Complexification of Gene Networks by Co-evolution of Genomes

and Genomic Parasites

David M. Holloway

, Alexander B. Kazansky

and Alexander V. Spirov

2,3

Mathematics Department, British Columbia Institute of Technology, Burnaby, B.C., Canada

The Sechenov Institute of Evolutionary Physiology & Biochemistry, St.-Petersburg, Russia

Computer Science and CEWIT, SUNY Stony Brook, Stony Brook, New York, U.S.A.

Keywords: Evolution in Silico, Evolutionary Design, Genomes, Genomic Parasites, Artificial Transposons, Co-

evolution, Gene Networks, Gene Co-option, Complexification, Genetic Algorithms.

Abstract: The co-evolution of species with their genomic parasites (transposons) is thought to be one of the primary

ways of rewiring gene regulatory networks (GRNs). In this communication, we computationally explore

some of the essential co-evolution aspects of hosts (GRNs) with their transposons. We implemented an

evolutionary search of an appropriate GRN model design on the example of the Drosophila gap-gene

network. Simple artificial transposons capable of spreading and transposition were implemented. With the

model, we explored the hypothesis that targeting destruction of some of the regulatory connections in the

GRN via the action of transposons can produce negative selection pressure. Functionally external genes can

be recruited (co-opted) into the GRN under this selection pressure following transposon rewiring of the

GRN. Over evolutionary time, transposition events are able to disrupt these new regulatory connections,

leading to repeated cycles of recruitment, rewiring and optimization. This process can produce increasingly

large GRNs with the same basic functions.

1 INTRODUCTION

The extensive area of modern evolutionary

computation (EC) was inspired by ideas from

biological evolution. Contemporary biological

evolution theories inspire computer science fields to

work out and implement novel evolutionary

algorithms. In turn, biology, especially in the area of

systems biology, has been and is currently

influenced by contemporary EC ideas and

approaches. One product from the cross-

dissemination of ideas between systems biology and

EC (in particular, genetic algorithms, GA) is a set of

modern techniques to design real genetic network

models, termed the evolution in silico approach.

The evolutionary design of GRNs in nature

involves the establishment of gene-gene connectivity

(wiring) and tuning of the connection strengths,

followed by multiple rounds of rewiring and

retuning to optimize the GRN for a particular

function. These wiring and rewiring events involve

specific molecular mechanisms. One such

mechanism is the co-evolution of gene networks and

their parasites, termed transposons. Co-evolution is

proposed to be one of the key mechanisms of gene

network evolution. The co-evolutionary

relationships of the hosts (gene networks) and

parasites (transposons) can be roughly subdivided as

competitive or mutualistic. The ‘arms race’ nature of

competitive relationships can lead to high levels of

complexity, a manifestation of which is gene

network outgrowth.

Gene Network outgrowth by Recruitment of

Novel Members: In early metazoan evolution, gene

networks specifying developmental events in

embryos may have consisted of no more than two or

three interacting genes. Over time, new genes were

incorporated into the primitive networks (Wilkins,

2002). While an initial hypothesis might be that new

functions require novel genes, whole genome

sequencing has shown that the apparent increases in

developmental complexity do not correlate with

increasing total numbers of genes. Therefore, the

evolution of developmental pathways may most

commonly proceed by recruiting pre-existing

external genes into pre-existing networks to create

novel functions (True and Carroll, 2002).

Developmental evolution may act primarily at the

238

M. Holloway D., B. Kazansky A. and V. Spirov A..

Complexiﬁcation of Gene Networks by Co-evolution of Genomes and Genomic Parasites .

DOI: 10.5220/0004170802380244

In Proceedings of the 4th International Joint Conference on Computational Intelligence (ECTA-2012), pages 238-244

ISBN: 978-989-8565-33-4

 2012 SCITEPRESS (Science and Technology Publications, Lda.)

level of genetic regulation (Carroll et al., 2001).

