVRHYN
gi|29827656:  SLSTGVSRSFQSVNYPTRYWQ

A global alignment of the two using the BLOSUM62 substitution matrix with the gap penalties -12 to open, -1 to extend yields the following.

gi|115372949: GQAGDIR-----RLQSFNFQTYFVRHYN
gi|29827656:  SL----STGVSRSFQSVNYPT---RYWQ

The corresponding alignment string looks like this…

gi|115372949: GQAGDIR-----RLQSFNFQTYFVRHYN
gi|29827656:  SL----STGVSRSFQSVNYPT---RYWQ
Align String: MMDDDDMIIIIIMMMMMMMMMDDDMMMM

Remember, the alignment is described such that the top string is modelled as occurring earlier than the bottom string which occurs later — this is why a gap in the top string is an insertion (that new material is inserted in the later, bottom string) while a gap in the bottom string is a deletion (that material is deleted to make the later string). Notice in reality, it doesn’t really matter what’s on top and what’s on bottom– the important thing is that the alignment now contains gaps.

Why we should probably use e-strings instead

An alignment string describes the relationship between two strings and their gaps — we are actually recording some redundant information if we only want to take one string at a time into consideration and the path needed to construct profiles it participates in. The top and bottom sequences are also treated differently, where both ‘M’ and ‘D’ indicates retention of the original characters for the top string and both ‘M’ and ‘I’ indicates retention for the bottom string; the remaining character of course implies the inclusion of a gap character. A pair of e-strings would give each of these sequences their own data structure and allow us to cleanly render the sequences as they appear in the deeper nodes of a phylogenetic tree using the multiply operation described last time.

Here are the corresponding e-strings for the above examples.

gi|115372949: GQAGDIR-----RLQSFNFQTYFVRHYN
e-string:     < 7, -5, 16 >
gi|29827656:  SL----STGVSRSFQSVNYPT---RYWQ
e-string:     < 2, -4, 16, -3, 4 >

Recall that an e-string is a list of alternating positive and negative integers; positive integers mean to retain a substring of the given length from the originating sequence, and negative integers mean to place in a gap of the given length.

Converting a-strings to e-strings

Below is a C# code listing for an implementation I used in my project to convert from a-strings to the more versatile e-strings. The thing is — I really don’t use a-strings to begin with anymore. In earlier versions of my project, I used to keep track of my movement across the score matrix using an a-string by dumping down a ‘D’ for a vertical hop, a ‘I’ for a horizontal hop and a ‘M’ for a diagonal hop. I now just count the number of relevant steps to generate the matching pair of e-strings.

The function below, astring_to_estring takes an a-string (string u) as an argument and returns two e-strings in a list (List<List<int>>) — don’t let that type confuse you, it simply breaks down to a list with two elements in it: the e-string for the top sequence (List<int> v), and the e-string for the bottom sequence (List<int> w).

public static List<List<int>> astring_to_estring(string u) {
    /* Defined elsewhere are the constant characters ...
       EDITSUB = 'M';
       EDITINS = 'I';
       EDITDEL = 'D';
    */
    var v = new List<int>(); // Top e-string
    var w = new List<int>(); // Bottom e-string
    foreach(var uu in u) {
        if(uu == EDITSUB) { // If we receive a 'M' ...
            if(v.Count == 0) { // Working with e-string v (top, keep)
                v.Add(1);
            } else if(v[v.Count -1] <= 0) {
                v.Add(1);
            } else {
                v[v.Count -1] += 1;
            }
            if(w.Count == 0) { // Working with e-string w (bottom, gap)
                w.Add(1);
            } else if(w[w.Count -1] <= 0) {
                w.Add(1);
            } else {
                w[w.Count -1] += 1;
            }
        } else if(uu == EDITINS) { // If we receive a 'I' ...
            if(v.Count == 0) { // Working with e-string v (top, gap)
                v.Add(-1);
            } else if(v[v.Count -1] >= 0) {
                v.Add(-1);
            } else {
                v[v.Count -1] -= 1;
            }
            if(w.Count == 0) { // Working with e-string w (bottom, keep)
                w.Add(1);
            } else if(w[w.Count -1] <= 0) {
                w.Add(1);
            } else {
                w[w.Count -1] += 1;
            }
        } else if(uu == EDITDEL) { // If we receive a 'D' ...
            if(v.Count == 0) { // Working with e-string v (top, keep)
                v.Add(1);
            } else if(v[v.Count -1] >= 0) {
                v[v.Count -1] += 1;
            } else {
                v.Add(1);
            }
            if(w.Count == 0) { // Working with e-string w (bottom, keep)
                w.Add(-1);
            } else if(w[w.Count -1] >= 0) {
                w.Add(-1);
            } else {
                w[w.Count -1] -= 1;
            }
        }
    }
    var vw = new List<List<int>>(); // Set up return list ...
    vw.Add(v); // Top e-string v added ...
    vw.Add(w); // Bottom e-string w added ...
    return vw;
}

