Re: getting the center of mass of each part of a molecule
On Saturday, May 20, 2017 at 9:13:39 AM UTC-7, qasi...@gmail.com wrote > I have more than 100 ligand molecules. The image I showed at the beginning of > this discussion was only an example. It had missing atoms. > See it without missing any atom in the pdb format (coordinates in Angstrom > unit): [snip atomic coordinate tables] > I am doing molecular dynamics simulation of protein-ligand complex. The issue > is to keep the ligand in the binding site of the protein during simulation > when turned off the interactions (van der waals, coulomb...) between the > ligand and protein. In that case, to keep the ligand in the bindind site I > need to apply the translational and rotational restraints (distance, angle, > dihedral restraints). The more detail is here > http://pubs.acs.org/doi/abs/10.1021/jp0217839 Well now, that's Ph.D level work. I work with GROMACS myself. I tried to obtain a copy of the paper. Why is a 14 year old article behind a paywall? I requested a reprint from the authors through ResearchGate. > My aim is to get the COM of the whole ligand (I already do it) and divide the > ligand in two parts and find to the COM of each part. Then I will apply the > distance, angle and dihedral restraints on the atoms of the ligand and > protein. > -The first distance restraints will be between one of the ligand heavy atom > closest to the ligand COM (COM for whole ligand atoms) and one of the protein > atoms closest to the ligand COM. > -The second distance restraints will be between one of the ligand heavy atom > closest to the COM of the first part of ligand in two parts and one of the > protein atoms closest to the COM of the first part of ligand in two parts. > -And the third distance restraints will be between one of the ligand heavy > atom closest to the COM of the second part of ligand in two parts and one of > the protein atoms closest to the COM of the second part of ligand in two > parts. > > That is, I will form 3 bonds between ligand and protein. Hope that makes > clear what I am trying to do. Is that the method that was used in the research paper, or is that something that you devised on your own? > Please tell me on the python code what I need to do. Your requirements are still rather more vague than you realize. I think that you are counting on the fact that the atomic coordinates in a PDB file include a certain amount of noise, and possibly also any strain in the ligand molecule. If you have a truly symmetrical ligand, your center of mass computations will not be robust. But I see the general idea behind what you are trying to do. And I suppose any method that forms three virtual bonds between three distinct atoms in ligand and the protein will do the job. Maybe you don't care that you get the true center of mass, just that you get close to it. How much Python do you want to learn? I am going to suggest a basic modification to your approach to coding. You will have several steps in this algorithm. Learn to structure your code in in a way which allows you to read your algorithm in plain language using comments, descriptive variable names, or descriptive function names. Right now you show one function called heavy_atoms. That is not a very descriptive name. I'm not even sure why it's a function at all, because it doesn't return any values to whatever called it. If your program is short and you only want to work with global variables, you can skip the use of functions. I would like to see your whole program. However, at this stage it's probably not of interest to other readers of the newsgroup. Please consider continuing through email. Thanks. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
I have more than 100 ligand molecules. The image I showed at the beginning of this discussion was only an example. It had missing atoms. See it without missing any atom in the pdb format (coordinates in Angstrom unit): ATOM 1 O1 LIG 1 46.050 50.290 26.860 ATOM 2 O2 LIG 1 46.070 47.530 27.170 ATOM 3 C1 LIG 1 47.630 49.260 23.730 ATOM 4 C2 LIG 1 48.200 49.870 22.500 ATOM 5 C3 LIG 1 47.090 50.070 24.730 ATOM 6 C4 LIG 1 46.570 49.490 25.890 ATOM 7 C5 LIG 1 47.650 47.870 23.890 ATOM 8 C6 LIG 1 46.590 48.100 26.040 ATOM 9 C7 LIG 1 47.120 47.290 25.050 ATOM 10 C8 LIG 1 47.160 50.610 21.680 ATOM 11 C9 LIG 1 46.450 51.660 26.860 ATOM 12 C10 LIG 1 46.910 51.920 21.790 ATOM 13 H1 LIG 1 48.640 49.150 21.820 ATOM 14 H2 LIG 1 48.980 50.600 22.700 ATOM 15 H3 LIG 1 47.080 51.150 24.610 ATOM 16 H4 LIG 1 48.070 47.240 23.110 ATOM 17 H5 LIG 1 47.140 46.210 25.170 ATOM 18 H6 LIG 1 46.580 50.030 20.960 ATOM 19 H7 LIG 1 45.570 