Methods 59 (2013) 349–362

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Methods

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Combined analytical ultracentrifugation, light scattering and fluorescencespectroscopy studies on the functional associations of the bacterial division FtsZprotein

Begoña Monterroso a, Carlos Alfonso a, Silvia Zorrilla b, Germán Rivas a,⇑a Centro de Investigaciones Biológicas, Madrid, Spainb Instituto de Química-Física Rocasolano, Consejo Superior de Investigaciones Científicas, Madrid, Spain

a r t i c l e i n f o a b s t r a c t

Article history:Available online 5 January 2013

Communicated by Peter Schuck

Keywords:Physical biochemistryProtein–protein interactionsProtein polymerizationPhospholipid bilayer nanodiscsEscherichia coliZipA

1046-2023/$ - see front matter � 2013 Elsevier Inc. Ahttp://dx.doi.org/10.1016/j.ymeth.2012.12.014

Abbreviations: Cc, critical concentration of assegradient static light scattering; DLS, dynamic lightcorrelation spectroscopy; GDP-FtsZ, GDP bound F[(a,b)-methylene] triphosphate sodium salt; GTP-FtsZpolymers of FtsZ where assembly was triggered by GMALLS, multiangle laser light scattering; Nd-ZipA, wnanodiscs; Nd⁄-ZipA, labeled nanodiscs containingregeneration system; SE, sedimentation equilibriumSV, sedimentation velocity; sZipA, soluble mutant of⇑ Corresponding author. Address: CIB-CSIC, Ramiro

Spain.E-mail addresses: monterroso@cib.csic.es (B. Monte

Alfonso), silvia@iqfr.csic.es (S. Zorrilla), grivas@cib.csi

The combined application of different biophysical techniques – analytical ultracentrifugation, light scat-tering and fluorescence-based assays – to study the ligand-linked self-association and assembly proper-ties of the cell division protein FtsZ from Escherichia coli is described. These reactions are thought to beimportant for the formation of the dynamic division ring that drives bacterial cytokinesis. In addition, theuse of this orthogonal experimental approach to measure the interactions between FtsZ oligomers (GDPforms) and polymers (GTP forms) with two variants (a soluble form and a full-length protein incorpo-rated in phospholipid bilayer nanodiscs) of the ZipA protein, which provides membrane tethering to FtsZ,is described as well. The power of a global analysis of the results obtained from complementary biophys-ical methods to discriminate among alternative self- and hetero-associating schemes and to propose amore robust description of the association reactions involved is emphasized. This orthogonal approachwill contribute to complete our quantitative understanding of the initial events of bacterial division.

� 2013 Elsevier Inc. All rights reserved.

1. Introduction

Bacterial cell division is mediated by a multiprotein machinerywhose components gather together at midcell towards the end ofthe cell cycle to form a dynamic ring that drives cytokinesis. Thering is formed by at least ten division specific proteins, most ofthem integral membrane proteins. In the case of Escherichia coli,the division process is thought to be initiated by the interactionof three proteins (the GTPase FtsZ, a tubulin ancestor; the amphi-tropic protein FtsA; and the membrane protein ZipA) at the cyto-plasmic membrane to form the first molecular complex of thedivisome, the proto-ring, that is followed by the incorporation ofthe rest of the essential division proteins (reviewed in [1,2]).

ll rights reserved.

mbly; CG-SLS, compositionscattering; FCS, fluorescencetsZ; GMPCPP, guanosine-50-

and GMPCPP-FtsZ polymers,TP or GMPCPP respectively;ild type ZipA inserted intowild type ZipA; RS, GTP

; SLS, static light scattering;ZipA.de Maeztu 9, 28040 Madrid,

rroso), carlosa@cib.csic.es (C.c.es (G. Rivas).

The functions of these assemblies depend upon the ability of theconstituent macromolecules to dissociate and re-associate in areversible manner, either to regulate the biochemical activity ofthe functional entity active in division or to facilitate function-linkedstructural reorganizations of the division machinery [3]. To fullydescribe the function of such complex assembly and to completeour understanding on how division works, it is necessary to knowhow changes in the concentrations of the division proteins andregulatory substances, as well as changes in environmental vari-ables, such as pH and ionic strength or excluded-volume effectsdue to the natural crowding [4], affect the relative abundance ofthe various states of association of the interacting macromoleculesinvolved in bacterial division. There exist a variety of powerful andversatile techniques for the quantitative characterization ofreversible macromolecular associations, including protein–ligand,protein–protein, protein–nucleic acid and protein–membraneinteractions [5–9].

