Biological significance of autoregulation through steadystate analysis of genetic networks

Malkhey Vermaa, Subodh Rawoola, Paike Jayadeva Bhatb, K.V. Venkatesha,b,∗a Department of Chemical Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400076, India

b 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 ofa genetic regulatory network besides protein–protein and protein–DNA interactions, stoichiometry, multiple binding sites andcooperativity. Although the biological significance of autoregulation has been studied before, its significance in presence of othermechanisms is not clearly enumerated. We have analyzed at steady state the significance of autoregulation in presence of othermolecular mechanisms by considering hypothetical genetic networks. We demonstrate that autoregulation of a regulatory proteincan impart amplification to the response. Further, autoregulation of an activator binding to the DNA as a dimer can introducebistability, thus forcing the system to reside in two distinct steady states. In combination with autoregulation, cooperative bindingcan further increase the sensitivity and can yield a highly ultrasensitive response. We conclude that autoregulation with the help ofother molecular mechanisms can impart distinct system level properties such as amplification, sensitivity and bistability. The resultsare further discussed in relation to various examples of genetic networks that exist in biological systems.

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eywords: Gene; Activator/repressor; Binding sites; Dimerization; Cooperativity; Bistability; Amplification and sensitivity

. Introduction

Genetic regulatory networks are complex system con-tituting various interactions and molecular mechanismshat are essential for their operation. These mechanismsnclude protein–DNA and protein–protein interactions,

ultiple binding sites, cooperativity and autoregulationf regulatory proteins. Regulatory protein, either as anctivator or repressor, binds to the upstream activationequence (UAS) or upstream repression sequence (URS)espectively, to constitute protein–DNA binding (Lohr

et al., 1995). Further, the regulatory protein can alsregulated through protein–protein interaction by oregulatory elements in the system (Melcher and2001). Genes can have multiple binding sites for spetranscriptional activator or repressor, which can inence the expression profile (Lohr et al., 1995; Melcand Xu, 2001). The binding characteristic for the sond site can alter depending on the binding state ofirst site constituting cooperativity (Lohr et al., 19Magnuson and Yarmolinsky, 1998). The above menisms are further compounded by autoregulation oregulatory proteins.

The synthesis of an autoregulatory protein is ctrolled by the same switch that it regulates (Simpsoal., 2003). The feedback constituted by autoregulacan either be positive (activation) or negative (inh

40

tion). They are ubiquitous and are observed in geneticsystems like bacteriophage-lamda (Ackers et al., 1982)andGAL (Verma et al., 2003) regulatory networks. Vari-ous roles have been attributed to autoregulation, such asamplification of gene expression, buffering response ofgenes to environmental changes (Sonneborn et al., 1965)and maintaining constant protein concentration indepen-dent of cell size and growth parameters (Simpson et al.,2003; Sompayrac and Maaløe, 1973; Haber and Adhya,1987; Becskei and Serrano, 2000). Further, autoregu-lation also provides stability to the genetic switches(Becskei and Serrano, 2000; Savageau, 1974) and reducethe time necessary to reach the steady state concentration(Rosenfeld et al., 2002).

Autoregulation typically does not operate indepen-dently of other mechanisms in a regulatory network.For example, a regulatory protein, which is autoregu-lated, can either bind as a monomer or a dimer to theupstream activation sequence (UAS) of a gene. Whileexpression fromTyr R gene inEscherichia coli (Bhartiyaet al., 2003) andSOCS3 gene in human (Auernhammeret al., 1999) is regulated by autoregulation of proteinsbinding as a monomer,rho gene inE. coli (Haber andAdhya, 1987) and Lac gene inKluyveromyces lactis(Zachariae and Breunig, 1993) are regulated by autoreg-ulated proteins binding as a dimer. Further, autoregu-lation can exist for a regulatory protein, which bindsto the multiple binding sites with cooperativity.TRAgene inF-plasmid (Fekete and Frost, 2002) and TORgene inE. coli (Ansaldi et al., 2000) are regulated by

ingor-

enenents a

tran-mer.ind-e, itgnif-ence

notionhiom-

theari-orks,statents

. Fur-

ther, these parameters are relatively easy to determinethrough in vitro experiments. Whereas, dynamic mod-els require kinetic rate constants for transcription, whichare difficult to obtain. Although dynamic analysis yieldstemporal details, steady state models are more commonand have been used to simulate genetic networks such aslactose operon (Isaacs et al., 2005), bacteriophage-lamda(Ackers et al., 1982), GAL regulatory network (Verma etal., 2003), etc.

