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sampling with very small volumes
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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Fri Apr 14, 2006 6:08 pm    Post subject: Re: sampling with very small volumes Reply with quote

Quote:


second: what about two or more solutes? suppoose that you want to sample
a smaall volume containing an enzyme and a substrate, can we calculate
the statistics of co-sampling?






I realized that many authors used a Poisson distribution to model one
solute sampling in very small volumes.
But: how to treat the problem of two-uninteracting solutes? Is the
size-less approximation valid? in which limits??
than kyou


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Borek
science forum Guru Wannabe


Joined: 02 May 2005
Posts: 157

PostPosted: Mon Jan 02, 2006 7:13 pm    Post subject: Re: sampling with very small volumes Reply with quote

On Fri, 23 Dec 2005 17:02:29 +0100, <rekuci@gmail.com> wrote:

Quote:
Good luck sampling 1 picoliter volumes. That's smaller than the volume
of a water molecule.

???

3.3*10^13 molecules...

Best,
Borek
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Marvin
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Joined: 24 Mar 2005
Posts: 224

PostPosted: Sat Dec 24, 2005 6:38 pm    Post subject: Re: sampling with very small volumes Reply with quote

Fabio Mancini wrote:
Quote:
I am interested in "sampling" a solution of macromolecules, for example.
when you consider a solute without size (null size) the problem is
shifted
to a probability problem of finding a certain number of solute molecules
into
the sampled volume. Now I know that those can be calculated according
to Poisson distribution.
When you have - however - solutes that have not infinitesimal size,
there is
a problem, because the space for one molecule is no longer available for
others.
what is the approach I can develop to solve this problem
(theoretically).

It will follow counting statistics. Each sample either will or will not have a solute
molecule. The classical model of counting statistics is pulling balls out of a container
containing a certain muber of white balls and black balls. There are no gray balls - you
only pull out one or the other.

Quote:

second: what about two or more solutes? suppoose that you want to sample
a smaall volume containing an enzyme and a substrate, can we calculate
the statistics of co-sampling?

In that case, your would have three kinds of "balls" - enzyme alone, substrate alone,
enzyme-substrate complex. To know the distribution of the "balls" in the solution, you
need to know the total concentrations of both enzyme and substrate, and the association
constant. The total concentration of substrate is presumably changing with time, due to
the catalyzed reaction. A messy calculation by hand, but it could be programmed for a
computer.

Quote:

thank you very much anyway

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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Fri Dec 23, 2005 9:10 pm    Post subject: Re: sampling with very small volumes Reply with quote

I am interested in "sampling" a solution of macromolecules, for example.
when you consider a solute without size (null size) the problem is
shifted
to a probability problem of finding a certain number of solute molecules
into
the sampled volume. Now I know that those can be calculated according
to Poisson distribution.
When you have - however - solutes that have not infinitesimal size,
there is
a problem, because the space for one molecule is no longer available for
others.
what is the approach I can develop to solve this problem
(theoretically).

second: what about two or more solutes? suppoose that you want to sample
a smaall volume containing an enzyme and a substrate, can we calculate
the statistics of co-sampling?

thank you very much anyway


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rekuci@gmail.com
science forum addict


Joined: 22 Sep 2005
Posts: 98

PostPosted: Fri Dec 23, 2005 4:02 pm    Post subject: Re: sampling with very small volumes Reply with quote

This is pretty simple probability...calculate the number of molecules
of solute and solvent you have in the total volume, assuming random and
complete mixing. Knowing your sampling volume (assuming it is large
enough for the solute to still be dilute in all samples), calculate the
number of molecules in a sample.

Good luck sampling 1 picoliter volumes. That's smaller than the volume
of a water molecule. A picomolar quantity of say an enzyme in solution
is enough molecules to guarantee that at any feasible sampling volume,
you will have an average quantity of enzyme. Of course if you do a few
million 10:1 dilutions, things might get more interesting...
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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Thu Dec 22, 2005 7:23 pm    Post subject: Re: sampling with very small volumes Reply with quote

Quote:
Well, that rather depends on the concentration of solute X, doesn't it?