In this work, we have concentrated in the application of a set ofbiophysical techniques (analytical ultracentrifugation, light scat-tering and fluorescence-based methods) to study the activity, inter-actions and assembly of the protein FtsZ (from E. coli), a centralcomponent of the division machinery. FtsZ (40 kDa) is widely con-served among prokaryotic organisms and it is taken to be the ances-tor of tubulin, sharing the nucleotide-binding and GTPase activitiesand the capacity to form polymers [10,11]. The self-association of

350 B. Monterroso et al. / Methods 59 (2013) 349–362

FtsZ in the presence of GDP and its polymerization in the presenceof GTP have been extensively studied ([10,11]; and referencestherein; see also section 4). While the mechanism of GDP-FtsZ oli-gomer formation is relatively well understood, that is not the casefor the GTP-linked FtsZ polymerization. In the presence of GTP, FtsZassembles in an apparent cooperative manner to form plastic poly-mers able to associate into multi-stranded flexible structures. FtsZpolymers have been described as very dynamic both in vitro andin vivo, with a rapid exchange of FtsZ between the Z-ring and thecytoplasm [12,13]. However, the implications of these processeson the kinetics governing fiber or Z-ring assembly are not at allclear. The dynamic character of FtsZ polymers, linked to the rela-tively high GTPase activity of the protein, constitutes an additionalchallenge to study FtsZ assembly in the presence of GTP as it re-quires special procedures to maintain polymer stability throughoutthe duration of a typical biochemical or biophysical experiment[14]. Consequently, the number of quantitative techniques appliedto study FtsZ assembly is lower than that used to study other pro-tein assembly systems [15,16]. Current research on FtsZ is aimedat determining the role of the Z-ring in division, describing thepolymerization and force-generating mechanisms and evaluatingthe roles of nucleotide exchange and hydrolysis [10,11].

E. coli FtsZ is anchored to the cytoplasmic membrane throughthe interaction with the other proto-ring proteins, ZipA or FtsA[1]. FtsA (48 kDa) is thought to be a member of the actin familyand its association to the membrane seems to be mediated by ashort amphipathic helix [17]. ZipA (39 kDa) contains a short N-ter-minal region that is integrated in the membrane, and connected tothe C-terminal FtsZ-interacting domain by a flexible, unstructured,linker region [18]. As the assembly of the proto-ring is a mem-brane-linked process, a considerable effort is being made to studythe interactions and assembly properties of FtsZ under topologi-cally restricted reconstructions of the proto-ring in biomimeticmembrane systems, such as nanodiscs, coated microbeads, bilayersand vesicles [19–24]. They provide the opportunity to investigatecomplex membrane-associated reactions under defined experi-mental conditions, as the biochemical parameters can be con-trolled precisely [25,26].

As this review is focused in the biophysical analysis of FtsZ asso-ciations in solution, results have been structured as a first sectionregarding Mg2+-linked self-association of GDP- and GTP-FtsZ (orits analog GMPCPP), which allowed estimating the polymer molarmasses in close to physiological conditions, and a second sectionwhere we have limited our description of membrane-based studiesto the analysis of the dynamic interactions between FtsZ oligo-mers/polymers and ZipA incorporated in nanodiscs. These struc-tures, formed by a membrane scaffold protein encircling aphospholipid bilayer, are promising novel tools to study interac-tions of membrane proteins while the system under study remainssoluble [27]. When a target membrane protein (e. g., ZipA) is in-cluded in the mixture, each nanodisc self-assembles and incorpo-rates the target protein preserving its natural properties. Asummary of the potential implications of the main findings ofthese studies - related with the features that FtsZ polymers donot grow indefinitely with protein concentration, and that ZipAin nanodiscs binds FtsZ oligomers and polymers with equal moder-ate affinity - is included.

2. Quantitative approaches used to study FtsZ-relatedassociating reactions: summary of general principles

The methods used to characterize FtsZ homo- and hetero-asso-ciations are described below emphasizing the information derivedfrom the individual techniques, and, more importantly, how theircombination allows discriminating among alternative association

schemes. Fig. 1 shows representative experimental data and maininformation derived from the biophysical methods employed.Fig. 2 schematically confronts the information obtained by eachmethod (Fig. 2A) and relates the trend of hydrodynamic parame-ters with changes in particle properties for a given mass (Fig. 2B).

2.1. Analytical ultracentrifugation

Analytical ultracentrifugation (AUC) is a powerful and versatiletechnique, based on the application of a centrifugal force and thedirect observation of the resulting spatial macromolecular redistri-bution, to characterize the size distribution and overall shape ofindividual macromolecular components in solution, and is speciallywell adapted to detect and measure macromolecular associationsunder physiological conditions [6,8,28]. Two complementary AUCapproaches are available: sedimentation velocity (SV) and sedi-mentation equilibrium (SE) (Fig. 1).

2.1.1. Sedimentation velocitySV is a hydrodynamic method in which the rate of transport is

measured and the macromolecules are fractionated upon theapplication of a high centrifugal force according to their differencesin buoyant mass and shape. SV is the method of choice to studystrong associations that are very slowly reversible during the timescale of the experiment, and it is possible to separate the differentstates of association to characterize them individually. Estimates ofthe sedimentation coefficient and molar mass of the sedimentingspecies can be obtained from the analysis of the time dependentgradients [29,30].

The rate of transport of solute species i, centrifuged at angularvelocity x in a sector-shaped centrifuge cell, is described by thefollowing relation:

Ji ¼ six2rSi � DidSi

drð1Þ

where Ji is the rate of transport of species i, x is the rotor angularvelocity, r the radial position, and Si and Di are the sedimentationand diffusion coefficients of species i, respectively. Si is a measur-able property or signal (S) of the solution that varies linearly withthe weight/volume concentration of each species of sedimentablesolute at radial position r:

SðrÞ ¼X

i

SiðrÞ ¼X

iaiwiðrÞ ð2Þ

where ai denotes the signal proportionality constant of species i.Suitable signals are UV–VIS absorbance, refractive index at agiven wavelength, or the radioactivity of a radiolabeled solute inAUC experiments with preparative ultracentrifuges coupled tomicrofractionation [31].