In this article, we employ steady state analysis toquantify the effect of autoregulation by considering var-ious examples of isolated genetic switches. Researchershave demonstrated that isolated gene networks coupledwith proper quantification, can be used to elucidatethe key properties of in vivo functional genetic net-works (Chung and Stephanopoulous, 1996). The analy-sis includes systems wherein an autoregulated regulatoryprotein binds as (i) monomer, (ii) dimer, and (iii) dimerwith cooperativity to the UAS or URS of a gene. Wehave analyzed the effect of both positive and negativeautoregulation. Our analysis clearly indicates that pos-itive autoregulation can yield bistable response, whilenegative autoregulation yields stable but a less sensi-tive response. Moreover, the bistability is only observedwhen the regulatory protein acts as a dimer.

2. Methodology

A steady state analysis for expression of a gene withand without autoregulation for the following systems

theving

S

Sity.thehav-

eneanaly-ionsntra-f the

thes.dyn-

autoregulated proteins interacting with multiple bindsites. Autoregulation is, thus, known to play an imptant role in regulating various genetic networks (Simpsonet al., 2003) and there are myriad examples of gexpression systems with an autoregulatory compoin addition to other mechanisms. Autoregulation amechanism exists in genetic networks, where thescriptional effectors bind either as a monomer or diFurther, these mechanisms may include multiple bing sites resulting in a complex network. At this stagmay be pertinent to ask a question regarding the siicance of autoregulation at the system level in presof various other mechanisms. The past studies doexplicitly mention the role of autoregulation in relatto the presence of other mechanisms such as stoicetry, multiple binding site, cooperativity, etc.

Mathematical models can help in understandingnatural complexity arising due to autoregulation. Vous strategies that are used to model genetic netwincludes steady state and dynamic modeling. Steadymodels require only equilibrium dissociation constaand total component concentration as parameters

was considered:

1. Monomer binding of transcriptional activator toupstream activation sequence (UAS) of a gene haone binding site.

2. Dimer binding of transcriptional activator to the UAof a gene having one binding site.

3. Dimer binding of transcriptional activator to the UAof a gene having two binding sites with cooperativ

4. Dimer binding of transcriptional repressor toupstream repression sequence (URS) of a geneing two binding sites with cooperativity.

Fig. 1shows the schematic representation of the gexpression systems discussed above. Steady statesis assumes equilibrium binding between all interactand molar balances of all the component concetions. In case of autoregulation, the concentration otranscriptional activator at steady state is related tofractional protein expression (fp) of the gene it activateLet the transcriptional factor “A” be present at a steastate having a concentration ofA0. The steady state co

41

Fig. 1. (a) Schematic representation for gene expression having one binding site with and without autoregulation. The mRNA molecules aresynthesized from transcription of gene (D) and are translated to protein (A). Protein (A) dimerizes with dissociation constantK1. The monomer(A) and dimer (A2) binds to upstream activation sequence (D) with dissociation constantKd for transcriptional expression of gene. Note that ifthe transcriptional activator (A2) does not interact with the gene ‘D’ the system lacks autoregulation mechanism. (b) Schematic representation ofpositive/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 constantK1. The dimer (A2) molecule binds to first binding site (D)with dissociation constantKd and with second binding site byKd/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 ofA will be altered due to activation of its ownsynthesis for a genetic switch defined by autoregulation.Thus, due to autoregulation the steady state concentra-tion of “A” shifts fromA0 toAt, whereA0 can be termed asconcentration of transcriptional activator at the onset ofregulation. The effect of autoregulation was incorporatedthrough relating the total concentration of the transcrip-tional regulator (At) to the fractional protein expression(fp) and the initial concentration present at the onset ofregulation (A0), as given below:

[A]t = A0(1 + qfp) (1)

where q represents the fold change in the concentra-tion of the transcriptional activator due to autoregulationandfp is the fractional protein expression. Typically thefractional protein expression (fp) and fractional tran-scriptional expression (f) are related through a nonlinearexpression given byfp = fn, wheref quantifies fractionaltranscription. In the current analysis, we assume a linearrelationship between protein expression and transcrip-tion and setn = 1, which is the case for most prokaryoticsystems. The derivations for the four cases describedabove are detailed below.

Case 1. Activator as a monomer

In this case, transcriptional activatorA binds to thegene (D) having one binding site as a monomer withdissociation constantKd. The equilibrium dissociationis represented by

D

K

The molar balances for the total gene and activator con-centration are as follows:

[D]t = [D] + [DA] (4)

[A]t = [A] + [DA] (5)

The probability of protein expression is defined as theratio of concentration of the activator bound DNA to thetotal DNA concentration. Thus

f = [DA]

[D]t(6)

Eqs.(2)–(6)can be used to relate total activator concen-tration to fractional protein expression as follows:

[A]t = f

1 − fKd + f [D]t (7)

The effect of autoregulation (At or A0) can be incorpo-rated by relating [A]t from Eq.(7) to [A]0 using Eq.(1)as follows:

[A]0 = f

(1 − f )(1 + qf )Kd + f [D1]t

(1 + qf )(8)

Eqs.(7) and (8)relate the input concentration (At or A0)required for a specific output fractional expression (f) forcases without and with autoregulation, respectively.