The conversion back from e-strings to a-strings is also easy, but I don’t cover that today. Enjoy and happy coding 😀

Eddie Ma

August 21st, 2010 at 9:03 pm

Bioinformatics: Edit Strings (Ruby, JavaScript)

without comments

>>> Attached: ( editStringAdder.rb — in Ruby | editStrings.js — in JavaScript ) <<<

I wanted to share something neat that I’ve been using in the phylogeny analyzing software I’ve been developing. In the MUSCLE3 BMC Bioinformatics paper (Robert Edgar, 2004), Edgar describes a way to describe all the changes required to get from one raw sequence to how it appears somewhere in an internal node, riddled with gaps. He calls the data structures Edit Strings (e-strings).

I started using these things in my visualizer because it is a convenient way to describe how to render a profile of sequences at internal nodes of my phylogenetic trees. Rather than storing a copy of the sequence with gaps at each of its ancestors, e-strings allow you to store a discrete pathway of the changes your alignment algorithm made to a sequence at each node.

You can chain e-strings together with a multiply operation so that the profile of any node in the tree can be created out of just the original primary sequences of the dataset (the taxa) and the set of corresponding e-strings for the given tree. You can choose to store the alphabet-distribution profiles this way at each node too, but I decided to use the e-strings only for my visualizer (where seeing each sequence within a profile is important).

Edit strings take the form of a sequence of alternating positive and negative integers; positive integers mean “retain a substring of this length” while negative integers mean “insert gaps of this length” — here’s a few example applications of edit strings on the sequence “ABCDEFGHI“:

<10>("ABCDEFGHIJ") = "ABCDEFGHIJ"
<10 -3>("ABCDEFGHIJ") = "ABCDEFGHIJ---"
<4, -2, 6>("ABCDEFGHIJ") = "ABCD--EFGHIJ"
<2, -1, 5, -4, 3>("ABCDEFGHIJ") = "AB-CDEFG----HIJ"

A few particulars should be mentioned. An application of an e-string onto a sequence is only defined when the sum of the positive integers equals the length of the sequence. The total number of negative integers is arbitrary, and refers to any number of inserted gaps. Finally, a digit zero is meaningless. Edit strings can be multiplied together. If you apply two edit strings in succession onto a sequence, the result is the same as if you had applied the product of two edit strings onto that same sequence. Here are some examples of edit strings multipled together.

<10> * <10> = <10>
<10> * <7, -1, 2> = <7, -1, 2>
<6, -1, 4> * <7, -1, 3, -2, 1> = <6, -2, 3, -2, 1>
<6, -1, 4> * <3, -1, 3, -1, 3, -1, 2> = <3, -1, 3, -2, 2, -1, 2>
<6, -1, 4> * <2, -1, 6, -5, 3> = <2, -1, 4, -1, 1, -5, 3>

The multiply function is a bit tricky to implement at first, but one can work backward from the result to get the intermediate step that’s performed mentally. The last two examples above can manually calculated if we imagine an intermediate step as follows. We convert the first e-string to its application on a sequence of ‘+’ symbols– in both the below cases, this results in ten ‘+’ symbols with one ‘-‘ (gap) inserted after the sixth position. We then apply the second edit string to the result of the first application. Finally, we write out the total changes as an e-string on the original sequence of ten ‘+’ symbols. Don’t worry, we don’t really do this in real life software — it’s just a good way for human brains to comprehend the overall operation.

