Biological significance of autoregulation through steady
state analysis of genetic networks
Malkhey Verma a , Subodh Rawool a , Paike Jayadeva Bhat b , K.V. Venkatesh a,b,∗
b
a Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
School of Biosciences and Bioengineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India
Abstract
Autoregulation of regulatory proteins is a recurring theme in genetic networks. Autoregulation is an important component of
a genetic regulatory network besides protein–protein and protein–DNA interactions, stoichiometry, multiple binding sites and
cooperativity. Although the biological significance of autoregulation has been studied before, its significance in presence of other
mechanisms is not clearly enumerated. We have analyzed at steady state the significance of autoregulation in presence of other
molecular mechanisms by considering hypothetical genetic networks. We demonstrate that autoregulation of a regulatory protein
can impart amplification to the response. Further, autoregulation of an activator binding to the DNA as a dimer can introduce
bistability, thus forcing the system to reside in two distinct steady states. In combination with autoregulation, cooperative binding
can further increase the sensitivity and can yield a highly ultrasensitive response. We conclude that autoregulation with the help of
other molecular mechanisms can impart distinct system level properties such as amplification, sensitivity and bistability. The results
are further discussed in relation to various examples of genetic networks that exist in biological systems.
Keywords: Gene; Activator/repressor; Binding sites; Dimerization; Cooperativity; Bistability; Amplification and sensitivity
1. Introduction
Genetic regulatory networks are complex system constituting various interactions and molecular mechanisms
that are essential for their operation. These mechanisms
include protein–DNA and protein–protein interactions,
multiple binding sites, cooperativity and autoregulation
of regulatory proteins. Regulatory protein, either as an
activator or repressor, binds to the upstream activation
sequence (UAS) or upstream repression sequence (URS)
respectively, to constitute protein–DNA binding (Lohr
et al., 1995). Further, the regulatory protein can also be
regulated through protein–protein interaction by other
regulatory elements in the system (Melcher and Xu,
2001). Genes can have multiple binding sites for specific
transcriptional activator or repressor, which can influence the expression profile (Lohr et al., 1995; Melcher
and Xu, 2001). The binding characteristic for the second site can alter depending on the binding state of the
first site constituting cooperativity (Lohr et al., 1995;
Magnuson and Yarmolinsky, 1998). The above mechanisms are further compounded by autoregulation of the
regulatory proteins.
The synthesis of an autoregulatory protein is controlled by the same switch that it regulates (Simpson et
al., 2003). The feedback constituted by autoregulation
can either be positive (activation) or negative (inhibi-
40
tion). They are ubiquitous and are observed in genetic
systems like bacteriophage-lamda (Ackers et al., 1982)
and GAL (Verma et al., 2003) regulatory networks. Various roles have been attributed to autoregulation, such as
amplification of gene expression, buffering response of
genes to environmental changes (Sonneborn et al., 1965)
and maintaining constant protein concentration independent of cell size and growth parameters (Simpson et al.,
2003; Sompayrac and Maaløe, 1973; Haber and Adhya,
1987; Becskei and Serrano, 2000). Further, autoregulation also provides stability to the genetic switches
(Becskei and Serrano, 2000; Savageau, 1974) and reduce
the time necessary to reach the steady state concentration
(Rosenfeld et al., 2002).
Autoregulation typically does not operate independently of other mechanisms in a regulatory network.
For example, a regulatory protein, which is autoregulated, can either bind as a monomer or a dimer to the
upstream activation sequence (UAS) of a gene. While
expression from Tyr R gene in Escherichia coli (Bhartiya
et al., 2003) and SOCS3 gene in human (Auernhammer
et al., 1999) is regulated by autoregulation of proteins
binding as a monomer, rho gene in E. coli (Haber and
Adhya, 1987) and Lac gene in Kluyveromyces lactis
(Zachariae and Breunig, 1993) are regulated by autoregulated proteins binding as a dimer. Further, autoregulation can exist for a regulatory protein, which binds
to the multiple binding sites with cooperativity. TRA
gene in F-plasmid (Fekete and Frost, 2002) and TOR
gene in E. coli (Ansaldi et al., 2000) are regulated by
autoregulated proteins interacting with multiple binding
sites. Autoregulation is, thus, known to play an important role in regulating various genetic networks (Simpson
et al., 2003) and there are myriad examples of gene
expression systems with an autoregulatory component
in addition to other mechanisms. Autoregulation as a
mechanism exists in genetic networks, where the transcriptional effectors bind either as a monomer or dimer.
