BIO-INSPIRED DATA AND SIGNALS CELLULAR SYSTEMS

Andr´e Stauffer, Daniel Mange and Jo¨el Rossier

Logic Systems Laboratory, Ecole polytechnique f´ed´erale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland

Keywords:

Self-organization, conﬁguration, cloning, cicatrization, regeneration.

Abstract:

Living organisms are endowed with three structural principles: multicellular architecture, cellular division,

and cellular differentiation. Implemented in digital according to these principles, our data and signals cellular

systems present self-organizing mechanisms like conﬁguration, cloning, cicatrization, and regeneration. These

mechanisms are made of simple processes such as growth, load, branching, repair, reset, and kill. The data

processed in the self-organizing mechanisms and the signals triggering their underlying processes constitute

the core of this paper.

1 INTRODUCTION

Borrowing three structural principles (multicellular

architecture, cellular division, and cellular differenti-

ation) from living organisms, we have already shown

how to grow cellular systems thanks to two algo-

rithms: an algorithm for cellular differentiation, based

on coordinate calculation, and an algorithm for cellu-

lar division (Mange et al., 2004). These cellular sys-

tems are endowed with self-organizing properties like

conﬁguration, cloning, cicatrization, and regeneration

(Stauffer et al., 2005).

In a previous work (Stauffer et al., 2006), the

conﬁguration mechanisms (structural and functional

growth), the cloning mechanisms (cellular and organ-

ismic growth), the cicatrization mechanism (cellular

self-repair), and the regeneration mechanism (organ-

ismic self-repair) were already devised as the result of

simple processes like growth, load, branching, repair,

reset, and kill. The goal of this paper is to point out the

data processed in these mechanisms and the signals

triggering their underlying processes. Starting with a

minimal system, a cell made up of six molecules, Sec-

tion 2 will introduce digital simulations to describe

the data and the signals involvedin the self-organizing

mechanisms and the corresponding processes. We de-

ﬁne then a small organism made of three cells, the

“SOS” acronym, as an application example for the

simulation of our mechanisms and processes (Sec-

tion 3). A brief conclusion (Section 4) summarizes

our paper and opens new research avenues.

2 SELF-ORGANIZING

MECHANISMS

2.1 Structural Conﬁguration

The goal of the structural conﬁguration mechanism is

to deﬁne the boundaries of the cell as well as the liv-

ing mode or spare mode of its constituting molecules.

This mechanism is made up of a structural growth

process followed by a load process. For a better un-

derstanding of these processes, we apply them to a

minimal system, a cell made up of six molecules ar-

ranged as an array of two rows by three columns, the

third column involving two spare molecules dedicated

to self-repair.

The growth process starts when an externalgrowth

signal is applied to the lower left molecule of the cell

(Fig. 1a) and this molecule selects the corresponding

eastward data input (Fig. 1b). According to the struc-

tural conﬁguration data or structural genome, each

molecule of the cell generates then successively an

internal growth signal and selects an input (Fig. 2),

in order to create a data path among the molecules of

the cell (Fig. 1b-g). When the connection path be-

tween the molecules closes, the lower left molecule

delivers a close signal to the nearest left neighbor cell

(Fig. 1h). The structural conﬁguration data is now

moving around the data path and ready to be trans-

mitted to neighboring cells.

The load process is triggered by the close sig-

nal applied to the lower right molecule of the cell

(Fig. 3a). A load signal propagates then westward

and northward through the cell (Fig. 3b-d) and each of

203

Stauffer A., Mange D. and Rossier J. (2008).

BIO-INSPIRED DATA AND SIGNALS CELLULAR SYSTEMS.

In Proceedings of the First International Conference on Bio-inspired Systems and Signal Processing, pages 203-207

DOI: 10.5220/0001057402030207

 SciTePress

(e)

(f)

(g)

(a)

(b) (c)

(d)

(h)

Figure 1: Structural growth process of a minimal system, a

cell made up of six molecules. (a) External growth signal

is applied to the lower left molecule. (b-g) Generation of

internal growth signals to build the structural data path. (h)

Closed path and close signal delivered to the nearest left

neighbor cell.

(a) (b) (c) (d)

Figure 2: Data input selection. (a) Northward. (b) East-

ward. (c) Southward. (d) Westward.

its molecules acquire a molecular mode (Fig. 4) and

a molecular type (Fig. 5). We ﬁnally obtain an homo-

geneous tissue of molecules deﬁning both the bound-

aries of the cell and the position of its living mode and

spare mode molecules (Fig. 3e). This tissue is ready

for being conﬁgured by the functional conﬁguration

data.

(b)

(c)

(d)

(e)

Figure 3: Load process. (a) External close signal applied

to the lower right molecule by the nearest right neighbor

cell. (b-e) Generation of internal load signals propagating

westward and northward to store the molecular modes and

types of the cell.