52.300 26.810 ATOM 20 H8 LIG 1 47.090 51.850 26.000 ATOM 21 H9 LIG 1 47.000 51.860 27.780 ATOM 22 H10 LIG 1 46.190 48.140 27.920 ATOM 23 H11 LIG 1 46.220 52.400 21.250 ATOM 24 H12 LIG 1 46.750 52.530 22.680 The same ligand coordinate file in gro format (coordinates in nanometer unit) is here as well: 1LIG O11 4.605 5.029 2.686 1LIG O22 4.607 4.753 2.717 1LIG C13 4.763 4.926 2.373 1LIG C24 4.820 4.987 2.250 1LIG C35 4.709 5.007 2.473 1LIG C46 4.657 4.949 2.589 1LIG C57 4.765 4.787 2.389 1LIG C68 4.659 4.810 2.604 1LIG C79 4.712 4.729 2.505 1LIG C8 10 4.716 5.061 2.168 1LIG C9 11 4.645 5.166 2.686 1LIGC10 12 4.691 5.192 2.179 1LIG H1 13 4.864 4.915 2.182 1LIG H2 14 4.898 5.060 2.270 1LIG H3 15 4.708 5.115 2.461 1LIG H4 16 4.807 4.724 2.311 1LIG H5 17 4.714 4.621 2.517 1LIG H6 18 4.658 5.003 2.096 1LIG H7 19 4.557 5.230 2.681 1LIG H8 20 4.709 5.185 2.600 1LIG H9 21 4.700 5.186 2.778 1LIGH10 22 4.619 4.814 2.792 1LIGH11 23 4.622 5.240 2.125 1LIGH12 24 4.675 5.253 2.268 I am doing molecular dynamics simulation of protein-ligand complex. The issue is to keep the ligand in the binding site of the protein during simulation when turned off the interactions (van der waals, coulomb...) between the ligand and protein. In that case, to keep the ligand in the bindind site I need to apply the translational and rotational restraints (distance, angle, dihedral restraints). The more detail is here http://pubs.acs.org/doi/abs/10.1021/jp0217839 My aim is to get the COM of the whole ligand (I already do it) and divide the ligand in two parts and find to the COM of each part. Then I will apply the distance, angle and dihedral restraints on the atoms of the ligand and protein. -The first distance restraints will be between one of the ligand heavy atom closest to the ligand COM (COM for whole ligand atoms) and one of the protein atoms closest to the ligand COM. -The second distance restraints will be between one of the ligand heavy atom closest to the COM of the first part of ligand in two parts and one of the protein atoms closest to the COM of the first part of ligand in two parts. -And the third distance restraints will be between one of the ligand heavy atom closest to the COM of the second part of ligand in two parts and one of the protein atoms closest to the COM of the second part of ligand in two parts. That is, I will form 3 bonds between ligand and protein. Hope that makes clear what I am trying to do. Please tell me on the python code what I need to do. Thanks. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Friday, May 19, 2017 at 4:17:23 PM UTC-7, qasi...@gmail.com wrote: > The center of mass of the whole ligand that I calculated is the center of > geometry (the average/mean atomic positions) from the sample input file > provided. I don't take other things into account, such as knowledge of the > mass of each atom and so on. The difference between the center of mass and > the center of geometry/atom positions is probably small, and my aim is only > to select the atom closest to the center of geometry. Just a quick note, the image that you showed at the beginning of this discussion would not have picked C1 as the closest atom to the center of the molecule. If your molecule consisted of only the benzene ring C1...C6, the center of mass would be exactly at the center. Adding C7 would shift the center directly toward C2. C8 and C9, as you have drawn them, shift the center further, in a direction pointing somewhere between C2 and C4. > Dear Gregory Ewing, lets consider I get the center of geometry (the average > positions of atoms - X, Y, Z) of the whole molecule. Then I can compare those > average positions X, Y and Z and find the greatest one, and list separately > the ligand atoms according to the greatest average position out of X, Y and Z > (The greatest one is the "longest" axis of the molecule in some sense). This > way, the ligand atoms will have been divided in two parts, right? After that, > I can calculate the center of geometry of each part. Does this procedure make > sense? If no, what do you suggest me to divide the ligand/molecule in two > parts? Any procedure that serves your intended purpose is the one that makes sense. Personally, I don't understand the goal of dividing a molecule into two parts and then computing separate centers of mass for each, but maybe you can explain why this is a useful thing to do. As you have described it, here is one possible way to proceed? 