CD4+ T-cell fate optimization for leukemia thresholds

I think that with regard to thymus (T) cell CD4+, and its heterogeneity, 

it has already been established, (Carbo, Ghosh, Rothenberg, etc, etc).

This optimization problem, should not be too terribly difficult. 

Ie., there are only eight T-help (AKA “types”) that CD4+ can differentiate into

what they call that “Plasticity”.

I think that a useful application is a mixed-integer linear-programming 

optimization application can be realized.  The problem is a constrained CQM solver problem.

The optimization uses a linear objective and constraints.

The objects are "real-valued" and "integer" values. Eg.,

this relates to the Big-8 proteins(Pts), ie., the subsets of the CD4 T-help

cell in which the "Units" will be;

"continuous", (0 < inf in this app). These are AKA:

"REAL-VALUED" variables."Discrete" units (eg., ACTivation, DIFFerentiation, and Expression, 

can be construed to be an ON/OFF state, they are AKA: "INTEGER-VALUED" variables.

The attributes, 6 of them, are embedded into a Pts{{..}} dict, and processed by user input.

( I'll call "Big-8" as (=::) {Tfh, Th9, Th2, iTreg, Tr1, Th22, Th17, Th1})

These may or may not evolve (a threshold exists) from the CD4+ t-cell, (heterogeneity).

Again, there may not be that much of a challenge the hybrid solver for this.

WHAT I’D LIKE HOWEVER, :) is to use this type of optimization on determining the threshold

of CLL, chronic lymphocytic leukemia onset. Any type of leukemia research, CS-wise is

my passion, actually : ) According to Carbo et al, there are 104 proteins, (transcription factors, 

receptors, cytokines, interlukens, “component complexes”, up/down regulators etc, in the CD4+ T-cell 

compartment). I believe that similar to the above optimization CQM problem, an approach or two

for leukemia thresholds can be accomplished using this CD4+ compartment of 104 proteins. 

I’ve already entered all 104 proteins including each of their associated/connected PTs in

an Excel spreadsheet for convenience.  

import dimod as dimod
from dwave.system import LeapHybridCQMSampler          
import re

# init

strattoamps1 = 0
strACTivation1 = 0
strEXPansion1 = 0
strDIFFerentiation1 = 0
strExpression1 = 0
strPlasticity1 = 0
Units1 = 'continuous'
# This is done for each of the 8 proteins mentioned.

Pts = {'Tfh': {'Attoamps': strattoamps1, 'ACTivation': strACTivation1, 'EXPansion': strEXPansion1,
               'DIFFerentiation': strDIFFerentiation1, 'Expression': strExpression1, 'Plasticity': strPlasticity1,
               'Units': Units1}, # . . .
# This is also repeated for each of the 8 heterogenous CD4 candidates.

# User input is coded here.
# Constraints are established. 
# <Objective and constraint functions are coded>
# <Presentation to the solver is established>
# Lagrange parameters should be explored. 
# Analyzing and interpreting results are done.
# Tests and changes to fully optimize to infer E_min is done.
# Comments/notes in the IDE's code.