Computation with molecules

What is the data structure to store information?

You make a particular molecule
You have a certain distribution of molecular concentrations
? There is a certain multiway graph of transformations

How do we characterize “what’s going on a cell”?

Looking at how much of particular proteins get produced
Interactome
State of cell:
concentrations
? spatial information
[ e.g. CA running in microtubules ]

Spatial information

Coordinates by string matching : genome, docking, etc.
E.g. in bronchial trees, dendritic trees

What kinds of molecules to use?

Success story: biology [DNA + proteins]
Modular synthesis?
[[ a few repeating units ]]
Combinatorial chemistry [30-50 types of amines, ...]
Drug discovery: mostly shape + charge distribution

Sample goal : generate the primes with molecules

Generate only molecular sizes that are prime...

E.g. maybe there only certain buckyballs that are possible ; cf tiling problem
Set up constraints that are only satisfied by the result you want....
In[]:=
ResourceFunction["BuckyballGraph"][2]
Out[]=
Cf. find the ground state of a spin glass ... cf traveling salesman problem [[ with a substrate ]]
< Specifying the program with a substrate >
Is there a substrate [that we can make, as a metamaterial] so that we get e.g. the primes

Generate successive primes

Analogous example: freezing of complicated molecules

When don’t things crystallize? [Becomes amorphous]
In[]:=
EntityValue[EntityClass["Chemical",{"HillFormulaString"->"C8H18"}],"MeltingPoint"]
Out[]=
{
95.5
°C
,
-112.2
°C
,
-107.
°C
,
-91.
°C
,
-100.7
°C
,
-110.
°C
,
-124.
°C
,
-124.
°C
,
-91.
°C
,
-109.
°C
,
-126.1
°C
,
-64.
°C
,
-114.9
°C
,
-90.9
°C
,
-109.
°C
,
-121.
°C
,
-121.
°C
,
-57.
°C
}
In[]:=
KeyMap[Molecule,EntityValue[EntityClass["Chemical",{"HillFormulaString"->"C8H18"}],"MeltingPoint","EntityAssociation"]]
Out[]=
Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

95.5
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-112.2
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-107.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-91.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-100.7
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-110.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-124.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-124.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-91.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-109.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-126.1
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-64.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-114.9
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-90.9
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-109.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-121.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-121.
°C
,Molecule
Formula:
C
8
H
18
Atoms: 26 Bonds: 25

-57.
°C


Simpler goal: make the Thue-Morse sequence

Can there be a computation encoded in the chemical network?

Cf. circadian rhythm networks

BZ reaction : reaction/diffusion

Cicadas

http://mariomarkus.com/save/biological-primes.pdf

Perturbations in multiway graphs

Are there topologically stable structures in multiway graphs
[ Particles in branchial space? ]

How do you program the chemical system?

Put in certain initial compounds

Flash light at it, etc. / magnetic fields / temperature

Change pH / wash in some other compound

[ Flow through a tube ]

Given a background multiway structure ... what is the “effective physics” of making certain perturbations

Computation is through certain ?persistent perturbations etc.