1) Identify "the" atom which is closest to the center of mass. As I mentioned, there could be more than one atom which is the same distance from the center. You need to define what to do in that case. 2) Rank the atoms in order of Euclidean distance from the center; choose "the one" that is farthest from the center. Again, there could be ties. What do you do? 4) Define a vector from the center to the most distant atom. 5) The plane that divides the molecule in half is defined as passing through "the" central atom, and is normal to the vector. I'm not sure that's what you want. Using this algorithm, the picture that you show would not divide the molecule in the way you describe. I predict that C2 would be closest to the center of mass, so C2 would be the excluded atom. C9 would be the most distant from the center of mass. C1, C3, C5 and C6 would be on one side of the dividing plane. C7, C8, and C9 would be on the other. I'm not quite sure which side C4 would be on. In your data table, you did not give coordinates for all 9 atoms. With that information we could check whether your coordinates agree with your picture. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
The center of mass of the whole ligand that I calculated is the center of geometry (the average/mean atomic positions) from the sample input file provided. I don't take other things into account, such as knowledge of the mass of each atom and so on. The difference between the center of mass and the center of geometry/atom positions is probably small, and my aim is only to select the atom closest to the center of geometry. Dear Gregory Ewing, lets consider I get the center of geometry (the average positions of atoms - X, Y, Z) of the whole molecule. Then I can compare those average positions X, Y and Z and find the greatest one, and list separately the ligand atoms according to the greatest average position out of X, Y and Z (The greatest one is the "longest" axis of the molecule in some sense). This way, the ligand atoms will have been divided in two parts, right? After that, I can calculate the center of geometry of each part. Does this procedure make sense? If no, what do you suggest me to divide the ligand/molecule in two parts? -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
qasimp...@gmail.com wrote: "The atoms of the first part/half according to the main COM of the ligand are C2, C7, C8 and C9. As for the second part they are C3, C4, C5 and C6 atoms." Think *very* carefully about how you made that decision. Was it based *only* on the position of the centre of mass, or did you take other things into account, such as knowledge of which atoms are bonded to which other atoms? In other words, if someone just gave you a list of the positions of the atoms and nothing else, would you be able to figure out which atoms belonged to which half, without seeing a picture of the molecule? If so, how would you do it? If you need information about the bonds, then there's no way a program could do it from the sample input file you provided, because it only contains positions. -- Greg -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Thursday, May 18, 2017 at 2:44:54 PM UTC-7, qasi...@gmail.com wrote: > Yes, I wrote: "The atoms of the first part/half according to the main COM of > the ligand are C2, C7, C8 and C9. As for the second part they are C3, C4, C5 > and C6 atoms." It was just an example. In fact, I don't know which atoms > belong to each half. The code should do it of course. > > That is, I gave it as an example. I thought someone can understand what the > two parts of molecule are and what I am trying to do if I give such an > example. We are going in circles. Do you want your code to AUTOMATICALLY make the decision that atoms 2, 7, 8, and 9 comprise one "half" of your molecule, and atoms 3, 4, 5, and 6 comprise the other "half"? Then you need criteria, that you can turn into code. You said you wanted to exclude "the" atom which is nearest to the center of mass from either subset. (What if there's a tie? As in fact there could be, if you allowed for all the possible rotamers in the C2-C7 and C7-C8 bonds?) You also stated that you wanted the code "to find which atoms belong to each half." You still don't say HOW you choose halves. ONE example is obviously not enough to determine a general pattern. There is no "right" answer to the question, "which half of the molecule is this?" A human can't figure it out. A computer can't figure it out. If you don't know what you mean, we can't help you. (This link is relevant: http://dilbert.com/strip/2006-01-29) Where are you getting this problem? Do you have a reference of any kind? I am actually interested in your problem, because I do computational chemistry as well as program in Python. Alternately: could a user manually enter the subset information into the computer at a prompt? Then, you don't need code to do anything except select the subsets that the user wants. That's considerably easier. Maybe you should start there. Write code which lets the user name the atoms in the two subsets (possibly after automatically excluding "the central atom"). Make the code modular, so that you can go back later and add a function to automatically create the two subsets -- once you know what you actually want. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