Further, these mechanisms may include multiple binding sites resulting in a complex network. At this stage, it
may be pertinent to ask a question regarding the significance of autoregulation at the system level in presence
of various other mechanisms. The past studies do not
explicitly mention the role of autoregulation in relation
to the presence of other mechanisms such as stoichiometry, multiple binding site, cooperativity, etc.
Mathematical models can help in understanding the
natural complexity arising due to autoregulation. Various strategies that are used to model genetic networks,
includes steady state and dynamic modeling. Steady state
models require only equilibrium dissociation constants
and total component concentration as parameters. Fur-
ther, these parameters are relatively easy to determine
through in vitro experiments. Whereas, dynamic models require kinetic rate constants for transcription, which
are difficult to obtain. Although dynamic analysis yields
temporal details, steady state models are more common
and have been used to simulate genetic networks such as
lactose operon (Isaacs et al., 2005), bacteriophage-lamda
(Ackers et al., 1982), GAL regulatory network (Verma et
al., 2003), etc.
In this article, we employ steady state analysis to
quantify the effect of autoregulation by considering various examples of isolated genetic switches. Researchers
have demonstrated that isolated gene networks coupled
with proper quantification, can be used to elucidate
the key properties of in vivo functional genetic networks (Chung and Stephanopoulous, 1996). The analysis includes systems wherein an autoregulated regulatory
protein binds as (i) monomer, (ii) dimer, and (iii) dimer
with cooperativity to the UAS or URS of a gene. We
have analyzed the effect of both positive and negative
autoregulation. Our analysis clearly indicates that positive autoregulation can yield bistable response, while
negative autoregulation yields stable but a less sensitive response. Moreover, the bistability is only observed
when the regulatory protein acts as a dimer.
2. Methodology
A steady state analysis for expression of a gene with
and without autoregulation for the following systems
was considered:
1. Monomer binding of transcriptional activator to the
upstream activation sequence (UAS) of a gene having
one binding site.
2. Dimer binding of transcriptional activator to the UAS
of a gene having one binding site.
3. Dimer binding of transcriptional activator to the UAS
of a gene having two binding sites with cooperativity.
4. Dimer binding of transcriptional repressor to the
upstream repression sequence (URS) of a gene having two binding sites with cooperativity.
Fig. 1 shows the schematic representation of the gene
expression systems discussed above. Steady state analysis assumes equilibrium binding between all interactions
and molar balances of all the component concentrations. In case of autoregulation, the concentration of the
transcriptional activator at steady state is related to the
fractional protein expression (fp ) of the gene it activates.
Let the transcriptional factor “A” be present at a steady
state having a concentration of A0 . The steady state con-
41
Fig. 1. (a) Schematic representation for gene expression having one binding site with and without autoregulation. The mRNA molecules are
synthesized from transcription of gene (D) and are translated to protein (A). Protein (A) dimerizes with dissociation constant K1 . The monomer
(A) and dimer (A2 ) binds to upstream activation sequence (D) with dissociation constant Kd for transcriptional expression of gene. Note that if
the transcriptional activator (A2 ) does not interact with the gene ‘D’ the system lacks autoregulation mechanism. (b) Schematic representation of
positive/negative autoregulation for expression of gene having two binding sites. The mRNA molecules are synthesized from transcription of gene
(D) and are translated to protein (A). Protein (A) dimerizes with dissociation constant K1 . The dimer (A2 ) molecule binds to first binding site (D)
with dissociation constant Kd and with second binding site by Kd /m for transcriptional expression of gene. The term ‘m’ quantifies cooperativity.
Note that if the transcriptional activator (A) does not interact with the gene ‘D’ the system lacks autoregulation mechanism.
centration of A will be altered due to activation of its own
synthesis for a genetic switch defined by autoregulation.
