Catalyzed Molecule Replication in an Artificial Chemistry

Abstract

This paper instantiates an architecture for an artificial chemistry featuring continuous physics and discrete chemical reactions. A system of bonded complementary molecular strands replicates in the presence of a catalyst. The catalyst causes the strands to disengage; each strand subsequently replicates its missing complement by bonding to free atoms.

Full text

Catalyzed Molecule Replication in an Artificial Chemistry
Thomas E. Portegys
Illinois State University
Campus Box 5150
Normal, Illinois, USA 61790-5150
portegys@ilstu.edu
Abstract
This paper instantiates an architecture for an artificial
chemistry featuring continuous physics and discrete chemical
reactions. A system of bonded complementary molecular
strands replicates in the presence of a catalyst. The catalyst
causes the strands to disengage; each strand subsequently
replicates its missing complement by bonding to free atoms.
Introduction
Information only has meaning in the presence of an
interpreting system, like a musical composition played on
an instrument, or a message in a bottle found by a wanderer
on a beach. In one sense, a living organism is an
arrangement of elements interpreted by the rules of
chemistry. The goal of artificial chemistry research is to
examine this underlying substrate, and to identify its
essential properties. A major impetus for artificial
chemistry research is based on the belief that a sufficiently
rich physics and chemistry is necessary for the
development of artificial life (Bedau et al. 2000, Dittrich et
al. 2001).
The focus in artificial chemistry is on processes that
characterize chemical reactions: bonding, forces, kinetics,
energy, catalysis, etc. The ways that atoms bond determine
the shape and stability of molecules, which in turn has a lot
to do with their functionality, including their capacity to
bond with other molecules. The concept of bonding can be
generalized to that of connectedness, which is at the heart
of complex systems. Connections can of course take many
forms: the weighted links in natural and artificial neural
networks; the input-output sequences of attractor functions;
cellular automata neighborhoods; and the scale-free
networks that characterize the internet are other examples.
The attempt here is to combine a simple continuous
Newtonian particle physics with the well-known and
readily computable cellular automaton (CA) model as a
chemistry architecture. Reaction rules for bonding and
other actions are written in terms of CA neighborhood
templates. Continuous physics allows molecular
movements to occur en mass without the use of CA rules to
generate displaced structures, and is more akin to real
molecular motion.
This project is a system of reactions that permit bonded
complementary molecular strands to replicate in the
presence of a catalyst. The catalyst causes the strands to
disengage; each strand subsequently replicates its missing
complement by bonding to free atoms, a process
reminiscent of DNA replication during cell mitosis.
The paper was primarily inspired by three recent
efforts: Hutton’s artificial chemistry Squirm3 (2002),
Smith, Turney and Ewaschuk’s JohnnyVon (2003), and
my recent work (Portegys 2004), which it extends and
improves.
Prior to these, Dittrich et al. (2001) compared a wide
range of artificial chemistry approaches, including
assembler automata (Rasmussen et al. 1990, Ray 1992,
Adami and Brown 1994), Ono and Ikegami’s autocatalytic
membrane formation (1999), and lattice molecular systems
(McMullin and Varela 1997), in which the atoms
comprising a molecule map discretely to cellular space.
Squirm3 is a lattice molecular system in which mobile
molecules self-replicate using available atoms in a 2D
cellular space. Atoms have a fixed type and a variable
state. Chemical reaction rules based on type, state and
proximity determine the states and bonding status of atoms.
Atoms move by jumping from cell to cell through
simulated Brownian motion; however, atoms bound into
molecules are largely immobile (although this has been
since rectified in a later version (Hutton 2004)). Beginning
with a soup of inert atoms exposed to state-disrupting
cosmic rays, self-replication was shown to spontaneously
occur.
In JohnnyVon, by contrast, T-shaped atoms called
codons move through a continuous 2D space and interact
exclusively through force fields; collisions do not occur.
There are two types of codons, distinguished by their field
“colors”. Each codon is an automaton containing a set of
rules governing its field strengths in response to signals
represented by the proximity of other codon fields.
My recent artificial chemistry project, Maxwell,
involved another example of a concerted set of bonding
reactions that produces “foraging” behavior. Bonding is
the most observable improvement in this project over
Maxwell. In Maxwell, bonds (and thus molecules) were
stiff and often created through an awkward “grapple”