Yes, I wrote: "The atoms of the first part/half according to the main COM of the ligand are C2, C7, C8 and C9. As for the second part they are C3, C4, C5 and C6 atoms." It was just an example. In fact, I don't know which atoms belong to each half. The code should do it of course. That is, I gave it as an example. I thought someone can understand what the two parts of molecule are and what I am trying to do if I give such an example. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Thursday, May 18, 2017 at 1:43:20 PM UTC-7, qasi...@gmail.com wrote: > Dear Gregory Ewing, > > As I said before, I need to divide the molecule into two parts but don't know > how to do it? It seems that I need to choose/determine a plane in 3D space > which cuts the molecule in two parts. As John Ladasky suggested, I need to > describe the criteria that cut needs to satisfy as well. Could you please > tell me on the code how to do those steps? You define the criteria, and then you write the code. In your original post, you wrote: "The atoms of the first part/half according to the main COM of the ligand are C2, C7, C8 and C9. As for the second part they are C3, C4, C5 and C6 atoms." HOW did YOU make that decision? That's what you need to specify in order to write code. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
Dear Gregory Ewing, As I said before, I need to divide the molecule into two parts but don't know how to do it? It seems that I need to choose/determine a plane in 3D space which cuts the molecule in two parts. As John Ladasky suggested, I need to describe the criteria that cut needs to satisfy as well. Could you please tell me on the code how to do those steps? -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Thursday, May 18, 2017 at 3:55:01 AM UTC-7, qasi...@gmail.com wrote: > @jladasky and @Gregory: > > 3) Divide the ligand molecule into two parts (except for ligand heavy atom > closest to the COM of the whole ligand) based on the COM previously > calculated. OK, now I agree with Gregory Ewing. This part of your problem is incompletely defined. Divide the molecule into two parts... how? You need to choose a plane in 3-dimensional space which cuts your molecule in two. Describe the criteria that this cut needs to satisfy. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
@jladasky and @Gregory: Thanks your replies. The code should do the steps below: 1) Calculate the center of mass (COM) of the whole ligand molecule with the atomic coordinates (x,y,z) 2) Find the ligand heavy atom closest to the COM of the whole ligand molecule 3) Divide the ligand molecule into two parts (except for ligand heavy atom closest to the COM of the whole ligand) based on the COM previously calculated. 4) Calculate the COM of each part divided. I do the first two steps and get correct result. The difficult task/step I couldn't overcome is to divide the ligand molecule into two parts (except for ligand heavy atom closest to the COM of the whole ligand) based on the COM previously calculated and to find which atoms belong to each half. Any help will be appreciated. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
jlada...@itu.edu wrote: I took the OP at their word. S/he wants the center of mass of the whole molecule, with the atomic coordinates as shown. Then s/he wants the center of mass of two subsets of those atoms. Unless I misunderstood, this isn't a particularly difficult task. He said he wanted to divide the molecule into two parts based somehow on the centre of mass previously calculated, which sounds like the division isn't predetermined. But yes, if you already know which atoms belong to each half, then there's no difficulty. Either way, the problem statement needs some refining before we can help much more. -- Greg -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Wednesday, May 17, 2017 at 12:14:10 AM UTC-7, Gregory Ewing wrote: > I think the problem is ambiguous as stated. There are many planes > you could pick through the centre of mass that divides the atoms > into two groups. Some other rule is needed to decide which is the > "right" one. I took the OP at their word. S/he wants the center of mass of the whole molecule, with the atomic coordinates as shown. Then s/he wants the center of mass of two subsets of those atoms. Unless I misunderstood, this isn't a particularly difficult task. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
