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I graduated last year with a degree in Applied Mathematics and just this month I started a PhD in molecular genetics. I was accepted into a program specifically for individuals with a quantitative background, though the differences between my program and the general graduate program seems fairly minimal.

The department is fantastic and I'm enjoying learning the experimentation, but I haven't had the opportunity yet to use my actual skills.

The more talks I attend, the more I realize that much of the "computational" side of molecular genetics seems to be split between machine learning, bioinformatics and statistics or some combination of the three. In my undergrad I studied topics such as differential equations (partial and ordinary, extensively), dynamical systems, vector calculus (though I never took any fluids courses, I was more of a systems guy), computational mathematics, control theory and some computer science (about 5 courses).

I've talked to a few of the faculty so far and when I mention the possibility of differential equation modeling, they don't seem comfortable giving me guidance. In addition, I read a review paper today that seems to suggest this kind of modeling is fairly uncommon.

So, my questions are these: Are differential equation models useful to geneticists and biologists? Why are they not done more often? How difficult would it be to create my own project that involves differential equation modeling coupled with experimental parameter finding and model verification?

Nobody seems to be able to give me an answer, so I hope the Stack Exchange community has some insight.

Thanks in advance!

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closed as primarily opinion-based by WYSIWYG Sep 17 '16 at 8:12

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ @WYSIWYG This hardly seems a matter of opinion. I cited two seminal papers in biology and genetics that model biological phenomena with differential equations. Clear diff. eq. are useful in biology. $\endgroup$ – Charles E. Grant Sep 17 '16 at 16:53
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    $\begingroup$ @CharlesE.Grant It is opinion based. OP is seeking opinion on how easy or difficult something would be and whether something would be useful or not. Moreover, it is also broad and not really about a biological question. There are several papers on mathematical models of genetic systems (I personally also work on such problems). This question is off-topic on several grounds. $\endgroup$ – WYSIWYG Sep 17 '16 at 18:16
  • $\begingroup$ Differential equation could be applied anywhere, may it be light-and-darks of a picture or taste-distribution in a cone of ice-cream. Just like +, -, * and / they could be applied in so many places. Rather I think it would be troublesome to find a field where diffirential equations does not work in the nature. $\endgroup$ – Always Confused Sep 17 '16 at 19:04
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Are differential equation models useful to geneticists and biologists?

Well yeah, of course they are. Look up Alan Turing and "The chemical basis of morphogenesis", or look up "differential equations and gene regulatory networks" But folks have to specialize, and not every department studies every aspect of a field. You may just have ended up in a department where nobody is studying an aspect of genetics that can be well modeled by differential equations. At lot of molecular genetics is still figuring out the coarse grained phenomenology of the genome, like "How does a cell figure out which copy of the X chromosome gets condensed into a Barr body?" A lot of these problems involve picking out subtle signals from noisy data, thus the interest in statistics and machine learning.

If diff. eqns. are the passion of your life, you might have to look 'next door', to departments studying biochemistry and population genetics, both of which do huge amounts of modeling using differential equations. There are also applications of differential equations to molecular genetic methods like QPCR and next generation sequencing, but you'll either have to sell your mentor on the topic, or move to a different department.

On the other hand, if it's just a matter of diff. eq. being your undergrad emphasis, you may want to find a biological problem that interests you, branch out beyond diff. eq., and use your general mathematical maturity to pick up the relevant mathematical tools: say statistics, optimization, or dynamic programming.

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