The sedimentation coefficient of species i is given by:

Si ¼M�

i

NAfsed;ið3Þ

where M�i denotes the actual buoyant molar mass. M�

i ¼ Midi, whereMi is the molar mass and di the specific density increment of speciesi [32]. NA is the Avogadro’s number and fsed;i is the frictional coeffi-cient of species i.

The diffusion coefficient is given by:

Di ¼RT

NAfdiff ;ið4Þ

where R is the molar gas constant, T the temperature, and fdiff ;i thediffusion frictional coefficient of species i.

In the ideal limit the two frictional coefficients (which are sizeand shape-dependent macromolecular properties) are equal andeqs. (3) and (4) can be combined to yield the Svedberg relation:

Fig. 1. Analytical methods used for the characterization of homo- and/or hetero- associations of FtsZ. Main characteristics of each method are stated, and examples ofrepresentative data obtained after measurements are shown. SV: simulation of the sedimentation of a single species with sequential radial concentrations scans (min). SE:panel shows an approach to equilibrium experiment at sequential time intervals (h). The final gradient (bold) represents a close approximation to sedimentation equilibrium.DLS: normalized autocorrelation function describing the time dependence of scattering intensity of a given particle. MALLS: multiangle laser light scattering data showing therelation of scattered light with detector angle and particle concentration. FCS: normalized autocorrelation of the fluorescence intensity fluctuations of a particle. Anisotropy:steady-state fluorescence anisotropy of a particle as a function of its concentration. Figures modified from references [6,45,68].

B. Monterroso et al. / Methods 59 (2013) 349–362 351

Si

Di¼ M�

i

RTð5Þ

2.1.2. Sedimentation equilibriumSE is a method in which a lower centrifugal field is applied and

that yields information about the dependence upon solutioncomposition of the signal-average buoyant molar mass and theequilibrium distributions can be analyzed in the context of ther-modynamic association models. This technique is uniquelyadapted to detect and measure dynamic self- and/or hetero-associations leading to the formation of non-covalent complexesthat exist in composition-dependent equilibrium mixtures. Atsedimentation equilibrium the sedimenting and diffusing forcesequilibrate and therefore no further net transport of species in

the centrifuge cell is observed (Ji = 0, for all species i) which yieldsthe following SE relation:

d ln Si

dr2 ¼M�

i;appx2

2RTð6Þ

where M�i;app is the apparent buoyant molar mass of species i, which

is equal to M�i under ideal solution conditions.If the previous rela-

tion is integrated with respect to r2 the expression for the equilib-rium gradient of an ideally sedimenting macromolecule is obtained:

SiðrÞ ¼ Siðr0Þ expM�

i;appx2

2RTðr2 � r2

0Þ" #

ð7Þ

where r0 is an arbitrarily selected reference position.The signal–average buoyant molar mass is given by:

Fig. 2. Information derived from the application of different analytical methods and dependence with particle characteristics. (A) Schematic representation of the informationobtained by the different hydrodynamic and thermodynamic techniques and their combinations. (B) Dependence of the translational diffusion coefficient (D), sedimentationcoefficient (s) and diameter with an increase in compactness, flexibility, hydration and asymmetry for particles of a given mass.

352 B. Monterroso et al. / Methods 59 (2013) 349–362

M�S ¼

PiaiwiðrÞM�

iPiaiwiðrÞ

ð8Þ

For any given model scheme for self- or hetero-association, thevalues of M�

S may be calculated as a function of the total concentra-tions of all chemically distinct components, the buoyant molarmasses of each component (as monomer) and the equilibriumassociation constants describing each postulated association[33,34].

Analysis of SE using Eqs. (6)–(8) may be complicated in the gen-eral case by the fact that, in principle, all solute concentrationspresent in the solution mixture are functions of the radial position.For this reason, strategies of global analysis of actual gradients inthe context of self- and hetero-association schemes have beendeveloped (see [6], and references therein). However, the situationbecomes considerably simplified when solution columns are shortand when SE rotor speeds are sufficiently low to yield shallow gra-dients (such as the ratio of concentrations of all the solute compo-nents at the base and meniscus of the solution column do notexceed 5–6:1). This experimental strategy is the one used to studyFtsZ-related association reactions (see below). Under these condi-

tions the value of d ln SðrÞ=dr2 and hence M�i;app become indepen-

dent of the radius within experimental uncertainty and the latteris well described by the solution-average molar mass value, whichmay be expressed as a function of the loading composition of thesolution together with assumed equilibrium relationships betweenspecies, as described below (see also [35,36]).

The interpretation of M�S in more concentrated (non-ideal) solu-

tions requires consideration of repulsive interactions between pro-tein species and the background macromolecules, in addition toattractive interactions leading to the formation of equilibriumcomplexes. For a description of the special experimental ap-proaches and data analysis of non-ideal tracer sedimentation equi-librium (NITSE) the reader is referred to [37,38]. The application ofNITSE to study the effect of macromolecular crowders on FtsZ oli-gomer formation in the presence of GDP is described in [39].