Thus, due to autoregulation the steady state concentration of “A” shifts from A0 to At , where A0 can be termed as
concentration of transcriptional activator at the onset of
regulation. The effect of autoregulation was incorporated
through relating the total concentration of the transcriptional regulator (At ) to the fractional protein expression
(fp ) and the initial concentration present at the onset of
regulation (A0 ), as given below:
[A]t = A0 (1 + qfp )
(1)
where q represents the fold change in the concentration of the transcriptional activator due to autoregulation
and fp is the fractional protein expression. Typically the
fractional protein expression (fp ) and fractional transcriptional expression (f) are related through a nonlinear
expression given by fp = fn , where f quantifies fractional
transcription. In the current analysis, we assume a linear
relationship between protein expression and transcription and set n = 1, which is the case for most prokaryotic
systems. The derivations for the four cases described
above are detailed below.
Case 1. Activator as a monomer
In this case, transcriptional activator A binds to the
gene (D) having one binding site as a monomer with
dissociation constant Kd . The equilibrium dissociation
is represented by
D + A ↔ DA
[D][A]
Kd =
[DA]
(2)
(3)
The molar balances for the total gene and activator concentration are as follows:
[D]t = [D] + [DA]
(4)
[A]t = [A] + [DA]
(5)
The probability of protein expression is defined as the
ratio of concentration of the activator bound DNA to the
total DNA concentration. Thus
[DA]
f =
(6)
[D]t
Eqs. (2)–(6) can be used to relate total activator concentration to fractional protein expression as follows:
[A]t =
f
Kd + f [D]t
1−f
(7)
The effect of autoregulation (At or A0 ) can be incorporated by relating [A]t from Eq. (7) to [A]0 using Eq. (1)
as follows:
f
f [D1 ]t
[A]0 =
Kd +
(8)
(1 − f )(1 + qf )
(1 + qf )
Eqs. (7) and (8) relate the input concentration (At or A0 )
required for a specific output fractional expression (f) for
cases without and with autoregulation, respectively.
Case 2. Activator as a dimer
In this case, transcriptional activator (A) dimerizes
before binding to the DNA (see Fig. 1a). The equations
representing all the molecular interactions are as follows:
A + A ↔ A2
(9)
42
[A]2
[A2 ]
(10)
The molar balances for DNA and the activator protein
are as
D + A2 ↔ DA2
(11)
[D]t = [D] + [DA2 ] + [DA2 A2 ]
(22)
(12)
[A]t = [A] + 2[A2 ] + 2[DA2 ] + 4[DA2 A2 ]
(23)
K1 =
Kd =
[D][A2 ]
[DA2 ]
where K1 and Kd are the dissociation constants for dimerization of transcriptional activator and it’s binding to
UAS of the gene, respectively. The total molar balances
for the DNA and activator protein are as follows:
[D]t = [D] + [DA2 ]
(13)
[A]t = [A] + 2[A2 ] + 2[DA2 ]
(14)
The probability of transcription is defined as
f =
[DA2 ]
[D]t
Further, in the presence of autoregulation Eq. (16) can
be modified by substituting for [A]t using Eq. (1):
f
f
1−f (K1 Kd ) + 2 1−f Kd + 2f [D]t
[A]0 =
(17)
(1 + qf )
Eqs. (16) and (17), thus, represent the input–output relationship for the cases without and with autoregulation of
transcriptional activator binding to DNA as a dimer.
Case 3. Activator binds as a dimer to the gene having
two binding sites with cooperativity
Here, the transcriptional activator binds as a dimer
to the gene (D) having two binding sites (see Fig. 1b).
The dissociation constant for binding to the first site
is Kd and for the cooperative binding to the second
site is assumed to be Kd /m, where factor m quantifies
cooperativity (enhanced affinity of binding for the second binding site). The following equations represent the
molecular interactions:
(18)
[D][A2 ]
[DA2 ]
(19)
DA2 + A2 ↔ DA2 A2
(20)
Kd
[DA2 ][A2 ]
=
m
[DA2 A2 ]
(21)
Kd =
f =
[DA2 ] + [DA2 A2 ]
[D]t
(24)
The mass balance equations can be solved simultaneously to yield input–output relationship by relating At
and f for this case in absence of autoregulation. As before,
the relationship obtained by including Eq. (1) will yield
the input–output relationship for the case with autoregulation.