Case 2. Activator as a dimer

In this case, transcriptional activator (A) dimerizessows:

+ A ↔ DA (2)

d = [D][A]

[DA](3)

before binding to the DNA (seeFig. 1a). The equationrepresenting all the molecular interactions are as foll

A + A ↔ A2 (9)

42

K1 = [A]2

[A2](10)

D + A2 ↔ DA2 (11)

Kd = [D][A2]

[DA2](12)

whereK1 andKd are the dissociation constants for dimer-ization of transcriptional activator and it’s binding toUAS of the gene, respectively. The total molar balancesfor 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(15)

Eqs. (9)–(15) can be used to relate the total activatorconcentration required to achieve a specific fractionalprotein expression (f) as follows:

[A]t =√

f

1 − f(K1Kd) + 2

f

1 − fKd + 2f [D]t (16)

Further, in the presence of autoregulation Eq.(16) canbe modified by substituting for [A]t using Eq.(1):

[A]0 =√

f1−f

(K1Kd) + 2 f1−f

Kd + 2f [D]t

(1 + qf )(17)

la-n of

ing

mer

siteond

ec-t the

The molar balances for DNA and the activator proteinare as

[D]t = [D] + [DA2] + [DA2A2] (22)

[A]t = [A] + 2[A2] + 2[DA2] + 4[DA2A2] (23)

The probability of transcription is defined as follows:

f = [DA2] + [DA2A2]

[D]t(24)

The mass balance equations can be solved simultane-ously to yield input–output relationship by relatingAtandf for this case in absence of autoregulation. As before,the relationship obtained by including Eq.(1) will yieldthe input–output relationship for the case with autoreg-ulation.

Case 4. Repressor binds to the gene having two bindingsites as a dimer.

In this case, the repressor molecule binds to theupstream repression sequence (URS) of a gene for regu-lation of transcription (seeFig. 1b). All the equations forthis case are similar to that listed in case-3 except Eq.(23) defining f, the fraction for transcriptional expres-sion. Since regulator (A) is a repressor in this case, thetranscription occurs only when the operator gene is free.Thus

f = [D](25)

lvedof

a-larpen-ous

andgi-[meast.

asesach

Eqs.(16) and (17), thus, represent the input–output retionship for the cases without and with autoregulatiotranscriptional activator binding to DNA as a dimer.

Case 3. Activator binds as a dimer to the gene havtwo binding sites with cooperativity

Here, the transcriptional activator binds as a dito the gene (D) having two binding sites (seeFig. 1b).The dissociation constant for binding to the firstis Kd and for the cooperative binding to the secsite is assumed to beKd/m, where factorm quantifiescooperativity (enhanced affinity of binding for the sond binding site). The following equations represenmolecular interactions:

D + A2 ↔ DA2 (18)

Kd = [D][A2]

[DA2](19)

DA2 + A2 ↔ DA2A2 (20)

Kd

m= [DA2][A2]

[DA2A2](21)

[D]t

For each of the four cases, the equations were sosimultaneously by using function solve algorithmMATLAB-12 (The Math Works Inc., USA) and eqution solve algorithm of Mathematica 4.1. The total mobalances on DNA and activator/repressor were indedently verified by adding the concentrations of varicomplexes.

3. Model parameters

The dissociation constants for protein–proteinDNA–protein interactions were taken in the physiolocal range as given in the figure legend. The value ofD]twas fixed for a model organism with cellular volu70�m3, equal to the cellular volume of a haploid yecell (Sherman, 1991) having single copy per genome

4. Results

The steady state response curves for the four cwere obtained by solving the model equations. For e

43

Fig. 2. Fractional protein expression through a positively autoregu-lated gene expression system as predicted by the steady state analysiswhen the transcriptional activator binds to the operator site (bind-ing 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 withq = 10-, 100- and 1000-fold changes in the activator concentrations due toautoregulation. Numbers next to curves show values of Hill coef-ficients. It can be noted that autoregulation brings about amplifi-cation by shifting the response curve to the left. Parameter valuesare as follows;Kd = 2.0× 10−10 M, K1 = 1.0× 10−7 M, m = 30 andDt = 2.37× 10−11 M.

case, the fractional transcriptional expression was plot-ted with respect to the concentration at the onset of tran-scription (A0) to represent autoregulation. To comparethe performance of the network without autoregulation,the fractional expression was plotted with respect toAtexcluding Eq.(1).

Fig. 2shows the fractional transcription for the casewhen transcriptional activator binds as a monomer (Case1). In absence of autoregulation, the response showsa typical Michaelis–Menten type response with a Hillcoefficient of one (curvei). Whereas, the responseobtained in the presence of autoregulation is sensitive.Further, the Hill coefficient (as a measure of sensi-tivity) increases with higher degree of autoregulation(i.e., increasing value ofq). The curves also shift tothe left indicating that the expression switches on at alower concentration of the activator required to switchon the expression. Thus, autoregulation causes not onlyan increase in the sensitivity but also amplifies the acti-vator signal.