2.2. Static light scattering

Static light (or Rayleigh) scattering is one of the most reliablethermodynamic methods for the assessment of the mass of thecomplexes providing a valuable tool to identify and quantify

B. Monterroso et al. / Methods 59 (2013) 349–362 353

biological complexes [40–43]. It measures the intensity of lightscattered by a particle (or particles) in solution, allowing the directdetermination of an average molecular weight and, in the case ofbig sized species with scattering angular dependence, also anestimation of the radius of gyration (Fig. 1).

In light scattering, reversible non-covalent macromolecularinteractions have been conventionally studied by means of batchmeasurements, in which multiple samples containing differentconcentrations of solute(s) are sequentially introduced into thelight-scattering measuring cell, and the signal-averaged molarmass of each sample measured. The composition dependence ofthis quantity is then modeled in the context of an associationscheme [41]. However, these batch measurements are time-con-suming and labor-intensive and hence rarely utilized. Recentinstrumental and methodological developments (compositiongradient SLS, described in section 3.4) have greatly facilitated therapid (order of minutes) acquisition of continuous light scatteringdata from a solution whose composition is being varied with timein a controlled and known fashion; the resulting time-dependentscattering and composition profiles are globally modeled in thecontext of molecular schemes for composition-dependent scatter-ing [40].

The scattering data are processed to yield the Rayleigh ratio Rscaled to an optical constant:

Kopt ¼4pn2ðdn=dwÞ2

k4NA

ð9Þ

where k, and n denote the wavelength of incident light (690 nm)and the refractive index of the solution, respectively. dn=dw denotesthe specific refractive increment of the scattering species.If solutespecies are small relative to the wavelength of incident light, thescaled Rayleigh ratio is independent of scattering angle, anddepends only upon the solute composition [44]:

RKopt¼X

i

Miwi ¼X

i

ciM2i ð10Þ

where Mi, wi, and ci respectively denote the molar mass, w/v con-centration, and molar concentration of the ith solute species. Thescattering relations for ideal multi-component mixtures (such asGDP-FtsZ oligomers and sZipA) are described in [36,40].

The fractional contribution of a given species to the total scat-tering intensity is then given by:

fj ¼cjM

2jP

iciM2i

ð11Þ

The composition dependence of R/Kopt is modeled in the contextof equilibrium schemes described below (see also [40]) that specifythe molar masses of all significant scattering species, and thedependence of all ci upon one or more postulated equilibrium asso-ciation constants and the total concentrations of the scatteringspecies.

The scattering analysis of large particles, such as FtsZ proteinfibers [45,46], requires taking into account the angular dependenceof scattering, as formulated in the Zimm-Debye generalizedrelation of static light scattering:

RKopt¼ M 1� R2

G16p2n20

3k2

!sin2ðh=2Þ þ . . .

" #ð12Þ

where M is the molar mass, RG is the radius of gyration, n0 is therefractive index of solvent, k the wavelength of incident light, andh the scattering angle [47].The analysis of scattering data in non-ideal solutions is described in [48].

2.3. Dynamic light scattering (DLS)

Dynamic light scattering measures the random diffusive(Brownian) motion of particles in solution, related with their massand shape. This motion yields a randomness to the phase of thelight scattered from the moving macromolecules, such that whenthe scattered light from two or more particles is added together,there will be a changing destructive or constructive interferenceleading to time-dependent fluctuations in the intensity of the scat-tered light. The correlation function describes the time-dependentfluctuations (on the microsecond timescale) in the scattered light,measured at a single angle (commonly 90�). The correlationfunction for a monodisperse spherical particle, expressed as thedependence of the second-order autocorrelation function on delaytime s (Fig. 1), can be analyzed by a single decaying exponentialexpression [49]:

ACFðsÞ ¼ ACF1 � ACF0 expð�2CsÞ½13� ð13Þ

where ACF0 and ACF1 respectively denote the values of the autocor-relation function (ACF) in the short and long time limits, C is thedecay rate and s is the delay time. The decay rate can be convertedto the diffusion constant D for the particle by:

D ¼ C=q2 ð14Þ

where q denotes the scattering vector which, at a scattering angle ofh, is given by:

q ¼ ð4pn0=k0Þ sinðh=2Þ ð15Þ

where n0 and k0 are the refractive index of solvent and the vacuumwavelength of incident light, respectively. The translational diffu-sion coefficient of the scattering species, D, may vary with total pro-tein concentration when the protein is undergoing equilibrium self-association [49]. For single species (or mixtures of species with adifference in mass smaller than or equal to four times, i.e. mono-mers and tetramers, as only bigger differences are traduced in accu-rately measurable changes in the diffusion time) a singleexponential model properly accounts for the ACF data.The diffusionconstant thus determined from the fluctuations in scattered lightcan be interpreted as the hydrodynamic radius, Rh, of a sphericalparticle of the same mass via the Stokes–Einstein equation:

Rh ¼ kT=6pgD ð16Þ

where k is Boltzmann’s constant, T is the temperature in K, and g isthe solvent viscosity.