Second last example above — expanded out…

<6, -1, 4> * <3, -1, 3, -1, 3, -1, 2> = ...
++++++-++++ * <3, -1, 3, -1, 3, -1, 2> = ...
+++-+++--++-++ = <3, -1, 3, -2, 2, -1, 2>

Last example above — expanded out…

<6, -1, 4> * <2, -1, 6, -5, 3> = ...
++++++-++++ * <2, -1, 6, -5, 3> = ...
++-++++-+-----+++ = <2, -1, 4, -1, 1, -5, 3>

Here’s the code in Ruby for my take on the multiply function. I derived my version of the function based on the examples from Edgar’s BMC paper (mentioned before). When you think about it, the runtime is the sum of the number of elements of the two e-strings being multiplied. This becomes obvious when you realize that the only computation that really occurs is when a positive integer is encountered in the second e-string. The function is called estring_product(), it takes two e-strings as arguments (u, v) and returns a single e-string (w). This function internally calls an estring_collapse() function because we intermediately create an e-string that may have several positive integers or several negative integers in a row (when this happens, it’s usually just two in a row). Consecutive same-signed integers of an e-string are added together.

def estring_product(u, v)
    w = []
    uu_replacement = nil
    ui = 0
    vi = 0
    v.each do |vv|
        if vv < 0
            w << vv
        elsif vv > 0
            vv_left = vv
            uu = uu_replacement != nil ? uu_replacement : u[ui]
            uu_replacement = nil
            until vv_left == 0
                if vv_left >= uu.abs
                    w << uu
                    vv_left -= uu.abs
                    ui += 1
                    uu = u[ui]
                else
                    if uu > 0
                        w << vv_left
                        uu -= vv_left
                    elsif uu < 0
                        w << -vv_left
                        uu += vv_left
                    end
                    vv_left = 0
                    uu_replacement = uu
                end
            end
        end
        vi += 1
    end
    return estring_collapse(w)
end

If you aren’t familiar with Ruby, the “<<” operator means “append the right value to the left collection”. Everything else should be pretty self-explanatory (leave a comment if it’s not).

def estring_collapse(u)
    v = []
    u.each do |uu|
        if v[-1] == nil
            v << uu
        elsif (v[-1] <=> 0) == (uu <=> 0)
            v[-1] += uu
        else
            v << uu
        end
    end
    return v
end

The “<=>” lovingly referred to as the spaceship operator compares the right value to the left value; if the right value is greater, then the result is 1.0; if the left value is greater, then the result is -1.0; if the left and right values are the same, then the result is 0.0.

A Few Notes on the Attached Files (Ruby, Javascript)

The Ruby source has a lot of comments in it that should help you understand when and where to use the included two functions. The Javascript is actually used in a visualizer I’ve deployed now so it has a few more practical functions in it. A function called sequence_estring() is included that takes a $sequence and applies an $estring, then returns a new gapped sequence. A utility signum() function is included which takes the place of the spaceship operator in the Ruby version. A diagnostic function, p_uvw() is included that just uses document.write() to print out whatever you give as (estring) $u, (estring) $v and (estring) $w. Finally, the JavaScript functions sequence_estring() and estring_product() will print out error messages with document.write() when the total sequence length specified in the first argument is not the same as the total sequence length implied by the second argument. Remember, the sum of the absolute values of the first argument describes the total length of the sequence– each of these tokens must be accounted for by the positive values of the second argument, the estring that will operate on it.

The Null Coalescing Operator (C#, Ruby, JS, Python)

without comments

Null coalescence allows you to specify what a statement should evaluate to instead of evaluating to null. It is useful because it allows you to specify that an expression should be substituted with some semantic default instead of defaulting on some semantic null (such as null, None or nil). Here is the syntax and behaviour in four languages I use often — C#, Ruby, JavaScript and Python.

C#

Null coalescencing in C# is very straight forward since it will only ever accept first class objects of the same type (or null) as its operator’s arguments. This restriction is one that exists at compile time; it will refuse to compile if it is asked to compare primitives, or objects of differing types (unless they’re properly cast).

Syntax:

<expression> ?? <expression>

(The usual rules apply regarding nesting expressions, the use of semi-colons in complete statements etc..)

A few examples:

DummyNode a = null;
DummyNode b = new DummyNode();
DummyNode c = new DummyNode();

return a ?? b; // returns b
return b ?? a; // still returns b
DummyNode z = a ?? b; // z gets b
return a ?? new DummyNode(); // returns a new dummy node
return null ?? a ?? null; // this code has no choice but to return null
return a ?? b ?? c; // returns b -- the first item in the chain that wasn't null

No, you’d never really have a bunch of return statements in a row like that — they’re only there to demonstrate what you should expect.