The invertebrate segmentation network is among

the best studied gene ensembles, with a wealth of

diverse experimental data providing a unique

opportunity for investigating known and

hypothetical evolutionary scenarios in detail. In

particular, the level of understanding of the

segmentation gene network for the fruit fly

(Drosophila melanogaster) has made it, for many

years, extremely popular for functional and

evolutionary computer simulations (Reinitz and

Sharp, 1995; Jaeger et al., 2004; Sánchez and

Thieffry, 2001; Manu et al., 2009ab). Modelling this

gene ensemble has become a benchmark test in

modern systems biology (e.g. Azevedo et al., 2006;

Umulis et al., 2008; Bieler et al., 2011; Gursky et al.,

2011). This network has also been used in the

development of evolution in silico approaches

(François et al., 2007; Spirov and Holloway, 2009;

2010; 2012).

Comparisons of segmentation networks between

primitive and higher insects indicate that evolution

proceeds in the direction of network

complexification (Patel, 1994; Sommer and Tautz,

1993). The transition from grasshoppers to flies,

with an (at least) doubling of the number of genes in

the network, appears to have been solved by

evolution over a short geological time span. Increase

in the segmentation network size often involved

recruitment of genes from other networks.

Transposons, Genomic Parasites: A universal

property of life is that all successful systems attract

parasites. Parasites are so common that hosts

eventually co-evolve immunity. The parasites then

co-evolve strategies to circumvent the new

immunity. And the hosts respond by co-evolving

defences to repel the parasites again.

Transposons are a unique type of parasite

residing in the host genome. Co-evolution of

transposons and host genomes are thought to

produce arms races within the DNA of organisms.

Transposons jump between different parts of a

genome to propagate themselves, and these events

are usually to the detriment of the host (Makalowski,

1995). Many transposons have a unique DNA

sequence that acts as a forwarding address and

directs the transposon to a complementary DNA

sequence

in the host genome (Makalowski, 1995).

Transposons are a major source of genetic

change (Lozovskaya et al., 1995; King, 1992). It has

been estimated that 80% of spontaneous mutations

are caused by transposons (Makalowski, 1995).

Transposons have co-evolved with their hosts

through selection. The activities of transposons are

likely to participate in the rewiring of pre-

established regulatory networks (for example,

Wallace et al., 1991; Girard and Freeling, 1999).

While the problem of growth and

complexification of GRNs has received much

attention in recent years, the mechanism remains

unknown. How does recruitment happen? What

exactly forces the GRNs to co-opt genes? Some

studies assume that recruitment occurs by chance (at

a very low level) and is then subject to evolution.

Other researchers believe that there are special

evolutionary mechanisms to perform this task. These

could involve complicated systems to re-arrange the

genetic material. Transposons might participate in

evolutionary events at this level. Even assuming that

transposons can drive complexification of GRNs, it

is unknown exactly how this could occur. An initial

hypothesis might be that transposons force GRNs

towards more complexity by forced evolution

(negative selection). In this communication, we

computationally explore some of the essential co-

evolutionary aspects of hosts (GRNs) and

transposons in regard to the problem of GRN

evolutionary growth. We show that particular

transposon-GRN interactions are capable of

producing GRN enlargement.

2 METHODS AND APPROACHES

The idea of implementing artificial transposons to

facilitate the evolutionary search in EC has been of

great interest since the mid-1990s (Spirov, 1996;

Spirov and Samsonova, 1997; Spirov and Kadyrov,

1998; Spirov and Kazansky, 2002ab; Spirov et al.,

2009). This approach has been developed by several

teams (Nawaz Ripon et al., 2007; Tang et al., 2008;

Chan et al., 2008; Simões and Costa, 1999ab; 2000;

2001; Liu et al., 2009). Our main interest in this area

is to use artificial transposons to facilitate gene

network model design.