For polydisperse particles, the autocorrelation function is a sumof contributions from the various particle sizes and diffusionalmodes, and the interpretation of D is less straightforward. Theautocorrelation functions can then be analyzed as particle size dis-tributions by the widely used cumulant expansion [50,51]:

ACFðsÞ ¼ ACF1 þ ACF0 exp½�ð2Dq2sþ as2Þ� ð17Þ

where the parameter a is a measure of the breadth of thedistribution.

2.4. Fluorescence spectroscopy methods

Fluorescence methodologies such as fluorescence correlationspectroscopy (FCS) and anisotropy are very sensitive methodsallowing relatively fast characterization of macromolecular assem-blies with very low sample consumption. This kind of methods hasbeen widely used for the quantitative investigation of the affinity,stoichiometry and cooperativity of the interactions involving bio-logical macromolecules [52]. They are particularly suitable forthe analysis of tracer fluorescently labeled biomolecules in the

354 B. Monterroso et al. / Methods 59 (2013) 349–362

presence of other unlabeled species and for the development ofsystematic screening assays [53,54].

2.4.1. Fluorescence correlation spectroscopyFCS is a technique that provides information about dynamic

events, such as the translational diffusion of macromolecules, lead-ing to changes in the fluorescence intensity emitted by the parti-cles within a small open volume element generated by a laserbeam focused into the sample [55–57]. Correlation of the fluores-cence intensity fluctuations detected gives rise to the autocorrela-tion function G(s):

GðsÞ ¼ 1þ hdFðtÞdFðt þ sÞi=hFðtÞi2½18� ð18Þ

where dF(t)=F(t)–hF(t)i denotes the spontaneous deviation of themeasured fluorescence intensity from the average fluorescenceintensity, hF(t)i and s is the lag time. Assuming that the sample isexcited by a three-dimensional Gaussian beam the autocorrelationfunction can be written as follows, allowing calculation of the trans-lational diffusion and concentration of the fluorescent species in thesample:

GðsÞ ¼ 1þ Gð0ÞX

i

fi 1þ s=sDið Þ�1 1þ s=S2sDi

� ��1=2� �

ð19Þ

where G(0) is the amplitude of the autocorrelation function that isinversely proportional to the average number of molecules withinthe effective detection volume. S is a structure parameter: S = z0/r0

where r0 and z0 are the lateral and axial dimensions of the effectivedetection volume. This parameter is obtained by calibration withdyes of known diffusion coefficient. sDi is the translational diffusiontime of the fluorescent particle from which its translational diffu-sion coefficient Di may be obtained (for two photon excitation,sDi = r0

2/8Di). fi is the fractional contribution of species i to the auto-correlation function. In the absence of changes in the brightness (i.e.the fluorescence intensity emitted per particle) fi is equal to the mo-lar fraction of species i in the solution. Macromolecular aggregation,polymerization as well as heterologous interactions giving rise tocomplexes displaying significantly different translational mobilitycompared with their free labeled elements can be detected andquantified by FCS with single molecule sensitivity. The restrictionsregarding the minimum change in mass upon interaction requiredto detect the complexes by FCS are comparable to those statedabove for DLS, since in both cases translational diffusion ismeasured.

2.4.2. Fluorescence anisotropyFluorescence anisotropy is a parameter extremely sensitive to

changes in the size, shape and flexibility of the macromolecules.The steady-state anisotropy r of a solution excited with linearlypolarized light can be obtained with the following expression [58]:

r ¼ ðIII � GI?Þ=ðIII þ 2GI?Þ ð20Þ

where III and I\ are the intensities emitted by the fluorophore in theparallel and perpendicular directions to the plane of polarization ofthe excitation beam, respectively. G is a scaling factor that accountsfor differences in the efficiency of the detector for the two polarizedintensities.

The steady-state anisotropy value measured for a fluorescentspecies depends on its rotational diffusion, and hence on its mass,and on its fluorescence lifetime. Local motions within the macro-molecule changing the orientation of the dye also contribute tothe resulting steady-state anisotropy value. Due to its additivecharacter, fluorescence anisotropy constitutes a valuable observa-ble to determine the affinity and cooperativity of biomolecularcomplexes [52]. Thus, when several fluorescent species are presentin the solution, for example a protein free in solution and in

complex with another biomolecule, the fluorescence anisotropyis given by [58]:

r ¼X

i

firi ð21Þ

where ri is the steady-state anisotropy of species i and fi its frac-tional contribution to the total intensity emitted, which in theabsence of spectral changes resulting from interaction is equal toits molar fraction. Although fluorescence anisotropy measurementsare, in principle, more sensitive to protein oligomerization than FCS,since they depend on the rotational diffusion rather than on thetranslational mobility, the presence of local motions of the dyesoften limits the sensitivity of the anisotropy based interactionassays [59].