Fig. 3. (a) Fractional protein expression through a positively autoreg-ulated gene expression system when the transcriptional activator bindsas 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 withq = 10-, 100-and 1000-fold changes in the activator concentration due to autoregula-tion. (b) A bistable response is observed due to positive autoregulationat the value ofq = 100. Non-linearity is caused due to ultrasensitiveresponse and autoregulation yields bistable response. Parameter val-ues are as follows;Kd = 2.0× 10−10 M, K1 = 1.0× 10−7 M, m = 30 andDt = 2.37× 10−11 M.

44

Fig. 4. Fractional protein expression through an autoregulated geneexpression system at different total concentrations of activator, whenthe activator binds as a dimer to gene having two binding sites withcooperativity. Curve (i) shows response for unautoregulated system andcurves (ii)–(iv) show the expression responses for autoregulated withq = 10-, 100- and 1000-fold changes in the activator concentrationsdue to autoregulation and with a cooperativity ofm = 30. It can benoted that bistability can be observed for responses obtained forq = 10,100 and 1000. Parameter values are as follows;Kd = 2.0× 10−10 M,K1 = 1.0× 10−7 M, m = 30 andDt = 2.37× 10−11 M.

Fig. 3a shows the transcriptional response when acti-vator dimerizes and binds to the operator site (i.e.,Case2). 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 theresponse to 5.2 atq = 10. It can be noted that on furtherincreasing the value ofq (higher degree of autoregula-tion), the response becomes switch like with a bistableresponse (seeFig. 3b). A bistable response has a distinctconcentration of activator at which it switches on and adifferent concentration at which it switches off. The fig-ure also shows that a certain concentration of activator atthe onset of expression is essential to switch on the tran-scription. Thus, a leaky transcription is necessary in theoff state for the operation of such positive autoregulatorysystems.

Fig. 4 shows the transcriptional response when theactivator dimerizes and binds to the gene having twobinding sites with cooperativity (i.e.,Case 3). Even inthis case, the response is highly sensitive in absenceof autoregulation (with a Hill coefficient of 3.5). Theincreased sensitivity is due to multiple binding sites

Fig. 5. Fractional protein expression through a negatively autoregu-lated system when the repressor binds as a dimer with cooperativityto a gene having two binding sites. Curve (i) shows response forthe unautoregulated system and (ii)–(iv) show expression responsesfor autoregulated withq = 10-, 100- and 1000-fold changes in therepressor concentrations due to autoregulation. Parameter valuesare as follows;Kd = 2.0× 10−10 M, K1 = 1.0× 10−7 M, m = 30 andDt = 2.37× 10−11 M.

and cooperativity. Further, in presence of autoregulation,bistability is observed at a lesser degree of autoregulation(i.e., even atq = 10).

Fig. 5 shows the case when a repressor is autoreg-ulated and binds as a dimer to the upstream repres-sion sequences (URSs) of a gene with cooperativity. Inabsence of autoregulation, the value of the sensitivityof the response as calculated from the Hill equation is3.5 and is also similar to that obtained by an transcrip-tional activator (curvei in Fig. 4). Further, the responsebecomes less sensitive in the presence of autoregula-tion. Further the sensitivity decreases with increase in thedegree of autoregulation (i.e., with increase in the valueof q). In a repressive system autoregulation imparts onlyamplification to the response, without yielding proper-ties such as sensitivity and bistability.

The different mechanisms analyzed in the abovesection yield specific transcriptional response and theresponses were dependent on the parameter values. It isrelevant to study the dependency of the output responseto system parameters. This entails representing the out-put response by a curve. We use Hill equation, which ischaracterized by the Hill coefficient (ηH) and half satu-ration 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 variationsin key system parameters (a) and (b). Solid line: variation with respect to dimerization constant for a transcriptional activator binding to a gene asa dimer; dotted line: variation with respect to the degree of cooperativity for the transcriptional activaotr binding as a dimer to two binding siteswith cooperativity; (c) variation of Hill coefficient with respect to degree of autoregulation (q in Eq. (1)); (d) variation of half saturation constantwith respect to degree of autoregulation. Dotted line represents curve for switching on while solid line represents curve for switching off indicatingbistability. Note that bistability was lost at low degree of autoregulation, as both the curves merge.

as given below:

O = IηH

KηH0.5 + IηH

(26)

whereO andI indicate output response and input, respec-tively. The dependency ofηH andK0.5 on a parametersignifies the sensitivity of the response to a given changein a parameter value.Fig. 6a shows the variation ofHill coefficient to changes in dimerization constant (Kd),when a transcriptional activator binds as a dimer to theoperator site (solid line inFig. 6a). As the dimeriza-tion constant increases, the Hill coefficient decreases to1 from 2. This is due to the fact that the binding of thedimer to the operator site controls the response ratherthan the dimerization of the activator. The half satura-tion constant increases with the dimerization constant(see solid line inFig. 6b). This implies that the outputresponse requires larger amounts of input to switch onthe system with increase in theKd value.