2.1 Modelling the Segmentation

Network

We use an in silico approach to simulate evolution

of the gap gene network which is central to fly

segmentation. Our model for the gap gene network

(adapted from Reinitz and Sharp, 1995; Manu et al.,

2009a) is a system of differential equations

describing the regulatory interactions of 4 gap genes

(giant, gt; hunchback, hb; Krüppel, Kr; knirps, kni)

under the control of a maternal Bicoid (Bcd) protein

gradient. Real spatial patterns of gene expression

ComplexificationofGeneNetworksbyCo-evolutionofGenomesandGenomicParasites

239

were used to fit the model (see Spirov and

Holloway, 2009, Fig. 1A-C). The model parameters

for the gene interaction strengths are varied, and the

solutions are selected by GA (details below) based

on how well they fit the gap gene data. This

selection produces networks that describe the

particular interactions (and quantitative strengths)

between the component genes (e.g., Spirov and

Holloway, 2009, Fig. 1D). In this way, we can use a

model of our current understanding of fly

segmentation to study the evolutionary dynamics of

how the segmentation network may have arisen and

how this might reflect on its current characteristics.

Gene-gene regulatory matrix W: The gap gene

proteins (Kr, Gt, Kni and Hb) are variables in the

model, with the rates of their concentration changes

(for each gene product

in each nucleus i),

defining a system of number of proteins times

number of nuclei ODEs given by

(1)

where

represents protein synthesis,

represents diffusion, and



represents decay.



is a sigmoid regulation-expression function.

Figure 1: The gene-gene interaction matrix, a core element

of modelling GRNs. Each gene (horizontal arrow) is

regulated by the products of other genes via upstream

enhancer elements (boxes). The strength and direction of

regulation (depicted as differently coloured saturation

levels) are a function of both the regulatory element and

the abundance of its corresponding gene product. The left-

most column W

corresponds to the regulatory elements

for the action of the spatially-graded morphogen, M =

Bicoid (external factor for the GRN). The genotype is

represented as the matrix, W, of the regulatory

interactions, and the phenotype is the vector, Ŝ, of the

gene product levels at equilibrium. Modified from Siegal

and Bergman (2002).

is given by





aBcd

aba

hvWvWu

Parameters

constitute a gene interconnectivity

matrix,

Bcd

represents the concentration of Bcd in

nucleus i, which is constant in time.

describes

the regulatory input of Bcd to each gene. Bcd is a

general activator for all four considered gap genes.

h represents the regulatory input from ubiquitous

factors.

The gene interconnectivity matrix,

, is

the key component for describing the GRN. Fig. 1

depicts this matrix in detail. The elements

represent the activation of gene

by the product of

gene

(with concentration

) if positive,

repression if negative, and no interaction if close to

zero.

2.2 Evolution in Silico to Design the

Gene Network Model

We simulate population dynamics by repeated

cycles of mutation, selection and reproduction (the

general GA approach). The program generates a

population of double string chromosomes (described

in more detail in 2.3). The genome of each host

consists of N chromosomes represented in the W

matrix (Fig. 1). The main chromosome string

consists of N+1 floating-point values (Fig. 1).

The initial floating-point strings of the

chromosomes are generated at random. All of the

chromosome sets are consecutively evaluated

(according to their fit to the data, see eqn. 2), an

average score is calculated and the winners’

offspring substitutes for the losers in the process of

reproduction. Next, a predetermined proportion of

the chromosome population undergoes mutation

(small changes are made to selected chromosomes’

coefficients). The cycle is then repeated for each

generation.

The set of ODEs (1) was solved numerically by

Euler’s method (Press et al., 1988). We minimized

the cost function, E, by adjusting parameters

in equation (1):

(2)

The remaining parameters were found in preliminary

runs and then used as fixed parameters.

We extended this standard scheme with our own

procedures to simulate the interaction between hosts



()

aaiai

Rgu D







mod

)(





data

vvE

IJCCI2012-InternationalJointConferenceonComputationalIntelligence

240

and transposons.

2.2.1 Introduction and Withdrawal of New

Genes

We used a Gene Introduction operator to add a new

gene to the network (at a rate of 5 – 10% per

generation, depending on the computation).