Ruby, Python and Javascript

These languages are less straight forward (i.e. possess picky nuances) since they are happy to evaluate any objects of any class with their coalescing operators (including emulated primitives). These languages however disagree about what the notion of null should be when it comes to numbers, strings, booleans and empty collections; adding to the importance of testing your code!

Syntax for Ruby, Javascript:

<expression> || <expression>

Syntax for Ruby, Python:

<expression> or <expression>

(Ruby is operator greedy :P.)

The use of null coalescence in these languages are the same as they are in C# in that you may nest coalescing expressions as function arguments, use them in return statements, you may chain them together, put in an object constructor as a right-operand expression etc.; the difference is in what Ruby, Python or Javascript will coalesce given a left-expression operand. The below table summarizes what left-expression operand will cause the statement to coalesce into the right-expression operand (i.e. what the language considers to be ‘null’-ish in this use).

Expression as a left-operand Does this coalesce in Ruby? Does this coalesce in Python? Does this coalesce in JavaScript?
nil / None / null Yes Yes Yes
[] No Yes No
{} No Yes n/a*
0 No Yes Yes
0.0 No Yes Yes
“” No Yes Yes
No Yes Yes
false / False / false
Yes Yes Yes

*Note that in JavaScript, you’d probably want to use an Object instance as an associative array (hash) so that the field names are the keys and the field values are the associated values — doing so means that you can never have a null associative array.

Contrast the above table to what C# will coalesce: strictly “null” objects only.

The null coalescing operator makes me happy. Hopefully it’ll make you happy too.

Eddie Ma

July 7th, 2010 at 11:00 am

Parsing a Newick Tree with recursive descent

with 12 comments

>>> Attached: ( parse_newick.js – implementation in JS | index.html – example use ) <<<

Update: Fixed parse_newick.js source code that caused a field to be mislabelled in index.html (2010 Dec. 19)

This method of parsing works for any language that allows recursive functions — basically any of the curly bracket languages (C#, C, Java) and the fast-development languages (Ruby, JavaScript, Python) can do this. This particular example will include JavaScript code which you can take and do whatever you want with — recursive descent parsing is a well-known and solved problem, so it’s no skin off my back. Before we begin, I should probably explain what a tree in Newick format is.

What exactly is the Newick format?

Remember back in second year CS when your data structures / abstract data types / algorithms instructor said you can represent any tree as a traversal? Well, if not — don’t fret, it’s not hard to get the hang of.

A traversal is a finite, deterministic representation of a tree which can be thought of as a road map of how to visit each node of the tree exactly once. The phylogeny / bioinformatics people will know each of these nodes as either taxa / sequences (the leaves) or profiles (the internal nodes — i.e. not the leaves). A tree in Newick format is exactly that — a traversal. More specifically, it is a depth-first post-order traversal. When traversing a tree, we have a few options about how we want to visit the nodes — depth-first post-order means we want to start at the left-most, deepest leaf, and recursively visit all of the nodes before we end at the root.

A tree expressed in Newick format describes a tree as an observer has seen it having visited each node in a depth-first post-order traversal.

A node in the Newick format can be…

  • A leaf in the form: “<name>:<branch_length>”
    • e.g. “lcl|86165:-0
    • e.g. “gi|15072471:0.00759886
    • e.g. “gi|221105210:0.00759886
  • Or a node in the form “(<node>,<node>):<branch_length>”
    • This is where it gets tricky and recursive — the “node” item above can be another node, or a leaf — when a node is composed of at least another node, we call that a recursive case; when a node is composed of only leaves, we call that a base case. We make this clearer in the next section.
  • Or a node in the form “(<node>,<node>);”
    • The semi-colon at the end means that we have finished describing the tree. There is no branch length as the root of the tree is not connected to a parent.

Understanding recursion in a Newick Tree

Base case e.g.: The below node is composed of two leaves.

(lcl|86165:-0,gi|87118305:-0):0.321158

Recursive case e.g.: The below node is composed of a leaf on the left, and another node on the right; this right-node is composed of two leaves.

“(gi|71388322:0.0345038,(gi|221107809:0.00952396,gi|221101741:0.00952396):0.0249798):0.0111081

If the names look a bit funny, that’s because these are sequences pulled out of a blastp search.

The Newick tree itself may have any number of nodes, the base case being a single node. The only restriction is that any node either is a leaf (has zero children) or must have two children (never a single child). These two children again are allowed to be either leaves or other nodes.