Fig. 6a also shows the variation of Hill coefficientwith respect to extent of cooperativity (m in Eq. (21)).

Increase in cooperative binding to the second site bya transcriptional activator increases the Hill coefficient,but was bounded between values 1 and 2 (dotted line inFig. 6a). WhileK0.5 decreases with increase in the valueof m indicating that the signal gets amplified (dotted lineFig. 6b).

Autoregulation of the transcriptional activator canyield ultrasensitive response with bistability (seeFig. 4).The Hill coefficient increases with increase in the degreeof autoregulation (parameterq in Eq. (1) and shownin Fig. 6c). The half saturation constant decreases withincrease in the value ofq indicating amplification (seeFig. 6d). Bistability was observed at a very high degreeof autoregulation resulting in a different value ofK0.5for switching on (dotted line inFig. 6d) and switch-ing off (solid line in Fig. 6d) the genetic switch. Abistable response typically has a very high Hill coeffi-cient with a steep switch like output and can take valueshigher than two. The value of Hill coefficient was thusnot bounded in this case (values of 50–100 can also beobtained).

46

5. Discussion

Autoregulation of regulatory proteins is a recurrenttheme observed in many regulatory networks. Autoreg-ulation operating in tandem with other mechanisms likedimerization, multiple binding sites and cooperativitycan impart distinct properties to regulatory networks.Therefore, autoregulation as a fundamental mechanismis observed in many genetic regulatory systems rang-ing from bacterial systems to higher organisms. Varioussystems wherein transcriptional activation and repres-sion with autoregulation have been reported in liter-ature and are listed inTables 1 and 2, respectively.While autoregulation as a phenomenon has been demon-strated in many disparate systems, its role in the oper-ation of genetic networks has been peripherally dis-cussed. Our steady state analysis clearly demonstratesthat autoregulation is a fundamental mechanism ingenetic networks and is highly context dependent. Fur-ther, autoregulation in combination with other knownmechanisms like cooperativity can impart system levelproperties like multiple steady state, ultrasensitivity andamplification.

Steady state analysis indicates that positive autoreg-ulation yields a sensitive response with amplification.

Table 1Examples of genetic networks exhibiting autoregulation with positivefeedback in tandem with other mechanisms

)

)

3)

Table 2Examples of genetic networks exhibiting autoregulation with negativefeedback in tandem with other mechanisms

Protein binding as a monomerMASH1 gene inDrosophilla

Meredith and Johnson (2000)

SOCS-3 gene inhuman Auernhammer et al. (1999)torCAD operon inEscherichia coli

Gon et al. (2001)

IE2 gene inhumancytomegalovirus (CMV)

Macias and Stinski (1993)

FTZ gene inDrosophilla Yu et al. (1999)PDC5 genes inSaccharomyces cerevisiae

Muller et al. (1999)

AnCF gene inAspergillusnidulans

Steidl et al. (2001)

CYS-B gene inSalmonellatyphimurium

Ostrowski and Kredich (1986)

TyrR gene inEscherichiacoli

Camakaris and Pittard (1982)

MET-J gene inSalmonellatyphimurium

Urbanowski and Stauffer (1986)

SIG-A gene inT. maritium Camarero et al. (2002)EFG1 gene inCandidaalbicans

Tebarth et al. (2003)

RAF-1 gene inXanopuslevis

Cutler et al. (1998)

Protein binding as a dimer without cooperativityPER andTIM genesexpression infruit fly

Tyson et al. (1999)

GAL80 gene inSaccharomyces cerevisiae

Melcher and Xu (2001)

REP-E gene inminiF-plasmid

Ishiai et al. (1994)

rho gene inEscherichiacoli

Haber and Adhya (1987)

Monomer protein binding with cooperativityDoc H66y protein inbacteriophage P1

Dodd et al. (2002)

TOR gene inSaccharomyces cerevisiae

Ansaldi et al. (2000)

Amplification offers an advantage in the form of requir-ing lower amount of regulatory proteins to operate thegenetic network. Positive autoregulation is also capa-ble of yielding a bistable response indicating multiplesteady states. Bistability is typically observed when anon-linearity caused by sensitive response is superim-posed by a positive feedback loop. Thus, dimerizationand cooperativity by themselves can yield ultrasensitiv-ity resulting in non-linearity, while autoregulation con-stitute a positive feedback loop. In a bistable system,for a given activator concentration at the onset of tran-scription, the switch resides in two steady states, oneleaky off state and another in the on state. This makes theexpression completely switch like, as it cannot reside inany other intermediatery steps. Such bistable response

Protein binding as a monomerGene32 in bacteriophageT-4

von Hippel et al. (1982)