3. Experimental methods and analysis

3.1. Proteins and solution conditions

For a detailed description of the production of the proteins usedin the studies summarized in this review (FtsZ and full-length andsoluble variant of ZipA), the procedures to assemble FtsZ polymersand to study them using biochemical and biophysical methods, andthe incorporation of ZipA into nanodiscs, the reader is referred tothe original works [14,21,35,36,45,60]. Briefly, FtsZ was purifiedby the calcium-induced precipitation method [35], while His6-ZipAwas obtained following the protocol described in [21]. Nanodiscscontaining a monomer of ZipA and formed with a bilayer ofE. coli lipid ternary mixture of around 10 nm diameter were assem-bled according to [21]. Most of the studies described here weredone under close to physiological conditions (neutral pH and0.5 M potassium) in the presence of a given concentration ofmagnesium and nucleotides, as detailed in the original papers.

3.2. Sedimentation velocity

SV assays done to detect the concentration-dependent state ofassociation and size-homogeneity of the individual protein compo-nents, FtsZ under non-assembly promoting conditions (in the pres-ence of GDP) and the soluble variant of ZipA, are describedelsewhere [14,35,36,45,60]. In brief, the experiments were carriedout at 42,000–60,000 rpm in an Optima XL-A (equipped with aUV–VIS scanner) or an Optima XL-I (equipped also with an inter-ference detection system). The SV profiles were registered at thegiven time intervals using the appropriated optical signal (eitherUV–VIS absorbance or interference).

The sedimentation coefficient distributions were calculated byleast-squares boundary modeling of sedimentation velocity datausing the c(s) method [61], as implemented in the SEDFIT program,and the s-values were corrected to standard conditions (water,20�C, and infinite dilution) to obtain the corresponding standards-values (s20,w).

3.2.1. SV analysis of FtsZ polymers in the presence of GTP or analogsThe particulars of the assays on the behavior of FtsZ polymers

formed in the presence of GTP or analogs are briefly described asfollows. GTP-FtsZ studies were carried out in the presence of aGTP regenerating system (RS), containing 1 u/mL acetate kinaseand 15 mM acetyl phosphate, to maintain a constant nucleotideconcentration (and hence the stable polymer) during the durationof the experiment [14]. The elapsed time between the addition ofGTP + RS (or GMPCPP) and the last scan used in the analysis ofthe data was less than 60 min, time enough to prevent thedepletion of GTP. These experiments were carried out at lowerrotor speeds (25,000–30,000 rpm) than the ones with GDP-FtsZ

B. Monterroso et al. / Methods 59 (2013) 349–362 355

oligomers to avoid any possible pressure-induced polymer dissoci-ation (no effects were observed at the conditions used). Thesedimentation coefficient distributions of the polymers were cal-culated using 30–60 scans with the SEDFIT c(s) method [61] thatuses finite element solutions of the Lamm equation [62] combinedwith size distribution analysis techniques by maximum entropyregularization [61,63]. The conventional c(s) distribution is con-fined to a single frictional ratio, which is typically determined asa weight-average frictional ratio fr,w of all sedimenting materialfrom nonlinear optimization of this parameter [30,61]. The unitsof c(s) are such that integration over a peak gives the total signalof material sedimenting within the peak and a well-defined andprecise weight-average s-value (or signal average s-value, respec-tively) [64]. These s values are corrected to standard s20,w values(water, 20 �C, and infinite dilution) [65] using SEDNTERP [66].Similarly, the size distribution can be calculated as a molar massdistribution c(M) [63] directly from c(s) since, for each s-value inthe c(s) distribution, a diffusion coefficient D(s) is estimated basedon the weight-average frictional ratio fr,w. In the case of the FtsZpolymers, we used the independently measured D from dynamiclight scattering and fluorescence correlation spectroscopy to calcu-late fr,w, afterwards fixed in the c(s) analysis, which in turn madec(s) and c(M) distributions equivalent.

3.2.2. SV analysis of Nd-ZipA binding to FtsZ polymersThe great difference between the s-values of the full-length

ZipA incorporated in nanodiscs (Nd-ZipA) (5 S) and FtsZ fibers(13–14 S in GTP and 18–19 S in GMPCPP) allowed the use of SVassays to detect and measure the binding of Nd-ZipA to FtsZ poly-mers [21]. In this case, nanodiscs were labeled with a traceramount of fluorescent lipids to selectively detect the Nd-ZipA con-taining species (free and complexed to FtsZ). This lipid labelingprocedure ensured minimum interference with the interactionbetween the C-terminus of ZipA (exposed to the solvent) and FtsZ.

3.3. Sedimentation equilibrium

Low-speed SE assays using short columns (70–80 ll) were doneto determine concentration dependent state of association of theindividual components (GDP-FtsZ, sZipA and Nd-ZipA) and to mea-sure the association properties of sZipA-FtsZ and NdZipA-FtsZcomplexes as detailed elsewhere [21,35,36]. The absorbance gradi-ents at equilibrium were obtained at the appropriate wavelengthby using the UV–VIS detection system. The measured equilibriumconcentration (signal) gradients were fit by the equation that char-acterizes the equilibrium gradient of an ideally sedimenting soluteeqs. (6), (7) to get the corresponding whole-cell signal averagebuoyant molar masses M�

S. It was found that an association modelin which FtsZ self-associates from monomer in a non-cooperativeisodesmic manner linked to magnesium was the one that bestdescribed the dependence of M�

S with FtsZ concentration. Neithers-ZipA nor Nd-ZipA self-associate under the protein concentrationrange studied [21,36].

