# Finding discriminating positions for a sequence alignment column

I don't have any theoretical background in biology, so forgive me if my question is a bit.. well..dumb. I'm trying to use a Monte Carlo approach to find the discriminating position of a given sequence alignment column. So essentially, given a sequence alignment, I want to find the position at which we can distinguish active and inactive conformations.

So, here is my code for the Monte Carlo method:

def MonteCarlo(S, max_iter, threshold):
"""
Computes the discriminating position for a sequence column

Input: S = sequence column, max_iter = max iterations, threshold = threshold of acceptance for boltzmann distribution (between 0 and 1)
Output: 2 classes
"""
n = len(S)
S_copy = S.copy()
num_class1 = int(0.30*n) #number in class1
print(num_class1)
for _ in range(num_class1): #intialisation
rand_position = random.randint(0,len(S)-1)
if S_copy[rand_position] == 'X':
rand_position = random.randint(0,len(S)) #reselect if used position
S_copy[rand_position] = 'X'

#Monte Carlo with Insertions and Deletions

s_entropy = entropy(S)
n_iter = 0 #counter for iterations
class_1 = dict() #class 1 determined by X's
class_2 = dict() #class 2 is rest of S
for i in range(len(S)):
if S_copy[i] == 'X':
class_1[i] =S[i]
else:
class_2[i] =S[i]

res = score(S, class_1, class_2)

while n_iter < max_iter:
r = random.random()

if r < 0.25: #25% chance to do an insertion
(c1,c2,pos) = Insertion(S, class_1, class_2)

elif r < 0.5: #25% chance to do a deletion
(c1,c2,pos) = Deletion(S, class_1, class_2)

else: # 50% chance to do a swap
(c1,c2,pos) = Swap(S, class_1, class_2)

res2 = score(S, c1, c2)

#Boltzmann Distribution coefficient
delta_S = abs(res2 - res)
lambda_, N = 0.2, 19
size = 6000
ind1 = random.randint(0,size - 1)
rv = boltzmann.rvs(lambda_, N, size=size)/N
beta = rv[ind1] #pick float between 0 and 1 with boltzmann distribution
if  (res2 > res) or (beta*delta_S > threshold): #if better score i.e. higher entropy gain
res = res2
class_1 = c1
class_2 = c2

n_iter += 1

return class_1, class_2, pos



Here I'm using the Boltzmann distribution as a probability measure. All the other functions (swap, insertion, deletion, entropy) calculate pretty much what the name says (if you need more clarification on my side, I'd be happy to provide it!)

Let me explain what my code is trying to do: Given a sequence alignment (as a list) say ['M','M','M',...,'L','L','L'] I first set a bunch of random positions and mark them out as 'X' (the number of Xs are determined by num_class1). Next, in the while loop I do swaps,insertions, and deletions with the goal of obtaining a better score. This meansI'm adding, removing, or swapping positions between class1 and class2. Eventually, my code returns two classes and the discriminating position.

While my code works, I don't think it's giving the right result. When I use a base case example of a list with two letters 'M' and 'L with a clear discriminating position, I get random results.

Could someone explain theoretically (or via code) how one can find the discriminating position using a Monte Carlo method as above?

Thanks!

• It's not very clear what you mean by "discriminating position". Can you explain more or link to a source that describes in a little more detail what you are talking about? Apr 12 '20 at 22:09
• Hi! By discriminating position, I mean I'm trying to find a position within the sequence alignment that splits the columns into two classes such that the two have the lowest entropy possible. So, in my sample case with a clear division between Ms and Ls, I should've gotten the the position at which the Ls begin. Does that make sense? Here is a link: pubs.rsc.org/en/content/articlelanding/2019/sc/… Apr 13 '20 at 9:48
• Hi, the paper that you've linked to is talking about a discrimination between two structural states of a protein by a kinase; "discriminating position" does not appear to occur in its full text. It's not clear how this generalizes to alignments. From your explanation though I think I have a better sense of what you mean: for seq alignment $S$ with positions i = 1,2,3...n find the position $S_i$ such that a measure of entropy across aligned positions $S_1 : S_{i-1}$ and $S_{i+1} : S_n$ is minimized for both slices across each column of the aligned slice. (words are easier than code for me). Apr 13 '20 at 15:01
• Yes! no problem (: I also misunderstood what I was trying to solve actually, I have managed to fix the problem! But for future reference: the code is supposed to split the sequence column into two classes such that each distinctly has the highest entropy possible (or lowest for that matter) Apr 13 '20 at 18:37