Smart molecules - Biomatics.org

# Smart molecules

The above stereographic image (which can be viewed in crosseyed 3d) was created by simulating a chain of carbon atoms (similar to a protein backbone) fixed at one end and with a paintbrush at the other end. Is this system with it's output what physicists would call a "string"?  This structure has program code 0.004,0,0.004,1,2,0,1,2,0,4,2,0,4,2,0.004,4,4  B17=180.0  (The numbers represent the relative rotational velocities of succesive covalent bonds, B17=180 indicates the last bond in the chain started with a 180 degree rotation)

0.002,0,0.002,0.002,0,0.002,0,0,0,1,2,0,1,2,0,4,3,0,4,3,0,2,1,0,4,0.002,1,1,2

See Image Gallery for more such examples.

A single carbon atom, while possessing intriguing geometrical properties and being the basis of life as we know it, does not immediately appear very intelligent.  Two carbon atoms, however, bonded together covalently, have some interesting properties.  As the chain of the organic molecule grows, the more intelligent it seems to become.  At the head of the molecular class, we have the networked nucleic acids and proteins of the human brain.  In another sense, perhaps it should be the stem cell molecules.

Evidently, given some population of molecules M at time zero, given time to evolve… at some point in time life is achieved.  The transition from a dumb collection of molecules to intelligent being is a fuzzy one.  When does life begin?  Is it RNA molecules…or viruses?

Today, bioengineers aim development of novel or improved functional molecules ("smart molecules") in areas such as the following:

"Smart media"

"Smart catalysts and reagents"

"Smart materials and devices" (e.g. switchable and/or electro-optical materials,sensors, light-emitting diodes, solar cells)

Proteins are a class of molecules with many different biological functions and classified according to their biological roles.

·         Enzymatic Proteins
·         Transport Proteins
·         Structural Proteins
·         Storage Proteins
·         Hormonal Proteins
·         Receptor Proteins
·         Contractile Proteins
·         Defensive Proteins

Now we can add  “Computational or Information Processing Proteins” to the list.  Due to their ability to transition through multiple states and accept discrete inputs, the Histone proteins  are at the kernel of biological information processing…a sort of Holy Grail for logic and circuit designers.

## The  Intramolecular Cube Group

Consider two adjacent carbon atoms.  The hydrogen atoms will be in an energetically favorable position when they are in the staggered so called "trans" configuration.

Notice that each covalent bond could rotate one hundred and twenty degrees to the next favorable spot.  Each carbon thus has potentially three favorable states.

We now add a few more lines to complete the cube.

Consider a set of three carbon atoms that can each exist in one of two states. We therefore have 2**3 or eight possible states which can be labeled as 000, 001, 010, 011, 100, 101, 110, 111. To go from 000 to 001 requires the rotation of a single bond. To go from 000 to 110 requires rotation about two bonds etc. The following diagram, where the eight corners are the states and the twelve edges are the transitions between states, can depict this situation.

Label edges

E1 =  000,001
E2 =  001,011
E3 =  011,010
E4 =  010,000
E5 =  000,100
E6 =  100,110
E7 =  110,111
E8 =  111,011
E9 =  101,001
E10 = 111,101
E11 = 100,101
E12 = 010,110

Inverses
E1' = 001,000
E2' = 011,001
E3’ = 010,011
E4’ = 000,010
E5’ = 100,000
E6’ = 110,100
E7’ = 111,110
E8’ = 011,111
E9’ = 001,101
E10’= 101,111
E11’= 101,100
E12’= 110,010

If we consider all sequences of moves along the edges of the Cube, we notice the following:

Closure- One sequence followed by another sequence is a sequence.
Associativity- That is E1*(E2*E3) = (E1*E2)*E3.
Identity element- The do nothing sequence does nothing.
Inverses- Every sequence of moves can be done backwards and therefore undone, e.g. E1 and E1′.

Thus, the set of all sequences of moves on the above Cube is a group.

Coincidentally we could relabel the above cube as follows:

to represent the relation “containment” of one subset in another for the partially ordered set of all subsets of the set (a,b,c).

In addition, represent the relation of divisibility for the partially ordered set (1,2,3,5,6,10,15,30) as follows:

The following color coded cube demonstrates two more potential useful properties: (i) three sets of four orthogonal edges and (ii) a bipartite set of corners.

Histone Proteins, Karnaugh Maps and the Quine-McCluskey Algorithm

If the Histone protein is viewed as a boolean network then Karnaugh Maps and The Quine-Mccluskey algortihm can be used to minimize the boolean function describing the network.  Each gene serves as an output port.  In other words each gene reflects in an on/off way to the input into the boolean network.  Current estimates of the number of input sites on the Histone tails and body combined are currently at about fifty...and rising. The combinatorial numbers involved are large yet finite.  These procedures can be used to optimize pharmaceutical therapy and suggest new therapies. At any rate the potential uses for this knowledge would clearly be many.

Example-

In the followiing A,B,C,D represent binding sites on the histone tail or body. The table indicates the effect of each of the 16 possible binary possibilities (f). Every gene in the genome has it's own such table.

$f(A,B,C,D) =\sum m(4,8,10,11,12,15) + \sum d(9,14) \,$

A B C D   f

m0  0 0 0 0   0
m1  0 0 0 1   0
m2  0 0 1 0   0
m3  0 0 1 1   0
m4  0 1 0 0   1
m5  0 1 0 1   0
m6  0 1 1 0   0
m7  0 1 1 1   0
m8  1 0 0 0   1
m9  1 0 0 1   X

m10 1 0 1 0 1 m11 1 0 1 1 1 m12 1 1 0 0 1 m13 1 1 0 1 0 m14 1 1 1 0 X m15 1 1 1 1 1

The Quine-McCluskey algortihm minimizes the following corresponding equation

$f_{A,B,C,D} = A'BC'D' + AB'C'D' + AB'C'D + AB'CD' + AB'CD + ABC'D' + ABCD' + ABCD \$

to either of the two following functionally equivalent equations-

$f_{A,B,C,D} = BC'D' + AB' + AC \$

$f_{A,B,C,D} = BC'D' + AD' + AC \$