(15)
Eqs. (9)–(15) can be used to relate the total activator
concentration required to achieve a specific fractional
protein expression (f) as follows:
f
f
[A]t =
(K1 Kd ) + 2
Kd + 2f [D]t (16)
1−f
1−f
D + A2 ↔ DA2
The probability of transcription is defined as follows:
Case 4. Repressor binds to the gene having two binding
sites as a dimer.
In this case, the repressor molecule binds to the
upstream repression sequence (URS) of a gene for regulation of transcription (see Fig. 1b). All the equations for
this case are similar to that listed in case-3 except Eq.
(23) defining f, the fraction for transcriptional expression. Since regulator (A) is a repressor in this case, the
transcription occurs only when the operator gene is free.
Thus
[D]
f =
(25)
[D]t
For each of the four cases, the equations were solved
simultaneously by using function solve algorithm of
MATLAB-12 (The Math Works Inc., USA) and equation solve algorithm of Mathematica 4.1. The total molar
balances on DNA and activator/repressor were independently verified by adding the concentrations of various
complexes.
3. Model parameters
The dissociation constants for protein–protein and
DNA–protein interactions were taken in the physiological range as given in the figure legend. The value of [D]t
was fixed for a model organism with cellular volume
70 ␮m3 , equal to the cellular volume of a haploid yeast
cell (Sherman, 1991) having single copy per genome.
4. Results
The steady state response curves for the four cases
were obtained by solving the model equations. For each
43
Fig. 2. Fractional protein expression through a positively autoregulated gene expression system as predicted by the steady state analysis
when the transcriptional activator binds to the operator site (binding site) as a monomer to the gene having one binding site. Curve
(i) shows response for the unautoregulated system and (ii), (iii) and
(iv) show expression responses for autoregulated system with q = 10, 100- and 1000-fold changes in the activator concentrations due to
autoregulation. Numbers next to curves show values of Hill coefficients. It can be noted that autoregulation brings about amplification by shifting the response curve to the left. Parameter values
are as follows; Kd = 2.0 × 10−10 M, K1 = 1.0 × 10−7 M, m = 30 and
Dt = 2.37 × 10−11 M.
case, the fractional transcriptional expression was plotted with respect to the concentration at the onset of transcription (A0 ) to represent autoregulation. To compare
the performance of the network without autoregulation,
the fractional expression was plotted with respect to At
excluding Eq. (1).
Fig. 2 shows the fractional transcription for the case
when transcriptional activator binds as a monomer (Case
1). In absence of autoregulation, the response shows
a typical Michaelis–Menten type response with a Hill
coefficient of one (curve i). Whereas, the response
obtained in the presence of autoregulation is sensitive.
Further, the Hill coefficient (as a measure of sensitivity) increases with higher degree of autoregulation
(i.e., increasing value of q). The curves also shift to
the left indicating that the expression switches on at a
lower concentration of the activator required to switch
on the expression. Thus, autoregulation causes not only
an increase in the sensitivity but also amplifies the activator signal.
Fig. 3. (a) Fractional protein expression through a positively autoregulated gene expression system when the transcriptional activator binds
as a dimer to the promoter of the gene having one binding site. Curve
(i) shows response for the unautoregulated system and curves (ii)–(iv)
show expression responses for autoregulated system with q = 10-, 100and 1000-fold changes in the activator concentration due to autoregulation. (b) A bistable response is observed due to positive autoregulation
at the value of q = 100. Non-linearity is caused due to ultrasensitive
response and autoregulation yields bistable response. Parameter values are as follows; Kd = 2.0 × 10−10 M, K1 = 1.0 × 10−7 M, m = 30 and
Dt = 2.37 × 10−11 M.
44
Fig. 4. Fractional protein expression through an autoregulated gene
expression system at different total concentrations of activator, when
the activator binds as a dimer to gene having two binding sites with
cooperativity. Curve (i) shows response for unautoregulated system and
curves (ii)–(iv) show the expression responses for autoregulated with
q = 10-, 100- and 1000-fold changes in the activator concentrations
due to autoregulation and with a cooperativity of m = 30. It can be
noted that bistability can be observed for responses obtained for q = 10,
100 and 1000. Parameter values are as follows; Kd = 2.0 × 10−10 M,
K1 = 1.0 × 10−7 M, m = 30 and Dt = 2.37 × 10−11 M.