Ubx gene inDrosophilla Christen and Bienz (1992)Ultrabithorox gene inDrosophilla

Thuringer and Bienz (1993)

Beta1-adrenergic receptorgene in human

Bartholoma and Nave (1994

NEX1 gene inDrosophilla Bartholoma and Nave (1994GAL3 in Saccharomycescerevisiae

Lohr et al. (1995)

RAS genes expression inFibroblast

Quincoces et al. (1997)

MyoD gene inrat Benayoun et al. (1998)Siamois gene inXenopusembryos

Fan et al. (1998)

Siamois gene inXenopusembryos

Fan et al. (1998)

Sx1 gene inDroshophilla Cline et al. (1999)

Protein binding as a dimer without cooperativityLac9 protein inKluyveromyces lactis

Zachariae and Breunig (199

Protein binding as a dimer with cooperativityTRA gene in F plasmid Fekete and Frost (2002)CI gene expression inbacteriophage-�

Ackers et al. (1982)

47

is essential for a system, which require a yes or notype of decision. Whereas, in a system with positiveautoregulation of activator, which binds as a monomerto the upstream activation sequence, the response doesnot show bistability due to insufficient non-linearity inthe system.

Existence of bistability has been shown experimen-tally in cellular differentiation and cell cycle progres-sion inXenopus laevis egg (Sha et al., 2003). Howeversuch bistable response is not reported in transcriptionalregulation. The network structure associated with bista-bility (i.e. non-linearity with positive feed back loop)also exits in transcriptional regulatory systems. Theoret-ical analysis reported here indicates that systems withdimerization and cooperativity in the presence of posi-tive autoregulation can manifest bistable response. Suchstructures have been reported forTRA gene in F plas-mid (Fekete and Frost, 2002) and CI gene expressionin bacteriophage-lamda (Ackers et al., 1982). Autoreg-ulation and dimerization ofcl protein help in decidingbacteriophage-lamda to reside in the lytic or the lyso-genic states, which are two distinct phenotypic states.However, there are many other systems where positiveautoregulation would not yield bistability due to thenon-existence of non-linearity caused by dimerizationand multiple binding sites. Such systems would offer anadvantage of a sensitive response and amplification asdemonstrated here.

Unlike in a bistable system, systems with negativeautoregulation show a smooth transition from one state toa tatesc cen-t itive,b h as o notr rityi ityc duet ativea

medo etics qua-t luesw alfs thati riza-t wash thatt itch,w ns.R tream

interactions (like cascades) through a higher degree ofcomplexity.

As demonstrated here, mathematical models can beused to analyze regulatory networks containing autoreg-ulatory loops to provide insights into the properties ofthe inherent structure. Steady state analysis requiresonly equilibrium binding characteristics, which are easyto obtain. A dynamic model involves detailed kineticanalyses that are tedious. As demonstrated here, steadystate analysis can also be used to enumerate systemlevel properties. It is difficult and tedious to demon-strate some of these properties only through experimen-tal tools. Experiments can provide details about the exist-ing structure and prevailing mechanisms in the network.Thus, molecular biology has established the existenceof dimerization, cooperativity and autoregulation withprotein–protein and protein–DNA interactions as basicmechanisms prevalent in genetic regulatory networks.While, theoretical analysis provides insights into systemproperties such as sensitivity of response, amplificationof signal, bistability and multiple steady states. Theseproperties can manifest depending on the connectivityof various molecular mechanisms prevalent in a partic-ular genetic network.

References

Ackers, G.K., Johnson, A.D., Shea, M.A., 1982. Quantitative modelfor gene regulation by�-phage repressor. Proc. Natl. Acad. Sci.

orR--

lationn of

. 96,

ificres-

orks

.A.,ces

el ofural

e. J.

uber02.n-99,

nother, implying that many intermediatery steady san be achieved depending on the input activator conration. Thus, this makes the system less ultrasensut a distinct amplification can be achieved in sucystem and may be essential for systems, which dequire a yes or no type of status. Although non-linean the form of multiple binding sites and cooperativan exist in such systems, bistability is not observedo the presence of negative feed back loop (i.e., negutoregulation).

Parametric sensitivity analysis was also perforn the different mechanisms operating in the genwitch. The response was represented by Hill eion and the sensitivity to variations in parameter vaere obtained by evaluating Hill coefficient and haturation constant. It was clear from the analysisrrespective of the mechanism studied (that is dimeion, cooperativity or autoregulation), the responseighly dependent on the parameters. This indicated

hese basic mechanisms, operating in the genetic swould not yield robustness to parametric variatioobustness can be achieved through other ups

U.S.A. 79, 1129–1133.Ansaldi, M., Simon, G., Lepelletier, M., Mejean, V., 2000. The T

high-affinity binding site plays a key role in bothtorR autoregulation andtorCAD operon expression inEscherichia coli. J. Bacteriol. 182, 961–966.