We would visualize the above Recursive case e.g. as follows.:

Where the numbers beside the edges are edge length and the names of the named taxa are indicated inside the circles (leaves). The unnamed internal nodes are the profiles that have been calculated with alignments. You’ll notice that there’s a branch length leading out of the root of this subtree into the rest of the tree (not shown). If this was a complete tree on its own, the root would have no branch length there and no arrow coming out of it.

Finally, Parsing!

Now that we have reviewed the depth-first post-order traversal, the Newick format and how to interpret it; we can move onto parsing these things. In parsing, we hope to create an in-memory structure that represents the tree. The parser I discuss assumes that the Newick format string already has had all newlines stripped, as it uses regular expressions. If your trees aren’t stored that way, just make sure that newlines are stripped before feeding it into my function. The in-memory object that’s created will have the following fields as a minimum.

  • node_type $left – the left child of a node
  • node_type $right – the right child of a node
  • string_type $name – the name of a node (if it is a leaf)
  • float_type $branch_length – the length of the branch coming out of the top of a given node

I also use the following two fields to keep track of a few house keeping items and to make life pleasant for future tasks with this in-memory structure.

  • node_type $parent – the parent of a node
  • integer_type $serial – the order in which this node occurs when parsed

Note that in future, a depth-first post-order traversal will yield the nodes in the exact order that they were read — so in reality “this.serial” isn’t really needed, but it’s nice to have for future functions you might write as a shorthand. Have you understood why these nodes would occur in the same order?

Each language has its own quirks. Python and JavaScript have the advantage that you can define a class and define its properties (fields) on the fly — meaning there’s less code to download and to write, which is particularly good for blogs 😛

Here’s pseudo-code for the recursive descent parsing function “tree_builder(<newick_string>)” — I don’t indicate where to strip away newlines because I assume they’re gone. I also don’t indicate where to strip away whitespace (I did previously, but that took up like half the pseudocode). So if there’s a place where you suspect whitespace can occur, strip it away and increment the cursor by the length of that whitespace.

Note: We are assuming that there are no newlines in the file — that is, the entire newick traversal is one string on a single long unbroken line.

// Note:
// Call tree_builder() with a "new" operator in JavaScript
//     to allow it to use the 'this' keyword.
// In other languages,
//     you may need to explicitly create a new object instead of using 'this'.

var count = 0; // can be either a global variable or a reference
// keeps track of how many nodes we've seen

var cursor = 0; // also either a global or a reference
// keeps track of where in the string we are

function tree_builder(newick_string) {
    // Look for things relating to the left child of this node //
    if $newick_string [ $cursor ] == "(" {
        $cursor ++; // move cursor to position after "(".
        if newick_string [ $cursor ] == "(" {
            // Then the $left node is an internal node: requires recursion //
            $this.left = new tree_builder(newick_string); // RECURSIVE CALL.
            $this.left.parent = $this;
        }
        // try to find a valid $name next at the current cursor position //
        if $name = $newick_string [ $cursor ] . regex match ("^[0-9A-Za-z_|]+") {
            // Then the $left node is a leaf node: parse the leaf data //
            $this.left = new Object;
            $this.left.name = $name;
            $this.left.serial = $count;
            $count ++;
            $this.left.parent = $this;
            $cursor += length of $name;
            // move cursor to position after matched name.
        }
        // notice: if no $name found, just skip to finding branch length.
    }
    if $newick_string [ $cursor ] == ":" {
        // Expect left branch length after descending into the left child //
        $cursor ++; // move cursor to position after the colon.
        // look for the string representation of a floating point value "FPV"...
        $branch_length_string =
            $newick_string [ $cursor ] . regex match ("^[0-9.+eE-]+");
$this.$left.$score = $branch_length_string as a FPV;
        $cursor += length of the string $branch_length_string;
        // move cursor after FPV.
    }
    // Look for things related to the right node //
    if $newick_string [ $cursor ] == "," {
        $cursor ++; // move cursor after the comma
        if newick_string [ $cursor ] == "(" {
            // Then the $right node is an internal node: requires recursion //
            $this.right = new tree_builder($newick_string); // RECURSIVE CALL.
            $this.right.parent = $this;
        }
        // try to find a valid $name next at the current cursor position //
        if $name = $newick_string [ $cursor ] . regex match ("^[0-9A-Za-z_|]+") {
            // Then the $right node is a leaf node: parse the leaf data //
            $this.right = new Object;
            $this.right.name = $name;
            $this.right.serial = $count;
            $serial ++;
            $this.right.parent = $this;
            $cursor += $length of $name;
        }
        // again, accept if no $name found and move onto branch length.
    }
    // Now looking for the branch length ... //
    if $newick_string at $cursor == ":" {
        // Expect right branch length after descending into right child //
        $cursor ++; // moving past the colon.
        $branch_length_string =
            $newick_string [ $cursor ] . regex match ("^[0-9.+eE-]+");
        $this.right.score = $branch_length_string as a FPV;
        $cursor += length of the string $branch_length_string;
    }
    if $newick_string at $cursor == ")" {
        $cursor ++; // move past ")".
    }
    // Expect the branch length of $this node after analyzing both children //
    if $newick_string at $cursor == ":" {
        $cursor ++;
        $branch_length_string =
            $newick_string [ $cursor ] . regex match ("^[0-9.+eE-]+");
        $this.score = $branch_length_string as a FPV;
        $cursor += length of the string $branch_length_string;
    }
    if $newick_string at $cursor == ";" {
        // This case only executes for the root node-- //
        // --the very last node to finish parsing //
        $cursor ++; // to account for the semicolon (optional, consistency)
        $this.serial = $count; // no need to increment $count here
    }
    // Return to complete a recursive instance (internal) or base case (leaf) //
    return this; // not needed if "new" operator was used all along
}