Specifically, this added a new row and column to the

matrix, which could be then be operated on by

mutation and crossover (discussed below). For

simplicity, new rows are always added above

existing rows (cf. Fig. 1). To evaluate the

importance of this one-way process in forcing

networks to recruit new genes, we also introduced a

Gene Withdrawal operator which removes a row and

column from the

W matrix (at a rate of 2 - 10%

per generation, depending on computation). Gene

Withdrawal does not operate if the network is

minimal (N = 4 genes).

2.3 Artificial Transposons for

We define an artificial transposon as a marked block

of the host’s code. This mark is transmissible from

host to host. We use double-string chromosomes: the

main string (floating-point) is used for the host code

and a second string (binary) is used for the

transposon marks. Secondary string values are 1 for

a mark and 0 otherwise. Chromosomes are therefore

in the following format:

the mark string: 1

… 0

the main string: α

… α

where the α

are floating-point values (only the α

element is transposon-marked in this example).

(Each element α

is the value of W

, Fig. 1.)

Artificial Transposons as Mutators: As with

biological transposition, action of an artificial

transposon is deleterious to the host in our model.

For an example of how this is implemented within

the W

b←a

gene interaction matrix, consider a

transposon infection in the upper left element,

A←M

(highlighted):

The transposon’s deleterious action is then

implemented by decreasing the value of the infected

host element W

b←a

. Specifically, we halve the W

b←a

value in each generation. This quickly drops the

element value to near zero. In this manner, the

transposon effectively cuts the b←a regulatory

connection.

Spread of Artificial Transposons: Transposons

tend to form clusters in host chromosomes. We

simulated this feature by spreading transposon

infection by at most one element per generation. In

this operation a transposon can mark the W

b←a

element above it as a new transposon. The following

represents transposon infection spreading from the

row (1

column) to the 1

row:

Transmission of Transposons: We used fixed

transposon coordinates to transmit transposons from

host to host. (Whole transposons were never moved

along the chromosomes.) The two-place

transmission operator was implemented as follows:

First, a pair of hosts was chosen at random; then a

chromosome from either host was scanned for

transposon marks. If a transposon was found, it was

replicated in the partner chromosome, regardless of

the original string character in the target

chromosome. Copying only occurred if the

secondary strings had transposon marks.

3 RESULTS AND DISCUSSION

In all of the computational experiments described,

we begin from a four-gene ensemble of obligate

gene founders (the initial network). We fit this 4-

gene ensemble to experimental data for expression

of four Drosophila gap genes (section 2.1; for

further details see Spirov and Holloway, 2009). The

spatial patterns of these four genes are the only

selection criteria in the evolutionary computations;

they are a stabilizing selection. Starting from the

initial 4-member GRN (GRN

ini

= GRN

), up to 3

extra genes can be recruited to the network.

ComplexificationofGeneNetworksbyCo-evolutionofGenomesandGenomicParasites

241

Transposons invade all hosts of the initial

population. Transposon length can vary from 1 to 4

elements (TE

ini

= TE

1-4

For typical runs, the size of the host (and

transposon) population is 4000 chromosomes; the

mutation rate is 15% per generation; the 15% of

individuals with the highest scores are marked for

reproduction (truncation strategy); the rate of

transposon horizontal transmission is 25% per

generation; the rate of new gene recruitment is 25%

per generation; the transposon action occurs to 25%

of the infected elements per generation; and the rate

of transposon spread is 25% per generation.

We also ran computations for evolutionary

growth of the host’s GRN with lower transposition

pressure: with a mutation rate of 1.5% per

generation; 1.5% of the highest scoring individuals

marked for reproduction; a rate of transposon

horizontal transmission of 5.0% per generation; rate

of new gene recruitment 5.0% per generation; rate of

transposon action 5.0% per generation; and rate of

transposon spread 5.0% per generation.

3.1 GRN Outgrowth

Our computational experiments demonstrate that

artificial transposons, as defined above, are able to

force their host’s evolution towards greater GRN

complexity. This complexification is due to

recruitment of novel genes into the GRN to escape

the selection pressure of the transposons. Analysis of

the computational solutions shows that a substantial

proportion of the recruited genes participate

significantly in a network’s activity.