Auernhammer, C.J., Bousquet, C., Melmed, S., 1999. Autoreguof pituitary corticotroph SOCS-3 expression: Characterizatiothe murine SOCS-3 promoter. Proc. Natl. Acad. Sci. U.S.A6964–6969.

Bartholoma, A., Nave, K.A., 1994. NEX-1: a novel brain-spechelix-loop-helix protein with autoregulation and sustained expsion in mature cortical neurons. Mech. Dev. 48, 217–228.

Becskei, A., Serrano, L., 2000. Engineering stability in gene netwby autoregulation. Nature 405 (6786), 590–593.

Benayoun, B., Pelpel, K., Solhonne, B., Guillier, M., Leibovitch, S1998. Overexpression of Mosrat proto-oncogene product enhanthe positive autoregulatory loop of MyoD. FEBS 437, 39–43.

Bhartiya, S., Rawool, S., Venkatesh, K.V., 2003. Dynamic modEscherichia coli tryptophan operon shows an optimal structdesign. Eur. J. Biochem. 270, 2644–2651.

Camakaris, H., Pittard, J., 1982. Autoregulation of the tyrR genBacteriol. 150, 70–75.

Camarero, J.A., Shekhtman, A., Campbell, E.A., Chlenov, M., GrFT.M., Bryant, D.A., Darst, S.A., Cowburn, D., Muir, T.W., 20Autoregulation of a bacterial� factor explored by using segmetal isotopic labeling and NMR. Proc. Natl. Acad. Sci. U.S.A.8536–8541.

48

Christen, B., Bienz, M., 1992. A cis-element mediatingUltrabitho-rax autoregulation in the central nervous system. Mech. Dev. 39,73–80.

Chung, J.D., Stephanopoulous, G., 1996. On physiological multiplicityand population heterogeneity of biological systems. Chem. Eng.Sci. 51, 1509–1521.

Cline, T.W., Rudner, D.Z., Barbash, D.A., Bell, M., Vutien, R., 1999.Functioning of theDrosophila integral U1/U2 protein Snf inde-pendent of U1 and U2 small nuclear ribonucleoprotein particles isrevealed by snf+ gene dose effect. Proc. Natl. Acad. Sci. U.S.A.96, 14451–14458.

Cutler Jr., R.E., Stephens, R.M., Saracino, M.R., Morrison, D.K., 1998.Autoregulation of the Raf-1 serine/threonine kinase. Proc. Natl.Acad. Sci. U.S.A. 95, 9214–9219.

Dodd, E.S., Hemker, R.G., Huang, C.K., Wang, S., Ren, C., Mori,W.B., 2002. Hosing and sloshing of short-pulse gev-class wakefielddrivers. Phys. Rev. Lett. 88, 125001–125004.

Fan, M.J., Gruning, W., Walz, G., Sokol, S.Y., 1998. Wnt signalingand transcriptional control of Siamis in Xenopus embryos. Proc.Natl. Acad. Sci. U.S.A. 95, 5626–5631.

Fekete, R.A., Frost, L.S., 2002. Characterizing the DNA contacts andcooperative binding of F plasmid TraM to its cognate sites at oriT.J. Biol. Chem. 28, 1–33.

Gon, S., Jourlin-Castelli, C., Theraulaz, L., Mejean, V., 2001. Anunsuspected autoregulatory pathway involving apocytochromeTorC and sensor TorS inEscherichia coli. Proc. Natl. Acad. Sci.U.S.A. 98, 11615–11620.

Haber, R., Adhya, S., 1987. Autoregulation of gene expression:rho. J.Biosci. 11, 225–230.

Isaacs, F.J., Hasty, J., Charles, R.C., Colins, J.J., 2005. Predictionand measurement of an autoregulatory genetic module. Proc. Natl.Acad. Sci. U.S.A. 100 (13), 1714–1719.

Ishiai, M., Wada, C., Kawasaki, Y., Yura, T., 1994. Replication ini-tiator protein RepE of mini-F plasmid: functional differentiationbetween monomers (initiator) and dimers (autogenous repressor).

on inJ.

ansite-2 to

S.A.

P1351.centn.

ash1

.A.,n S,lationcere-

ysBth

Quincoces, A.F., Polanco, I., Thomson, T., Leon, J., 1997. Positiveautoregulation of ras genes expression in fibroblasts. FEBS 416,317–323.

Rosenfeld, N., Elowitz, M.B., Alon, U., 2002. Negative autoregulationspeeds the response times of transcription networks. J. Mol. Biol.323, 785–793.

Savageau, M.A., 1974. Significance of autogenously regulated andconstitutive synthesis of regulatory proteins in repressible biosyn-thetic systems. Nature 258, 208–214.

Sha, W., Moore, J., Chen, K., Lassaletta, A.D., Yi, C.S., Tyson, J.J.,Sible, J.C., 2003. Hysteresis drives cell-cycle transitions inXeno-pus laevis egg extracts. Proc. Natl. Acad. Sci. U.S.A. 100, 975–980.