3.3.1. SE analysis of sZipA�GDP-FtsZ complexesFor mixtures of two components, GDP-FtsZ (A) and sZipA (B),

the absorbance average molar mass is given by [67]:

Mabs;av ¼P

i;jðiMAaA þ jMBaBÞcijðiMA þ jMBÞPi;jðiMAaA þ jMBaBÞcij

ð22Þ

where MX is the molar mass of monomeric X, aX is the extinctioncoefficient of X at the measurement wavelength, and cij is the molarconcentration of AiBj. If the two components have the same densityincrement (dq/dwA) = (dq/dwB) = (dq/dw), then the experimentallymeasured buoyant signal average molar mass is just: M�

abs;av ¼

Mabs;avðdq=dwÞ. A model in which GDP-FtsZ (A) self-associatesisodesmically and one molecule of sZipA (B) can bind to a monomeror an oligomer of FtsZ of any size was written to calculate the buoy-ant absorbance average molecular weight as a function of the totalw/v concentrations of A and B. It was found that this associationmodel was the one that best described the SE data (and the lightscattering data as well – see below) [36].

3.3.2. SE analysis of Nd-ZipA�GDP-FtsZ complexesIn this case, the nanodiscs were fluorescently labeled as

described above and the gradients were monitored in the visibleregion, being Nd⁄-ZipA the only component that contributed tothe gradient signal. In these experiments, the average buoyantmolar mass ðM�

wÞ represents the average over the species contain-ing Nd-ZipA only. The average number of FtsZ molecules bound permolecule of Nd-ZipA was equal to ðM�

w �M�NdZipAÞ=M�

FtsZ ; whereM�

NdZipA and M�FtsZ denote the buoyant molar masses of Nd-ZipA

and of FtsZ monomer, respectively [21].

3.4. Composition gradient static light scattering

CG-SLS experiments were performed using the Calypso system(Wyatt Technology, Santa Barbara, CA) according to proceduresdeveloped by Minton and co-workers [40,43]. In brief, a program-mable three injector-syringe pump was used to generate stepgradients of concentration of a protein solution of defined compo-sition in 10% increments into parallel flow cells for concurrentmeasurement of Rayleigh light scattering at multiple angles(MALLS, using a DAWN-EOS multiangle laser light scattering detec-tor, Wyatt Technology, Santa Barbara, CA) and solute composition(using a Optilab rEX refractive index detector, Wyatt Technology,Santa Barbara, CA). A single composition gradient experimentyields several thousand values of scattering intensity as a functionof scattering angle and solution composition.

3.4.1. Scattering analysis of GDP-FtsZ, sZipA and mixturesExperiments with a single protein were performed by filling one

of the pump channels (syringe + reservoir) with a solution of eitherGDP-FtsZ or sZipA and the second channel with a buffer solution,as described in [36,40]. Stepwise gradients of protein concentra-tion were formed by increasing in incremental intervals the flowrate of one of the syringes and simultaneously decreasing by thesame amount the flow rate of the other syringe. Experiments withmixtures of the two proteins were performed by loading knownconcentrations of GDP-FtsZ (A) in one of the pump channels andof sZipA (B) in the second channel, as described in [36,40]. Initiallythe flow cells were filled with pure B, to allow determining thescattering intensity at multiple angles and absorbance of sZipA atthe loading concentration. Composition gradients were createdby simultaneously increasing the flow rate of pump channel Aand decreasing the flow rate of pump channel B, so that the frac-tion of B in the solution mixture gradually decreases from 1 to 0while that of A gradually increases from 0 to 1. Absorbance datawere processed to yield the concentration of either one protein(in a single protein experiment) or both proteins (in a two proteinexperiment), as described in [36].

Several equilibrium models were constructed to calculate themolar concentration of each macromolecular species present as afunction of the total concentration of each macromolecular compo-nent and one or more equilibrium association constants. Theresults of these models were then combined with eqn. [10] (orthe corresponding one for multi-component mixtures, see [36])to calculate the dependence of total scattering upon solutioncomposition.

356 B. Monterroso et al. / Methods 59 (2013) 349–362

3.4.2. Static scattering analysis of FtsZ polymersThe scattering behavior of FtsZ polymers formed either in the

presence of GTP + RS or the analog GMPCPP was studied usingtwo approaches:

3.4.2.1. Composition dependence 90� scattering. Concentrationdependence of scattering intensity at 90o of FtsZ was measuredin a modified mini-DAWN light scattering photometer (WyattTechnology Corp., Santa Barbara) using an automated dilution pro-tocol as described [48]. The composition of the sample and dilutionbuffers was the same so that the concentration of all the compo-nents of the GTP or GMPCPP solutions, except that of the protein,was constant during the entire duration of the experiment, hencemaintaining the stability of FtsZ polymers. Concentration of pro-tein at each dilution step was calculated from the initial concentra-tion and raw scattering intensity data was converted to the scaledRayleigh ratio R(w,90o)/Kopt as described in [45,48].