Fig. 3a shows the transcriptional response when activator dimerizes and binds to the operator site (i.e., Case
2). In this case even in the absence of autoregulation,
the response is sensitive (with a Hill coefficient of 1.9).
Autoregulation further, increases the sensitivity of the
response to 5.2 at q = 10. It can be noted that on further
increasing the value of q (higher degree of autoregulation), the response becomes switch like with a bistable
response (see Fig. 3b). A bistable response has a distinct
concentration of activator at which it switches on and a
different concentration at which it switches off. The figure also shows that a certain concentration of activator at
the onset of expression is essential to switch on the transcription. Thus, a leaky transcription is necessary in the
off state for the operation of such positive autoregulatory
systems.
Fig. 4 shows the transcriptional response when the
activator dimerizes and binds to the gene having two
binding sites with cooperativity (i.e., Case 3). Even in
this case, the response is highly sensitive in absence
of autoregulation (with a Hill coefficient of 3.5). The
increased sensitivity is due to multiple binding sites
Fig. 5. Fractional protein expression through a negatively autoregulated system when the repressor binds as a dimer with cooperativity
to a gene having two binding sites. Curve (i) shows response for
the unautoregulated system and (ii)–(iv) show expression responses
for autoregulated with q = 10-, 100- and 1000-fold changes in the
repressor concentrations due to autoregulation. Parameter values
are as follows; Kd = 2.0 × 10−10 M, K1 = 1.0 × 10−7 M, m = 30 and
Dt = 2.37 × 10−11 M.
and cooperativity. Further, in presence of autoregulation,
bistability is observed at a lesser degree of autoregulation
(i.e., even at q = 10).
Fig. 5 shows the case when a repressor is autoregulated and binds as a dimer to the upstream repression sequences (URSs) of a gene with cooperativity. In
absence of autoregulation, the value of the sensitivity
of the response as calculated from the Hill equation is
3.5 and is also similar to that obtained by an transcriptional activator (curve i in Fig. 4). Further, the response
becomes less sensitive in the presence of autoregulation. Further the sensitivity decreases with increase in the
degree of autoregulation (i.e., with increase in the value
of q). In a repressive system autoregulation imparts only
amplification to the response, without yielding properties such as sensitivity and bistability.
The different mechanisms analyzed in the above
section yield specific transcriptional response and the
responses were dependent on the parameter values. It is
relevant to study the dependency of the output response
to system parameters. This entails representing the output response by a curve. We use Hill equation, which is
characterized by the Hill coefficient (ηH ) and half saturation constant (K0.5 ) to represent the output response,
45
Fig. 6. Variation of Hill coefficient (ηH ) and half saturation constant (K0.5 ) for different mechanisms observed in a genetic switch with variations
in key system parameters (a) and (b). Solid line: variation with respect to dimerization constant for a transcriptional activator binding to a gene as
a dimer; dotted line: variation with respect to the degree of cooperativity for the transcriptional activaotr binding as a dimer to two binding sites
with cooperativity; (c) variation of Hill coefficient with respect to degree of autoregulation (q in Eq. (1)); (d) variation of half saturation constant
with respect to degree of autoregulation. Dotted line represents curve for switching on while solid line represents curve for switching off indicating
bistability. Note that bistability was lost at low degree of autoregulation, as both the curves merge.
as given below:
O=
I ηH
ηH + I ηH
K0.5
(26)
where O and I indicate output response and input, respectively. The dependency of ηH and K0.5 on a parameter
signifies the sensitivity of the response to a given change
in a parameter value. Fig. 6a shows the variation of
Hill coefficient to changes in dimerization constant (Kd ),
when a transcriptional activator binds as a dimer to the
operator site (solid line in Fig. 6a). As the dimerization constant increases, the Hill coefficient decreases to
1 from 2. This is due to the fact that the binding of the
dimer to the operator site controls the response rather
than the dimerization of the activator. The half saturation constant increases with the dimerization constant
(see solid line in Fig. 6b). This implies that the output
response requires larger amounts of input to switch on
the system with increase in the Kd value.
Fig. 6a also shows the variation of Hill coefficient
with respect to extent of cooperativity (m in Eq. (21)).
Increase in cooperative binding to the second site by
a transcriptional activator increases the Hill coefficient,
but was bounded between values 1 and 2 (dotted line in
Fig. 6a). While K0.5 decreases with increase in the value
of m indicating that the signal gets amplified (dotted line
Fig. 6b).