Sherman, F., 1991. Getting started with yeast. In: Guthrie, C., Fink,G.R. (Eds.), Methods in Enzymology. Guide to Yeast Geneticsand Molecular Biology, vol. 194. Academic Press, New York, pp.3–21.

Simpson, M.L., Cox, C.D., Sayler, G.S., 2003. Frequency domain anal-ysis of noise in autoregulated gene circuits. Proc. Natl. Acad. Sci.U.S.A. 100, 4551–4556.

Sompayrac, L., Maaløe, O., 1973. Autorepressor model for control ofDNA replication. Nat. New Biol. 241, 133–135.

Sonneborn, D.R., Levinel, L., Sussman, M., 1965. Serological analysesof cellular slime mold development. II. Preferential loss, duringmorphogenesis, of antigenic activity associated with the vegetativemyxamoebae. J. Bacteriol. 89, 1092–1106.

Steidl, S., Hynes, M.J., Brakhage, A.A., 2001. TheAspergillus nidu-lans multimeric CCAAT binding complex AnCF is negativelyautoregulated via its hapB subunit gene. J. Mol. Biol. 306, 643–653.

Tebarth, B., Doedt, T., Krishnamurthy, S., Weide, M., Monterola, F.,Dominguez, A., Ernst, J.F., 2003. Adaptation of the Efg1p morpho-genetic pathway in candida albicans by negative autoregulation andPKA-dependent repression of theEFG1 gene. J. Mol. Biol. 329,949–962.

oticatl.

odel

em5,

lysistitive9.W.,ativee T4Mol.

ter-lators

ional

Proc. Natl. Acad. Sci. U.S.A. 91, 3839–3843.Lohr, D., Venkov, P., Zlatanova, J., 1995. Transcriptional regulati

the yeastGAL gene family: a complex genetic network. FASEB9, 777–786.

Macias, M.P., Stinski, M.F., 1993. An in vitro system for humcytomegalovirus immediate early 2 protein (IE2)-mediateddependent repression of transcription and direct binding of IEthe major immediate early promoter. Proc. Natl. Acad. Sci. U.90, 707–711.

Magnuson, R., Yarmolinsky, M.B., 1998. Corepression of theAddiction Operon by Phd and Doc. J. Bacteriol. 180, 6342–6

Melcher, K., Xu, H.E., 2001. Gal80–Gal80 interaction on adjaGal4p binding sites is required for completeGAL gene repressioEMBO J. 20 (4), 841–851.

Meredith, A., Johnson, J.E., 2000. Negative autoregulation of Mexpression in CNS development. Dev. Biol. 222, 336–346.

Muller, E.H., Richards, E.J., Norbeck, J., Byrne, K.L., Karlsson, K1999. Pretorius GHJ, Meacock PA, Blomberg A, HohmanThiamine repression and pyruvate decarboxylase autoreguindependently control the expression of the Saccharomycesvisiae PDC5 gene. FEBS 499, 245–250.

Ostrowski, J., Kredich, N.M., 1986. Negative Autoregulation of cSalmonella typhimurium: in vitro interactions of CysB protein withe cysB promoter. J. Bacteriol. 173, 2212–2218.

Thuringer, F., Bienz, M., 1993. Indirect autoregulation of a homeDrosophila gene mediated by extracellular signaling. Proc. NAcad. Sci. U.S.A. 90, 3899–3903.

Tyson, J.J., Hong, C.I., Thron, C.D., Novak, B., 1999. A simple mof circadian rhythms based on dimerization and proteolysis ofPERandTIM. Biophys. J. 77, 2411–2417.

Urbanowski, M.L., Stauffer, G.V., 1986. Autoregulation by tandof theSalmonella typhimurium LT2 metJ gene. J. Bacteriol. 16740–745.

Verma, M., Bhat, P.J., Venkatesh, K.V., 2003. Quantitative anaof GAL genetic switch ofSaccharomyces cerevisiae reveals thanucleocytoplasmic shuttling of Gal80p results in a highly sensresponse to galactose. J. Biol. Chem. 278 (49), 48764–4876

von Hippel, P.H., Kowalczykowski, C., Lonberg, N., Newport, J.Paul, L.S., 1982. Autoregulation of gene expression, quantitevaluation of the expression and function of the bacteriophagGene 32 (single stranded DNA binding) protein systems. J.Biol. 162, 795–818.

Yu, Y., Yussa, M., Song, J., Hirsch, J., Pick, L., 1999. A Double inaction screen identifies positive and negative ftz gene reguand Ftz-interacting protein. Mech. Dev. 83, 95–105.

Zachariae, W., Breunig, K.D., 1993. Expression of the transcriptactivatorLAC9 (KlGAL4) in Kluyveromyces lactis is controlled byautoregulation. Mol. Cell. Biol. 13, 3058–3066.