Math Guide For Bioinformatics

Question

[sa9]

Like many other biologists , I learn to program for my bioinformatics daily needs by self-study. However, because I don't have strong Math / Statistics background most of the work I do is simple I/O parsing , database quires and straightforward R script on a fancy day.

I want to move the next level where I don't skip the mathematical equations in bioinformatics papers but actually read them and understand what do they mean.

I read a small guide to Math for Physics (http://www.superstringtheory.com/math/index.html, which is divided into three levels) and would like to see a similar but more detailed guide for bioinformatics (for biologists-with-weak-Math-background-and-want-to-work-in-bioinformatics to be more precise) .

I hope the answers to my question would cover the following points:

• A mathematical field/ concept (e.g. Matrix Algebra)
• Why and where we need this concept in bioinformatics (with example of a paper if possible)
• A concise (preferably practical) source for self-study (book, article, online course, etc)

Note: I expect some of the Math concepts are used frequently more than others in bioinformatics (core concepts) and some are advanced and rarely used. I'm interested in the former but I am open to all suggestions.

Thanks

[Russh]

before I write an answer (mathophile that I am) could I ask which area of bioinformatics you mostly dabble in (sequence analysis / networks / phylogenetics / microarray analysis ... ) and whether you're also interested in system modelling / cellular biophysics. It might be a few hours before I answer.

[sa9]

@russH. Thank you. At the moment I am involved in CNV genotyping , NextGen sequencing and networks analysis. Not much on system modeling / cellular biophysics but definitely interested to read your take on those topics. Hopefully, enough answers on different sub-bioinformatics fields will make this page useful resource for the community.

[basch]

I can see this an old thread, but I find myself in a very similar position. What would be your conclusion by now? Any approach/source that helped more than others?

Answer 1

[lh3]

Probably what I am going to say below offers you little help, but as you have asked me, I feel obliged to say something...

I had to take a "contemporary mathematics" course in my second year of my college. This was a tough course that taught me many things I rarely used today such as functional analysis, measurement theory and differentiable manifold. The teacher started the course by defining many "obvious" concepts in a rigorous way. At the beginning, this process is tedious and sounds really silly because I thought it only made things overcomplicated, but after several classes, I began to learn the necessity of the math way - when you have a rigorous system, mathematics can carry you much further than what you can initially imagine. It is really like a magic. Another important fact I learned is that we should not treat mathematics purely as symbols. We should learn to visualize them in mind. At times symbols are more descriptive than words. In my naive view, solving problems with mathematics follows this route: abstract the problem with symbols, deduce using symbols, "visualize" the symbols after the deduction, and deduce even further. In the end, this "useless" contemporary mathematics course becomes the most influential course I have even taken.

I am not asking you to take such a course. Different people learn the apperception in different ways. I mainly want to point out that to make the best use of mathematics to solve real problems, you should learn to abstract problems with symbols and vividly see the meaning of symbols. Skills in deriving equations are important, too, but IMO come in the second place. I also want to emphasize that to take the full advantage of mathematics, the notation system has to be very rigorous. Everything in the system must be consistent and without ambiguity; otherwise math will stop working.

I do not have a good suggestion about how to learn the essence of math as you and I probably have very different background. Nonetheless, if you want to read a book on the mathematical aspect of bioinformatics, I would recommend Richard Durbin's "sequence analysis", the only bioinformatics book I have finished reading. Ewan Birney has recently blogged his 5 statistical things I wished I had been taught 20 years ago. It is worth reading and probably of much more practical use than my empty words here.

[Daniel Standage]

+1 for abstraction.

[sa9]

You answer is more helpful than you think. Many thanks for taking the time to share your experience.

Answer 2

[Daniel Standage]

My last semester as an undergraduate, I took a class called "fundamentals of mathematics" or something like that. My only reason for taking the class was to get a math minor and I had no idea how it would relate to my future work in genomics and bioinformatics.