reaction that attempted to instantaneously move an atom
relative to another without regard to how it was bonded to
other atoms. This project features spring-like bonds with
variable strengths that smoothly move bonded atoms
using forces. This also provides for molecular bending
and tension. Another improvement involves discarding
the fixed CA grid as a neighborhood metric in favor of
“floating” neighborhoods centered over each reacting
atom. This eliminates absolute position as a factor in
reaction processes.
Description
This system is an artificial chemistry featuring atoms and
molecules moving and colliding in a continuous manner in
a viscous fluid filling a 2D space. A molecule consists of a
bound set of atoms. Chemical reactions are mappings of
discrete cellular configurations to parameterized actions on
atoms. Actions allow atom creation and destruction,
bonding and unbonding to make and break molecules,
orientation, and state and/or type change. Time proceeds in
discrete steps.
Atoms and molecules
Atoms are elementary particles possessing a type, state,
mass, radius, elasticity, charge, orientation, position, and
velocity. A molecule is a set of atoms connected by spring-
like bonds. Each atom has a maximum of eight bonding
sites corresponding to eight possible neighbors (see
Reactions section below). A bond may be of variable
strength. A bond exerts a force vector on a bonded atom to
move it to the “correct” alignment as defined by the
bonding site it is connected to. For example, if atom A
bonds atom B on A’s “north” bonding site, A will exert a
force on B to move it directly north of A at a specific
distance. As with physical springs, the force magnitude is
proportional to the distortion distance. Bonds are mutual: if
A bonds to B then B also bonds to A. The structural
integrity of a molecule is dependent on the cumulative
effect of the bonded atoms that comprise it.
Forces resulting from bonds, charges and collisions
result in continuous velocity and position updates of atoms
according to Newtonian physics. Collisions can be variably
elastic depending on the involved atoms. For this
implementation, rotational momentum is not supported.
The motion of bonded atoms can produce molecular
bending and tension by distorting the bonds between them.
An atom is oriented in one of the eight compass
directions. It may also be in a mirrored state to support
symmetric reactions. An atom’s bonding sites are also
relative to its orientation. The atom orientation attribute has
no counterpart in real chemistry to my knowledge.
However, it is quite useful in the reactions that I have
modeled.
Space
The space is a 2D bounded rectangle filled with a viscous
fluid that impedes the movement of atoms through it.
Random atomic movement is accomplished by simulated
Brownian motion.
Reactions
Reactions arise from the interaction of atoms. A floating
3x3 Moore neighborhood of cells is centered over each
atom, which is considered the “source” atom for reactions
within the neighborhood. A reaction specifies a
configuration of atom types residing within the
neighborhood. Cell residence is determined by whether the
center of an atom falls within the cell. Since atoms have an
orientation, their neighborhoods are oriented accordingly,
as shown by the two atoms in Figure 1.
Figure 1: Oriented Cell Neighborhoods
A neighborhood cell matches on both atom type and state.
A type match value is one of {atom type, empty, occupied,
ignore}. The neighborhood evaluation is a conjunction of
all 9 value matches. An empty value specifies that a cell
must not contain any atom. This could be used for
inhibitory control of a reaction. The occupied value
matches any atom type. The ignore value positively
matches any cell condition. A state match consists of
{atom state, ignore}. This allows reactions to be optionally
controlled by atom states as well as types.
A reaction consists of the following: {neighborhood,
action, target, next states, parameters}. Target is the
location of the cell where the action is directed. In the rare
instance that the targeted cell contains more than one atom
of the appropriate type, the reaction is applied to all of
them if possible (it is not possible to bond to more than one
from a given source bonding site, for example). The states
of atoms involved in a reaction are updated by the next
states values. Parameters apply to actions. These are:
{atom type, orientation, source and target bond sites, bond
strength}. The actions are:

 Create atom. Parameters: type and orientation of
created atom.
 Destroy atom. Parameter: target atom type.
 Bond atoms. Parameter: target atom type, bonding
sites and strength.
 Unbond atom. Parameter: bonding site.
 Orient atom relative to source atom’s orientation.
For example, if the source atom is oriented east, and
it orients a target atom to its west, the atom will
acquire a north orientation. Parameters: target atom
type and orientation.
 Modify atom type. Parameter: target atom old and
new types.
 Modify atom state.
Update cycle
1. Update positions and velocities of molecules based on
accumulated forces.
2. Clear forces.
3. Compute new bond, charge, and collision forces.
4. Perform reactions.
Results
The problem involves an orchestration of cooperating
reactions that permit bonded complementary molecular
strands to replicate in the presence of a catalyst. The
catalyst causes the strands to disengage; each strand
subsequently replicates its missing complement by
bonding to free particles. The double-stranded molecule is
shown in Figure 2.
Figure 2: The Replicating Molecule
The atom marked by a ‘*’ in the upper-left of the figure is
a catalyst atom. This image was taken just before the
catalyst bonded to the west of the ‘A’ atom to initiate the
strand splitting process. Reactions allow a catalyst to
initially bond with either with the ‘A’ or ‘W’ type of atom.
The splitting process begins by passing the catalyst down
the length of the strand, as shown in Figure 3.
Figure 3: Beginning of Molecule Split
Type ‘A-Z’ atoms can have the following possible state
values: {free, bonded, unbonded, handoff}. When situated
in a double-stranded configuration, they are in the bonded
state. When single stranded, they are in the unbonded state.
Free ‘A-Z’ atoms are in the free state. The handoff state is
used to coordinate strand splitting. For example, Figure 4
shows a reaction neighborhood that allows atom ‘A’ to
unbond from the catalyst, atom ‘B’ having
“acknowledged” the bond handoff by entering the handoff
state after bonding to the catalyst.
Figure 4: Catalyst Handoff Neighborhood
Figure 5 shows the near-completion of the strand split
reactions.
Figure 5: Conclusion of Splitting Reactions
After splitting, the two strands begin to replicate their
complements by bonding to free atoms of the appropriate
types. The bonding sequence proceeds from bottom to top.
Figure 6 shows this process under way.