Autoregulation of the transcriptional activator can
yield ultrasensitive response with bistability (see Fig. 4).
The Hill coefficient increases with increase in the degree
of autoregulation (parameter q in Eq. (1) and shown
in Fig. 6c). The half saturation constant decreases with
increase in the value of q indicating amplification (see
Fig. 6d). Bistability was observed at a very high degree
of autoregulation resulting in a different value of K0.5
for switching on (dotted line in Fig. 6d) and switching off (solid line in Fig. 6d) the genetic switch. A
bistable response typically has a very high Hill coefficient with a steep switch like output and can take values
higher than two. The value of Hill coefficient was thus
not bounded in this case (values of 50–100 can also be
obtained).
46
5. Discussion
Autoregulation of regulatory proteins is a recurrent
theme observed in many regulatory networks. Autoregulation operating in tandem with other mechanisms like
dimerization, multiple binding sites and cooperativity
can impart distinct properties to regulatory networks.
Therefore, autoregulation as a fundamental mechanism
is observed in many genetic regulatory systems ranging from bacterial systems to higher organisms. Various
systems wherein transcriptional activation and repression with autoregulation have been reported in literature and are listed in Tables 1 and 2, respectively.
While autoregulation as a phenomenon has been demonstrated in many disparate systems, its role in the operation of genetic networks has been peripherally discussed. Our steady state analysis clearly demonstrates
that autoregulation is a fundamental mechanism in
genetic networks and is highly context dependent. Further, autoregulation in combination with other known
mechanisms like cooperativity can impart system level
properties like multiple steady state, ultrasensitivity and
amplification.
Steady state analysis indicates that positive autoregulation yields a sensitive response with amplification.
Table 1
Examples of genetic networks exhibiting autoregulation with positive
feedback in tandem with other mechanisms
Protein binding as a monomer
Gene32 in bacteriophage
T-4
Ubx gene in Drosophilla
Ultrabithorox gene in
Drosophilla
Beta1-adrenergic receptor
gene in human
NEX1 gene in Drosophilla
GAL3 in Saccharomyces
cerevisiae
RAS genes expression in
Fibroblast
MyoD gene in rat
Siamois gene in Xenopus
embryos
Siamois gene in Xenopus
embryos
Sx1 gene in Droshophilla
von Hippel et al. (1982)
Christen and Bienz (1992)
Thuringer and Bienz (1993)
Bartholoma and Nave (1994)
Bartholoma and Nave (1994)
Lohr et al. (1995)
Quincoces et al. (1997)
Benayoun et al. (1998)
Fan et al. (1998)
Fan et al. (1998)
Cline et al. (1999)
Protein binding as a dimer without cooperativity
Lac9 protein in
Zachariae and Breunig (1993)
Kluyveromyces lactis
Protein binding as a dimer with cooperativity
TRA gene in F plasmid
Fekete and Frost (2002)
CI gene expression in
Ackers et al. (1982)
bacteriophage-␭
Table 2
Examples of genetic networks exhibiting autoregulation with negative
feedback in tandem with other mechanisms
Protein binding as a monomer
MASH1 gene in
Meredith and Johnson (2000)
Drosophilla
SOCS-3 gene in human
Auernhammer et al. (1999)
torCAD operon in
Gon et al. (2001)
Escherichia coli
IE2 gene in human
Macias and Stinski (1993)
cytomegalovirus (CMV)
FTZ gene in Drosophilla
Yu et al. (1999)
PDC5 genes in
Muller et al. (1999)
Saccharomyces cerevisiae
AnCF gene in Aspergillus
Steidl et al. (2001)
nidulans
CYS-B gene in Salmonella
Ostrowski and Kredich (1986)
typhimurium
TyrR gene in Escherichia
Camakaris and Pittard (1982)
coli
MET-J gene in Salmonella
Urbanowski and Stauffer (1986)
typhimurium
SIG-A gene in T. maritium
Camarero et al. (2002)
EFG1 gene in Candida
Tebarth et al. (2003)
albicans
RAF-1 gene in Xanopus
Cutler et al. (1998)
levis
Protein binding as a dimer without cooperativity
PER and TIM genes
Tyson et al. (1999)
expression in fruit fly
GAL80 gene in
Melcher and Xu (2001)
Saccharomyces cerevisiae
REP-E gene in mini
Ishiai et al. (1994)
F-plasmid
rho gene in Escherichia
Haber and Adhya (1987)
coli
Monomer protein binding with cooperativity
Doc H66y protein in
Dodd et al. (2002)
bacteriophage P1
TOR gene in
Ansaldi et al. (2000)
Saccharomyces cerevisiae
Amplification offers an advantage in the form of requiring lower amount of regulatory proteins to operate the
genetic network. Positive autoregulation is also capable of yielding a bistable response indicating multiple
steady states. Bistability is typically observed when a