The implementation that’s included in the attached JavaScript does two things differently than the above. First, I don’t force the user to break encapsulation by declaring globals. Instead, I use an object called “ref” which has two fields, “ref.count” and “ref.cursor”. The name “ref” is chosen to remind us that its fields are passed by reference. This is possible because the object “ref” itself is passed by reference (I could have called it anything, but I chose a name that suited its purpose). Imagine trying to pass “count” and “cursor” in this recursive function without an enclosing object — what would happen instead is that the value wouldn’t be updated, instead the integer values would be copied and modified locally in the span of single function instances. The “ref” object is passed as an argument to the “_tree_builder(<ref>, <newick_string>)” function internally where it is instantiated if “null” is passed in the place of “ref”. The calling user doesn’t even need to know about it, as it’s all wrapped together in a pretty package and the user just calls “tree_builder(<newick_string>)” as before — without the need for globals. The enclosing function even does the work of instantiating the root node with the “new” keyword so that the end user doesn’t even need to (and shouldn’t!) say “new”.

Finally, there is a traversal function, and an expose function. The traversal function returns the node objects in an array following in the natural depth-first post-order described previously. The expose function is a debugging function which writes the output using “thoughts_write(<message>)” which wraps “document.write(<message>)”. You can change “thoughts_write(<message>)” to print output elsewhere using “document.getElementById(<some_identity>).innerHTML += (<message>)” where “some_identity” is the “id” of some element in your HTML. Without going into detail, the traversal function also uses an internal “ref” object which refers to the array as it is filled.

Some other things you can try…

The JavaScript recursive descent parser is actually a simplified version of something that I threw together earlier. The major difference is that I tag leaf nodes with fasta protein sequences by passing a reference to an associative array (or hash) as an argument to “tree_builder(<newick_string>, <fasta_hash>)”. Remember, in JavaScript, an associative array is an instance of an Object, not an instance of an Array. Using non-integer field names in an Array is actually not well defined but kind of sort of works semi-consistently between browsers (i.e. don’t try!), but that’s a story for another day. Whenever the name of a leaf is parsed, I would look it up in the hash and put it in a field either “this.left.fasta” or “this.right.fasta” thereby conferring to the leaf nodes of the in-memory structure the appropriate fasta protein sequence.

Lessons Learned

In putting this thing together, I managed to relearn JS, recursive descent parsing and making JS pass things by reference up and down a recursive stack of function calls. Andre Masella helpfully reminded me that I didn’t need to use any kind of BNF or LALR(1) parser — just an easy single-function parser would do. This is actually a port of a C# parser which does the same thing that I wrote in an earlier step for phylogenetic analysis — the difference being that C# offers a “ref” keyword that allows one to specify arguments in a function’s parameter list as emulated references (functionally equivalent to using C’s asterisk and ampersand convention though not operationally equivalent).

Happy parsing! The code presented should be easy enough to understand for you to port it into the language of your choice for whatever purposes you design.