There's a great deal in the literature and various texts on sampling
theorem. A good chemometrics text might answer your question, or one
of the sampling/trace/environmental analysis standards.

I have read on some papers that a Poisson distribution should be used,
but
I miss the demonstration of this.
and... what about multiple solutes? Let's say a solution of 3 or 4
different
solutes... what is the probability that in the sampled volume we
have the macroscopic distribution of the 3-4 different compounds?






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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Thu Dec 22, 2005 7:02 pm    Post subject: Re: sampling with very small volumes Reply with quote

dear Dr. thank you very much for your answer. My original idea to write
here was
to have a kind of discussion about this problem.
However I thank you again for your contribution.
regards






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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Thu Dec 22, 2005 7:02 pm    Post subject: Re: sampling with very small volumes Reply with quote

dear Dr. Dickie
thank you very much for your answer. My original idea to write here was
to have a kind of discussion about this problem.
However I thank you again for your contribution.
regards


Quote:
Even thought the volume you list is not really small, I can guess at the
answer.
Your book.




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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Thu Dec 22, 2005 7:02 pm    Post subject: Re: sampling with very small volumes Reply with quote

dear Dr. Dickie
thank you very much for your answer. My original idea to write here was
to have a kind of discussion about this problem.
However I thank you again for your contribution.
regards






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Dr_Dickie
science forum beginner


Joined: 03 May 2005
Posts: 16

PostPosted: Thu Dec 22, 2005 5:42 pm    Post subject: Re: sampling with very small volumes Reply with quote

"Fabio Mancini" <p775184@yahoo.it> wrote in message
news:5689e832b5bec964206d4c36fa2af259.28560@mygate.mailgate.org...
Quote:
suppose that you have to sample a solution of a solute X present at C
concentration, by means of very small volumes (let's say 1 um^3).

Suppose that you can take 10^6 samples...

what is the distribution of
sample containing 0 molecule of X
sample containing 1 molecule of X
and so on...

what happen when you consider the distribution of two solutes?

do you know whether someone already did these calculations? where?

thank you



Even thought the volume you list is not really small, I can guess at the
answer.
Your book.

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Dr. Dickie
Skepticult member in good standing #394-00596-438
Poking kooks with a pointy stick.
"The most exciting phrase to hear in science, the one that heralds new
discoveries,
is not 'Eureka!' ('I found it!'), but rather 'hmm....that's funny...'"
- Isaac Asimov
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David C. Stone
science forum beginner


Joined: 05 May 2005
Posts: 48

PostPosted: Thu Dec 22, 2005 5:42 pm    Post subject: Re: sampling with very small volumes Reply with quote

In article
<5689e832b5bec964206d4c36fa2af259.28560@mygate.mailgate.org>, Fabio
Mancini <p775184@yahoo.it> wrote:

Quote:
suppose that you have to sample a solution of a solute X present at C
concentration, by means of very small volumes (let's say 1 um^3).

Suppose that you can take 10^6 samples...

what is the distribution of
sample containing 0 molecule of X
sample containing 1 molecule of X
and so on...

Well, that rather depends on the concentration of solute X, doesn't it?

There's a great deal in the literature and various texts on sampling
theorem. A good chemometrics text might answer your question, or one
of the sampling/trace/environmental analysis standards.

Good luck!
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Fabio Mancini
science forum beginner


Joined: 22 Dec 2005
Posts: 17

PostPosted: Thu Dec 22, 2005 5:41 pm    Post subject: sampling with very small volumes Reply with quote

suppose that you have to sample a solution of a solute X present at C
concentration, by means of very small volumes (let's say 1 um^3).

Suppose that you can take 10^6 samples...

what is the distribution of
sample containing 0 molecule of X
sample containing 1 molecule of X
and so on...

what happen when you consider the distribution of two solutes?

do you know whether someone already did these calculations? where?

thank you


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