Our simulations show that this effect of

transposons on gene recruitment is robust over a

wide range of parameter values (at least a ten-fold

variation). It is a sustainable and robust

characteristic of the host-transposon system.

In earlier experiments, we observed gene

recruitment and GRN outgrowth in the absence of

transposon operators (Spirov and Holloway, 2009).

Genes can become co-opted simply by chance; the

co-option of genes into existing GRNs is a very

general feature of the evolution of regulatory

networks. However, GRN outgrowth by random

recruitment can be very slow. With transposon

operators, selective pressure is greatly increased,

speeding up recruitment and GRN outgrowth. In

addition, as implemented here, the transposon

pressure results in very specific GRN architectures.

3.2 Co-evolution of GRNs and

Transposons

The GRNs in this study rely on a spatial gradient of

a morphogen, M (external to GRN feedback), to

establish appropriate spatial expression patterns. In

Drosophila segmentation, M corresponds to the

maternally supplied Bcd protein gradient. In our

simulations, we have focused on transposon

infections in the 1

column of the W matrix,

representing the effects of M on the network genes.

Infections in this column isolate the GRN from its

external input (M is the only activator of the network

genes; see Fig. 1).

Consider a transposon infection on the initial

GRN (of length, say, TE

) at the element of the first

gene (A) representing activation by M (Fig. 2). Once

Figure 2: Transposon infection affecting M activation of

the GRN. A) Representation of the gene interactions in the

network. B) Infection in the W column representing M

activation.

placed, the transposon systematically reduces the

strength of the element. In this way, the transposon

interferes with the reading of the M gradient by the

GRN. Because reading the spatial gradient is critical

to the function of the GRN, the transposon

drastically reduces the fitness score of the “infected”

GRN.

As evolutionary time continues, a novel gene,

e.g. R1, can be recruited to the GRN. If R1 becomes

activated by M, and gene A acquires the ability to be

activated by R1, the newly expanded GRN (R1-

GRN) can again appropriately form spatial pattern.

R1-GRN requires both a rewiring of connections and

retuning of parameter values from GRN

ini

. R1-GRN

can achieve a good score and is insensitive to the

initial length TE

. R1-GRN quickly becomes

abundant (even dominant) in the population.

However, as time proceeds, the transposon will

spread upwards in the matrix: the original TE

will

become TE

and infect the M element of R1 (Fig. 3).

With additional evolutionary time, this process

can reoccur with recruitment of a new gene, R2. I.e.,

R2 can become a target of the M gradient and be

recruited as an activator for A, R1 or other genes.

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242

Figure 3: Infection of a recruited gene, R1. A)

Representation of the network; B) matrix representation.

The new R2-GRN then escapes the transposon

pressure and becomes abundant in the population.

These co-evolutionary cycles can occur repeatedly,

in the process forming increasingly large GRNs, but

all with the same basic function of creating the

appropriate spatial gene expression patterns.

4 CONCLUSIONS

1) Targeted destruction of key regulatory

connections in a GRN by transposons can produce

negative selection pressure on the GRN.

2) Initially non-functional genes can be co-opted

into the GRN to respond to this selective pressure.

Co-opted genes substitute the regulatory connections

under transposon attack (i.e., they rewire the GRN).

3) We have focused on the co-option of genes to

restore disrupted connections to external morphogen

signalling. This is relevant to the maintenance of

gradient-reading GRNs (critical in biological

development) despite transposon attacks.

4) For gradient-reading GRNs, we have observed

outgrowth and complexification of the networks

under the selection pressure of targeted transposon

activity.

5) The co-option of novel genes by gradient-reading

GRNs to overcome transposon effects can repeat

over many cycles of co-evolution between the GRN

and the transposon. The increasingly large GRNs

solve the same basic function of gradient reading.

ACKNOWLEDGEMENTS

This work was supported by Joint NSF/NIGMS

BioMath Program, 1-R01-GM072022 and the

National Institutes of Health, 2R56GM072022-06,

2-R01-GM072022.

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