I think the problem is ambiguous as stated. There are many planes you could pick through the centre of mass that divides the atoms into two groups. Some other rule is needed to decide which is the "right" one. My guess is that what you have in mind involves finding the "longest" axis of the molecule in some sense. That's easy to determine visually, but not so easy when all you have to work with is numbers. One approach would be to find the axis around which the molecule has the smallest moment of inertia. That involves finding the eigenvectors of the rotational inertia matrix and picking the one with the smallest eigenvalue. -- Greg -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Monday, May 15, 2017 at 7:23:52 PM UTC-7, jeanbi...@gmail.com wrote: > What may make this tricky is that the vinyl group can rotate at the point > where it attaches to the benzene ring so the full molecule may not lie in a > plane. But the OP has coordinates for each atom which are used in the center of mass calculation for the whole molecule. Why would the atoms be stationary for that calculation, and yet free to move in the calculation performed on a subset of the atoms? -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Monday, May 15, 2017 at 10:23:12 PM UTC-7, qasi...@gmail.com wrote: > @Cameron: > Thanks, I will try what you suggest. I am not sure that I'll tackle it > because I am new to python. I teach programming to people with varying levels of expertise, from middle-school students to working professionals. Do you program in any other languages? What do you know how to do? Can you write loops? Why do you have a function named heavy_atoms() which takes all of your data and parses it internally, when you know that you sometimes want to work with subsets of that data? Also, can you show us the rest of the program? Right now you define a function that is never called, and it never returns anything either. One final point: I think you have complicated your task by jumping straight into using Numpy arrays. You may need to understand Numpy's vectorized function calls (the last line of your code). If you want to select subsets of data from Numpy arrays, you could use Numpy's fancy indexing, but you have to understand that. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
@Cameron: Thanks, I will try what you suggest. I am not sure that I'll tackle it because I am new to python. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On Monday, May 15, 2017 at 1:30:05 PM UTC-7, qasi...@gmail.com wrote: > Hi, > > I need to get the center of mass (COM) of each half of the ligand shown in > the figure (https://i.stack.imgur.com/dtdul.png). I get the main COM all the > ligand, lets say it is close to C1 atom. ... I don't quite follow your terminology. A ligand is typically something that hangs onto something - usually a metal atom or some other larger molecule. It looks like you want the center of mass of the styrene molecule. Why not consider it as a benzene ring (C6H6) with the vinyl group (CH2CH) as a ligand? The benzene group will have its c.o.m. in the middle of the ring, by symmetry. Make this the origin. The vinyl group's c.o.m can be calculated by the methods given in http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html Then you can find the c.o.m of the whole molecule by considering it as two masses in a specific geometry. This seems like the point of the exercise. What may make this tricky is that the vinyl group can rotate at the point where it attaches to the benzene ring so the full molecule may not lie in a plane. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On 15May2017 13:29, qasimp...@gmail.com wrote:
I need to get the center of mass (COM) of each half of the ligand shown in the
figure (https://i.stack.imgur.com/dtdul.png). I get the main COM all the
ligand, lets say it is close to C1 atom. In addition to the main COM of all
the ligand, I need to find the COM of each half of the ligand. The atoms of
the first part/half according to the main COM of the ligand are C2, C7, C8 and
C9. As for the second part they are C3, C4, C5 and C6 atoms. The question is
how can I divide the ligand in two parts according to the main COM and
calculate the COM of each divided part (except for the atom closest to the
main COM, C1)? By the way I have multiple ligands. The code should be user
firendly.