While I had to do a lot of proofs in that class, it was primarily designed to help mathematicians and scientists develop and communicate their ideas in mathematical terms. Among other things, it covered the basics of set theory and number theory, and really improved my mathematical terminology and understanding. I would have done much better in my CS classes related to data structures and advanced programming if I had taken this class first.

I highly recommend taking a course like this if you haven't, or if you prefer, reading a relevant textbook (we used this one). The experience you gain from this will improve your ability to break biological ideas down into mathematical ones (so that you can program a solution), and then subsequently communicate your ideas with others in a sensible way.

[sa9]

After your reply, I went and read the first few chapters of "How to Think Like a Mathematician" book (http://goo.gl/Ev8hZ which) which , based on the reviews, seems like an intro for the book you mentioned "Mathematical Proofs". I start to have a general sense of the point you made and I think your advice is really great. Thanks Daniel.

Answer 3

[Russh]

Sorry, I meant to reply earlier

There are some tutorials related to this book here..link

The most important parts of mathematics as far as bioinformatics is concerned is probability/statistics and discrete mathematics/combinatorics. As was stated earlier though, the value of mathemtics is more the mindset: abstracting problems, finding analogous problems for which a solution is already known. Sometimes mathematical language is the neatest way to describe a problem.

The neatest bit of biofx/dsicretemaths I've been obsessing about recently is the coding/mapping algorithms for NGS. R

(will reply again later when I find some more links; especially if I can find some good network symmetry stuff)

[sa9]

I got a copy of "Mathematics of Bioinformatics" and I can say this book is , more or less , what I am after. The book provides the big picture and describes the interface between the two fields. It introduces many Mathematical fields and explains how they are related to different biological questions (a list of contents can be found here http://goo.gl/5IPXW).

Although other answers provided great insights, recommendations and many valuable advices, I am accepting yours because it is the closest to answer the main question. Thanks russH.

[Hranjeev]

hmm ... looks interesting.

Answer 4

[Gjain]

I think this is a very good source.

http://www.khanacademy.org/

[lh3]

If one wants to find formulas, Bioinformatics and Journal of Computational Biology are much better places. Nature Methods only accepts Words document as I remember and Words is pretty hopeless when you have to write a lot of equations. Note that I am not commenting on which journal has better papers.

[Benm]

This is a nice website! I knows MIT Open Course (http://ocw.mit.edu/index.htm) and SciVee (http://www.scivee.tv/) are also the 'shortcut' to learn something you need.

[sa9]

Thanks Gjain. I am aware of both Khan Academy and MIT open course. There are plenty of resources in the internet on almost any Math topic. My question is to link Math concept(s) needed to solve a common problem in bioinformatics.

[Gjain]

your welcome. I would still refresh the basics of the topics from these tutorials and then slowly start reading papers and nature method articles and try to understand equations from there.

[Gjain]

yeah thats true

Answer 5

[Gww]

Something everyone really should read when they are getting into programming is a decent book on algorithms. It's arguably more computer science than math, but being able to choose and implement the most efficient algorithm can have a dramatic impact on your programs running time. This is especially useful when you are working with the massive amount of data produced during next generation sequencing. One of the best and most recommended books is Introduction to Algorithms by Cormen et al.

Next, if you want to get into stats and machine learning there's a great blog post on measuringmeasures with some excellent book recommendations broken down by category (I have personally purchased and read a few of them).

There are also quite a few good bioinformatics specific books such as Statistical Methods in Bioinformatics.

[sa9]

Although this doesn't answer my question directly but the links you provided will certainly be helpful down the road. Thanks GWW.

Answer 6

[Hranjeev]

I think sometimes (or probably just me) we get a little overwhelmed by all the math symbols. The following online reference helps me to figure out the abstract part of maths.

http://abstractmath.org/MM/MMIntro.htm

[Russh]

on a related note, it would be remiss of me (OU junkie) not to mention http://openlearn.open.ac.uk/course/search.php?search=m208 that is, if you need a refresher on mathematical language etc