(a) (b) (c) (d)

(e)

Figure 4: Molecular modes. (a) Living. (b) Spare. (c)

Faulty. (d) Repair. (e) Dead.

(b) (c) (d)

(a)

(e) (f)

(g) (h)

(i)

Figure 5: Molecular types. (a) Internal. (b) Top. (c) Top-

left. (d) Left. (e) Bottom-left. (f) Bottom. (g) Bottom-right.

(h) Right. (i) Top-right.

2.2 Functional Conﬁguration

The goal of the functional conﬁguration mechanism

is to store in the homogeneous tissue, which already

contains structural data (Fig. 3e), the functional data

needed by the speciﬁcations of the current applica-

tion. This mechanism is a functional growth process,

performed only on the molecules in the living mode

while the molecules in the spare mode are simply by-

passed. It starts with an external growth signal ap-

plied to the lower left living molecule (Fig. 6a). Ac-

cording to the functional conﬁguration data or func-

tional genome, the living molecules then successively

generate an internal growth signal, select an input,

and create a path among the living molecules of the

cell (Fig. 6b-f). The functional conﬁguration data is

now moving around the data path and ready to be

transmitted to neighboring cells.

(a)

(b) (c)

(d)

(e)

(f)

Figure 6: Functional conﬁguration of the cell performed as

a functional growth process applied to the living molecules.

(a) External growth signal is applied to the lower left

molecule. (b-e) Generation of internal growth signals in or-

der to build the functional data path. (f) Closed functional

data path.

2.3 Cloning

The cloning mechanism or self-replication mecha-

nism is implemented at the cellular level in order to

build a multicellular organism and at the organismic

level in order to generate a population of organisms.

This mechanism suppose that there exists a sufﬁcient

number of molecules in the array to contain at least

one copy of the additional cell or of the additional or-

ganism. It corresponds to a branching process which

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204

takes place when the structural and the functionalcon-

ﬁguration mechanisms deliver northward and east-

ward growth signals on the borders of the cell during

the corresponding growth processes (Fig. 7).

(a)

(b) (c)

(d)

Figure 7: Generation of growth signals triggering the

cloning mechanism. (a) Northward structural branching

process. (b) Eastward structural branching process. (c)

Northward functional branching process. (d) Eastward

functional branching process.

2.4 Cicatrization

Fig. 6f, shows the normal behavior of a healthy min-

imal cell, i.e. a cell without any faulty molecule. A

molecule is considered as faulty, or in the faulty mode,

if some built-in self-test detects a lethal malfunction.

Starting with the normal behavior of Fig. 6f, we sup-

pose that two molecules will become suddenly faulty

(Fig. 8a): (1) The lower left molecule, which is in the

living mode. (2) The upper right molecule, which is in

the spare mode. While there is no change for the up-

per right molecule, which is just no more able to play

the role of a spare molecule, the lower left one triggers

a cicatrization mechanism. This mechanism is made

up of a repair process involving eastward propagating

repair signals (Fig. 8b-c) followed by a reset process

performed with westward and northward propagating

internal reset signals (Fig. 8d-g). This tissue, com-

prising now two molecules in the faulty mode and

two molecules in the repair mode, is ready for be-

ing reconﬁgured by the functional conﬁguration data.

This implies a functional growth process bypassing

the faulty molecules (Fig. 9).

2.5 Regeneration

Our minimal system comprises a single spare

molecule per row and tolerates therefore only one

faulty molecule in each row. A second faulty

molecule in the same row will cause the death of the

whole cell, and the start of a regeneration mechanism.

Fig. 10 illustrates the repair process and kill process

involved in this mechanism. Starting with the nor-

mal behavior of the cicatrized cell (Fig. 9f), a new

(a)

(b) (c)

(d)

(e)

(f)

(g)

Figure 8: Cicatrization mechanism performed as a repair

process followed by a reset process. (a) Living and spare

molecules becoming faulty. (b-c) Generation of repair sig-

nals propagating eastward. (d-f) Generation of internal re-

set signals propagating westward and northward. (g) Cell,

comprising two faulty and two repair molecules, ready for

functional reconﬁguration.

(a)

(b)

(c)

(d)

(e)

(f)

Figure 9: Functional reconﬁguration of the living and repair

molecules. (a) External growth signal bypassing the lower

left faulty molecule. (b-e) Generation of internal growth

signals to build a functional data path bypassing the faulty

molecules. (f) Closed functional data path within the living

and repair molecules.

molecule, the upper middle one, becomes faulty. In a

ﬁrst step, the new faulty molecule sends a repair sig-

nal eastward, in order to look for a spare molecule,

able to replace it (Fig. 10b). In a second step, the sup-

posed spare molecule, which is in fact a faulty one,

enters the lethal dead mode and triggers kill signals

which propagate northward, westward and southward

(Fig. 10c-f). Finally in Fig. 10g, all the molecules of

the array are dead as well as our minimal system.