Leaving aside that you are using numpy arrays, if sources like you need to
partition an existing array into 2 parts around the dividing element (C1).
Figure out how to find the position of C1 in the array. If your atoms are
unique in the sense that C1 != C2 even if they are both carbon atoms) you could
use the .index method of a list (hoping numpy array support that). But
otherwise, loop over the array until you find the element C1 and return the
index. Write a short function for this purpose, eg (incomplete):
def find_atom(atom, atoms):
for i, a in enumerate(atoms):
if a is the target atom "atom":
return i
raise IndexError("no such atom")
Then all you need to do is:
- figure out _which_ atom is your "C1"
- locate it in the main array of atoms
- extract the left and half subarrays
For the last part, remember that to get a sublist you can write L[a:b] to get
all the elements of L from a up to but excluding b. And that omitting "a"
implies index 0 and omitting "b" implies len(L).
The homework suggestion that the "code should be user firendly" I would take to
imply that the last step should itself be a function, eg:
def partition_atoms(atom, atoms):
which takes your target atom (C1) and the original array, calls find_atom to
locate C1, and returns the left and right sublists.
Cheers,
Cameron Simpson
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Re: getting the center of mass of each part of a molecule
@Gary: No, I don't have any algorithm. Well, I can define what I want: 1) The script will read the atom coordinates of the ligand from the input file sent in previous message. 2) It will calculate the center of mass (COM) for all the ligand atoms and find the ligand heavy atom closest to its COM. I already do these two steps but 3. and 4.steps 3) The script should be able to seperate ligand atoms into two equal parts according to the main COM (COM for all atoms). Consider that the the main COM is reference point. 4) It should find the COM each of both equal parts. -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
The last line of your function already calculates a center of mass for all atoms. How can you separate out that calculation into its own (one-line) function? How can you send just a subset of your data to that new function? -- https://mail.python.org/mailman/listinfo/python-list
Re: getting the center of mass of each part of a molecule
On 05/15/2017 01:29 PM, qasimp...@gmail.com wrote:
Hi,
I need to get the center of mass (COM) of each half of the ligand shown in the
figure (https://i.stack.imgur.com/dtdul.png). I get the main COM all the
ligand, lets say it is close to C1 atom. In addition to the main COM of all the
ligand, I need to find the COM of each half of the ligand. The atoms of the
first part/half according to the main COM of the ligand are C2, C7, C8 and C9.
As for the second part they are C3, C4, C5 and C6 atoms. The question is how
can I divide the ligand in two parts according to the main COM and calculate
the COM of each divided part (except for the atom closest to the main COM, C1)?
By the way I have multiple ligands. The code should be user firendly.
A short part of the input file is here:
1LIG C11 4.434 5.366 1.780
1LIG C22 4.317 5.301 1.940
1LIG C33 4.430 5.286 1.888
1LIG C44 4.380 4.942 2.467
1LIG C55 4.148 4.929 2.443
A short snippet of the code used to get the main COM is here:
def heavy_atoms(atoms, xyz, ligand="LIG"):
ids = np.arange(len(atoms))
names = [(i[10:15].strip(),i[5:10].strip()) for i,j in atoms]
# Ligand atoms
lig_atoms = np.array([ rname == ligand and not aname.startswith('H') for
aname,rname in names ])
lig_xyz = xyz[lig_atoms,:]
# The main COM
lig_com = xyz[lig_atoms, :].mean(axis=0)
You seem to be asking a chemistry or biochemistry question on this
Python programming list. We're a diverse group, but still, that seems
to be a vast mismatch. Do you have any hint of an algorithm that will
do what you want? Can you find one somewhere, or define one yourself?
Once you have an algorithm, it would be appropriate to ask here for help
in translating it into a Python program.
Gary Herron
--
Dr. Gary Herron
Professor of Computer Science
DigiPen Institute of Technology
(425) 895-4418
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