Figure 6: Replication by Bonding to Free Atoms
Experiments show that replication occurs quite readily in a
mixture of replicants, free components and catalysts.
Conclusions
One of the aims of this project was to find a way to acquire
some of the benefits of a continuous physical medium,
such as that in which organic chemistry takes place, and
also retain the computability benefits of a cellular
automaton as a chemistry framework. For this iteration of
the architecture, several important improvements were
made, as previously mentioned. In addition, the code was
cleaned-up considerably and user-programmability
enhanced. Reactions were intentionally defined in
declarative rather than procedural form in order to aid in
evolvability. The reaction C++ class definition is given in
Appendix 1.
The evolvability topic is important in that it relates to the
question of how to choose a set of reactions that exhibit
interesting or desirable behavior. One of the impressions I
got after fastidiously coding the reactions for the
replicating molecule and getting it to work was of how
fragile and specific the reactions were – the smallest
mistake or omission would ruin everything. Real chemistry
supports a seemingly endless diversity of molecules and
reactions, yet the computational cost to simulate it can be
excessive (Zagrovic, et al. 2002); although using a 2D
world will certainly lessen this cost. Possible evaluation
metrics for an “interesting” chemistry might be:
1. Entropy. Interesting processes, including living ones,
appear to exist “on the edge of chaos”.
2. Autocatalytic cycles. Many researchers believe these
processes to be the key to the origin of life.
3. Semi-permeable membranes that create special
reaction environments.
4. Replication.
5. Symmetry of more complex forms.
As for extensions of the model that may possibly foster
more interesting chemical systems, such semi-permeable
membranes, some of the possibilities are:
1. The use of variables to symbolize various quantities,
such as target atom types and locations, would
improve the model’s power and flexibility. An
example of the use of variables can be seen in Squirm3
(Hutton 2004).
2. The use of a hexagonal 2D space would eliminate the
awkward difference between diagonal and
vertical/horizontal orientations.
3. The extra topological freedom of motion inherent in a
3D system should be explored. This would allow for
some interesting structures like pores or stomata to
exist.
4. Rotation and angular effects could be incorporated into
the physics. This might allow en mass alignments of
molecules to take place.
The open source C++/OpenGL code is available at
www.itk.ilstu.edu/faculty/portegys/research.html
References
Adami, C.; and Brown, C.T. 1994. Evolutionary learning in
the 2D artificial life system avida. In Brooks, R.A. and
Maes, P., editors, Artificial Life IV, Cambridge MA, MIT
Press, 377-381.
Dittrich, P.; Ziegler, J.; and Banzhaf, W. 2001. Artificial
chemistries – A review. Artificial Life 7:2245-275
Hutton, T. J. 2002. Evolvable Self-Replicating Molecules
in an Artificial Chemistry. Artificial Life 8(4):341-356.
Hutton, T. J. 2004. A Functional Self-Reproducing Cell in
a Two-Dimensional Artificial Chemistry Molecules in an
Artificial Chemistry. Artificial Life 9 Proceedings.
McMullin, B. and Varela, F.J. 1997. Rediscovering
computational autopoiesis. In Husbands, P. and
I. Harvey, editors, Fourth European Conference on
Artifcial Life, pages 38-47, Cambridge, MA,
MIT Press.
Ono, N. and Ikegami, T. 1999. Model of self-replicating
cell capable of self-maintenance. In Floreano,
D., J.-D. Nicoud, and F. Mondana, editors, Proc. Fifth
European Conference on Artifcial Life
(ECAL'99), pages 399-406, Berlin, Springer.
Portegys, T. E. 2004. An Evolvable Artificial Chemistry
Featuring Continuous Physics and Discrete Reactions,
Artificial Life 9 Proceedings.
Rasmussen, S., C. Knudsen, R. Feldberg, and M.
Hindsholm. 1990. The coreworld: Emergence and

evolution of cooperative structures in a computational
chemistry. Physica D, 42:111-134.
Ray, T. S. An approach to the synthesis of life. In Langton,
C. G., C. Taylor, J. D. Farmer, and
S. Rasmussen, editors, Artifcial Life II, pages 371-408,
Redwood City, CA, Addison-Wesley.
Smith, A.; Turney, P.; and Ewaschuk, R. 2003. Evolvable
Self-Replicating Molecules in an Artificial Chemistry.
Artificial Life 9(1):21-40.
Zagrovic, B.; Snow, C.D.; Shirts, M.R.; and Pande, V.S.
2002. Simulation of Folding of a Small Alpha-helical
Protein in Atomistic Detail using Worldwidedistributed
Computing. Journal of Molecular Biology.
Appendix 1 – Reaction Structure
// Reaction.
// Pattern matching is done against a Moore (3x3)
// neighborhood of cells centered on a particle.
// Various reaction types determine changes to particles
// in the neighborhood.
class Reaction
{// Matching neighborhood particle types.
static const int IGNORE_CELL;
static const int EMPTY_CELL;
static const int OCCUPIED_CELL;
int types[3][3];
// Matching neighborhood particle states.
static const int IGNORE_STATE;
int states[3][3];
// Reaction type.
int reactionType;
// Reaction target location in neighborhood.
int x,y;
// Next states of reacting particles.
int sourceState;
int targetState;
// Reaction parameters.
int type;
Orientation orientation;
int sourceBond,targetBond;
float bondStrength;
};