BIO-INSPIRED DATA AND SIGNALS CELLULAR SYSTEMS

205

(a)

(b) (c)

(d)

(e)

(f)

(g)

Figure 10: Regeneration mechanism performed as a repair

process followed by a kill process. (a) Living molecule be-

coming faulty. (b) Eastward repair signal. (c-f) Genera-

tion of internal and external kill signals propagating north-

ward, westward and southward. (g) Cell made up six dead

molecules.

3 SOS ACRONYM APPLICATION

3.1 Structural Conﬁguration,

Functional Conﬁguration and

Cloning

Even if our ﬁnal goal is the self-organization of com-

plex bio-inspired data and signals cellular systems,

we will use an extremely simpliﬁed application ex-

ample, the display of the “SOS” acronym, in order

to illustrate its basic mechanisms. The system that

displays the acronym can be considered as a one-

dimensional artiﬁcial organism composed of three

cells (Fig. 11). Each cell is identiﬁed by a X coor-

dinate, ranging from 1 to 3. For coordinate values

X = 1 and X = 3, the cell implements the S character,

for X = 2, it implements the O character. Such a cell,

capable of displaying either the S or the O character,

is a totipotent cell comprising 4× 6 = 24 molecules.

X=1

2 3

Figure 11: One-dimensional organism composed of three

cells resulting from the structural conﬁguration, functional

conﬁguration and cloning mechanisms applied to a totipo-

tent cell.

In order to build the multicellular organism of

Fig. 11, the structural conﬁguration mechanism, the

functional conﬁguration mechanism, and the cloning

mechanism are applied at the cellular level. Starting

with the structural and functional conﬁguration data

of the totipotent cell, these mechanisms generate suc-

cessively the three cells X = 1 to X = 3 of the organ-

ism “SOS”.

3.2 Cicatrization and Functional

Reconﬁguration

The cicatrization mechanism (or cellular self-repair)

results from the introduction in each cell of one col-

umn of spare molecules (Fig. 11), deﬁned by the

structural conﬁguration of the totipotent cell, and the

automatic detection of faulty molecules. Thanks to

this mechanism, each of the two faulty molecules

of the middle cell (Fig. 12) is deactivated, isolated

from the network, and replaced by the nearest right

molecule, which will itself be replaced by the near-

est right molecule, and so on until a spare molecule is

reached. The functional reconﬁguration mechanism

takes then place in order to regenerate the O charac-

ter of the organism “SOS”. As shown in Fig. 12, the

regenerated character presents some graphical distor-

tion.

X=1

2 3

Figure 12: Graphical distortion resulting from the cicatriza-

tion and reconﬁguration mechanisms applied to the middle

cell of the organism.

3.3 Regeneration

The totipotent cell of the organism “SOS” havingonly

one spare column allows only one faulty molecule per

row. When a second one is detected, the regeneration

mechanism (or organismicself-repair) takes place and

the entire column of all cells to which the faulty cell

belongs is considered faulty and is deactivated (col-

umn X = 2 in Fig. 13; in this simple example, the col-

umn of cells is reduced to a single cell). All the func-

tions (X coordinate and conﬁguration) of the cells to

the right of the column X = 1 are shifted by one col-

umn to the right. Obviously, this process requires as

BIOSIGNALS 2008 - International Conference on Bio-inspired Systems and Signal Processing

206

many spare cells to the right of the array as there are

faulty cells to repair. As shown in Fig. 13, the repara-

tion of one faulty cell needs one spare cell to the right

and leaves a scar in the organism “SOS”.

X=1

2 3

Figure 13: Scar resulting from the regeneration mechanism

applied to the organism.

4 CONCLUSIONS

The self-organizing mechanisms are made of simple

processes like growth, load, branching, repair, reset,

and kill. They allow the data and signals cellular

systems to possess three bio-inspired properties: (1)

Cloning or self-replication at cellular and organismic

levels. (2) Cicatrization or self-repair at the cellular

level. (3) Regeneration or self-repair at the organis-

mic level.

Starting with a very simple system, a cell made

of six molecules, we realized digital simulations in

order to describe the data and signals involved in the

self-organizing mechanisms. The “SOS” acronym, an

organism made of three cells, was introduced as an

application example for the simulation of our mecha-

nisms and processes.

The functional conﬁguration mechanism pre-

sented here will be implemented in the ubichip (Up-

egui et al., 2007), a programmable circuit that draws

inspiration from the multi-cellular structure of com-

plex biological organisms.

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