Re: [DIYbio] Re: A hypothetical protocol for DIYBIO DNA synthesis

sadly I'm a bit busy but I'll try to work through the maths quickly.

so we have 4 populations start oligos f0, oligos with one nucleotide additions f1 and oligos larger than that fm we also have a finite supply of nucleotides n. our system of ODEs is

dn/dt=-a n f0-a n f1-a n fm

df0/dt=-a n f0

df1/dt=a n f0-a n f1

dfm/dt=a n f1

the terms in turn are, a n f0 reactions where a nucleotide is consumed changing a start oligo to an oligo with one nucleotide, a n f1 reactions where the desired one nucleotide addition oligos are turned into longer many nucleotide added oligos. a n fm reactions where many nucleotide oligos grow still larger. Notice all reactions are equally likely as TdT doesn't care about oligo length once you get past oligos a few bases long. The non linear system can be simplified by noticing that df0/dt+df1/dt+dfm/dt=0 implies f0+f1+fm=I the initial number of start oligos. this means we can solve for n and substitute getting a linear system. if you solve this for initial condition then find the time t-max where f1 reaches a maximum and then find f1(t-max) you get I/e. all the other variables cancel out.

adding an exonuclease would be an interesting alteration. in vivo TdT works against exonuclease activity to produce short oligo additions maybe you can get past the 36% yield limit that way.

On Sun, Jul 17, 2016 at 5:15 AM, CodeWarrior <code.w...@gmail.com> wrote:
> sorry just to be clear your going to use a lab on a chip to perform TdT
> reactions, purify out single nucleotide addition oligos,

yep, on-chip, using one of the few single-molecule 'is there' analytic
techniques (impedance/stripping voltage, dye like YOYO-1 or gelred,
SERS raman photospec)

> transfect them into

eventually, either doing gibson/SLICE first in-vitro, or possibly
transforming fragments into something like b.subtilis that is known to
chew and re-assemble fragmented DNA during transformation. something
like that (getting to on-chip oligos would be an interesting enough
start for me!!)

> e coli, extract them from e coli and repeat the whole process several times?

I didn't really think of extraction, at the point post-transformation,
just let the cell divide for a few hours then flush into the macro
world to a user in a micro-fuge tube (or maybe there are a few
chambers on the chip that get progressively larger).

> Ok I won't say this is impossible but to construct such a lab on a chip
> would be a good deal harder than even doing something as ambitious as
> building your own surface plasmon resonance imager.

I have to definitely disagree with that.

> Also wouldn't it be far
> easier to use basic PCR than e coli to amplify the sequence.

Well e.coli basically does this kind of thing for you, and I think has
better overall fidelity than a single polymerase (or the more advanced
versions). At least they seem cheaper than in-vitro kits.

>
> actually I did a mathematical analysis based on modelling TdT reactions as a
> system of ODEs and the theoretical maximum efficiency is 100*e^-1% for one
> nucleotide additions which is approximately 36.7879%.

I'm interested in more details... I don't really understand what you
mean in this sense. In my arrangement, if tDt didn't add, I'd just
tell it to try again (or wait longer between cycles, or reduce chamber
volume to increase relative concentration), and it it added somehow
too many, either you could waste the molecule... or have an
alternative reaction loop that is some sort of really slow exonuclease
that only works on the growing end. Am I missing something about
efficiency? Regardless of assembly, etc, downstream?