non-linearity caused by sensitive response is superimposed by a positive feedback loop. Thus, dimerization
and cooperativity by themselves can yield ultrasensitivity resulting in non-linearity, while autoregulation constitute a positive feedback loop. In a bistable system,
for a given activator concentration at the onset of transcription, the switch resides in two steady states, one
leaky off state and another in the on state. This makes the
expression completely switch like, as it cannot reside in
any other intermediatery steps. Such bistable response
47
is essential for a system, which require a yes or no
type of decision. Whereas, in a system with positive
autoregulation of activator, which binds as a monomer
to the upstream activation sequence, the response does
not show bistability due to insufficient non-linearity in
the system.
Existence of bistability has been shown experimentally in cellular differentiation and cell cycle progression in Xenopus laevis egg (Sha et al., 2003). However
such bistable response is not reported in transcriptional
regulation. The network structure associated with bistability (i.e. non-linearity with positive feed back loop)
also exits in transcriptional regulatory systems. Theoretical analysis reported here indicates that systems with
dimerization and cooperativity in the presence of positive autoregulation can manifest bistable response. Such
structures have been reported for TRA gene in F plasmid (Fekete and Frost, 2002) and CI gene expression
in bacteriophage-lamda (Ackers et al., 1982). Autoregulation and dimerization of cl protein help in deciding
bacteriophage-lamda to reside in the lytic or the lysogenic states, which are two distinct phenotypic states.
However, there are many other systems where positive
autoregulation would not yield bistability due to the
non-existence of non-linearity caused by dimerization
and multiple binding sites. Such systems would offer an
advantage of a sensitive response and amplification as
demonstrated here.
Unlike in a bistable system, systems with negative
autoregulation show a smooth transition from one state to
another, implying that many intermediatery steady states
can be achieved depending on the input activator concentration. Thus, this makes the system less ultrasensitive,
but a distinct amplification can be achieved in such a
system and may be essential for systems, which do not
require a yes or no type of status. Although non-linearity
in the form of multiple binding sites and cooperativity
can exist in such systems, bistability is not observed due
to the presence of negative feed back loop (i.e., negative
autoregulation).
Parametric sensitivity analysis was also performed
on the different mechanisms operating in the genetic
switch. The response was represented by Hill equation and the sensitivity to variations in parameter values
were obtained by evaluating Hill coefficient and half
saturation constant. It was clear from the analysis that
irrespective of the mechanism studied (that is dimerization, cooperativity or autoregulation), the response was
highly dependent on the parameters. This indicated that
these basic mechanisms, operating in the genetic switch,
would not yield robustness to parametric variations.
Robustness can be achieved through other upstream
interactions (like cascades) through a higher degree of
complexity.
As demonstrated here, mathematical models can be
used to analyze regulatory networks containing autoregulatory loops to provide insights into the properties of
the inherent structure. Steady state analysis requires
only equilibrium binding characteristics, which are easy
to obtain. A dynamic model involves detailed kinetic
analyses that are tedious. As demonstrated here, steady
state analysis can also be used to enumerate system
level properties. It is difficult and tedious to demonstrate some of these properties only through experimental tools. Experiments can provide details about the existing structure and prevailing mechanisms in the network.
Thus, molecular biology has established the existence
of dimerization, cooperativity and autoregulation with
protein–protein and protein–DNA interactions as basic
mechanisms prevalent in genetic regulatory networks.
While, theoretical analysis provides insights into system
properties such as sensitivity of response, amplification
of signal, bistability and multiple steady states. These
properties can manifest depending on the connectivity
of various molecular mechanisms prevalent in a particular genetic network.
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