Although this method seems in principle more limited than themultiangle light scattering in terms of the amount of data collectedper experiment, it presents certain advantages, among others thesimplicity of the setup and collection of data and the lower samplevolume requirement. Given the size of FtsZ polymers, the charac-terization of the angular dependence of the scattering is criticalfor the determination of the molar mass. Once this information isavailable through MALLS measurements, a correction factor toscale the intensities of the different angles can be estimated for aspecific solution condition, allowing the analysis of the 90� scatter-ing data in terms of mass. The use of a modified static light scatter-ing device, where the measurement flow cell was substituted by astandard fluorometer cuvette, allowed discarding any artifact inCG-SLS measurements derived from heterogeneities in the samplesreaching the measuring cells due to a hindered flow of big poly-mers through HPLC lines and the measurement cells themselves.Noteworthy, the use of scattering at 90� was suitable for the esti-mation of the critical concentration of polymerization of FtsZ(Cc), too low as to be accurately determined with current experi-mental precision by MALLS.

The concentration dependence of 90� scattering was approxi-mately described by a two-state model, compatible with the con-centration dependence of sedimentation velocity of FtsZpolymers [45,60]:

Rðw;90oÞKopt

¼ wlowMw;low þwhighMapparentw;high ð23Þ

where the relative abundance of low (Mw,low) and high molecularweight scattering particles (Mapparent

w;high ), determined by the Cc, is calcu-lated assuming a pseudo-first order transition process compatiblewith the concerted formation of a narrow size distribution of poly-meric species experimentally observed [45]. Note that, as explainedabove, the mass of the polymeric species thus determined is anapparent mass, as the angle correction factor is needed.

3.4.2.2. Concentration and angular dependence of scattering of theFtsZ polymers. The angular dependence of scattering over a broadrange of FtsZ concentrations was measured using the CG-SLSprocedures previously described rendering constant concentra-tions of all the components of the GTP (or GMPCPP) solutions dur-ing the gradient steps, critical to maintain the stability of thepolymer species during the experiment. From these experimentsthe concentration and angular dependent scaled Rayleigh ratioR(w,h)/Kopt was obtained [45], allowing also the estimation of theradius of gyration as detailed in [46].

The concentration and angular dependence of scattering of FtsZpolymers was described by the following two-state (solubility)empirical model.

Rðwtot; hÞKopt

¼ wlowMw;low þwhighMw;highð1þ A1g þ A2g2Þ ð24Þ

where wlow, whigh, Mw,low and Mw,high are the concentrations andmolecular weights of low and high molecular weight scatterers,respectively, and g = sin2(h/2) [45].

3.5. Dynamic light scattering assays

Preparation of the samples for DLS experiments just beforemeasurements (filtered twice with 0.1 lm Anotop 10 Plus filters(Whatman) centrifuged at 4 �C for 30 min at 100,000�g, [45])was determinant to avoid deformations of the autocorrelationcurves due to air bubbles, dust particles or unwanted aggregates.

DLS autocorrelation functions of GTP- or GMPCPP-FtsZpolymers arise from an undefined mixture of scattering speciesand, therefore, analysis was conducted by fitting of an empiricalexponential function to the data from which an apparent averagediffusion coefficient, Dapp, was determined:

ACF ¼ ACF1 þ ðACF0 � ACF1Þ exp �ðDappq2sÞbh i2

ð25Þ

where b is a parameter that decreases from unity with the width ofthe distribution of diffusion coefficients. Autocorrelation functionsof FtsZ polymers were mostly contributed by the high molecularweight species (given the low concentration and substantially smal-ler size of unassembled species), hence providing accurate measure-ments of the diffusion of the polymer [45]. The best-fit value of theapparent diffusion coefficient was corrected to a standard tempera-ture and solvent viscosity (20 �C, water).

3.6. Fluorescence spectroscopy methods

FtsZ labeling with extrinsic dyes was usually a prerequisite toanalyze its interactions using FCS and fluorescence anisotropy. Thiswas done in its polymeric form to avoid any possible interferenceof the dye with FtsZ assembly [14,68]. Besides, the rather hydro-philic fluorophore Alexa 488 was selected to covalently label FtsZand the labeled protein was only used as a tracer (�0.005 g/L),keeping a very low ratio (typically well below 1:10) with respectto the total amount of FtsZ, achieved with the unlabeled protein[45,68].

For the analysis of the interaction of FtsZ polymers withNd-ZipA, the nanodiscs were labeled in the lipids (as explainedabove for the AUC experiments). Similar results were obtainedwith fluorescein labeled ZipA inserted in nanodiscs [21].

3.6.1. Fluorescence correlation spectroscopy assaysFCS measurements on FtsZ functional associations were carried

out under two-photon excitation on a MicroTime 200 system(PicoQuant, Berlin, Germany) as described in detail elsewhere[21,45,68]. Care was taken to avoid excitation saturation andphotobleaching effects [69] by selecting a suitable excitationpower (10–15 mW at the scope entrance). For each sample 5–10autocorrelation curves were acquired and globally analyzed withthe FFS Data processor software (Scientific Software TechnologiesCenter, Belarus) [70], which uses a Marquardt–Levenberg non-lin-ear method of least squares, employing models with the relevantdiffusion components (see below). Although FCS measurementsare quite fast (1 min/curve, 5–10 repetitions/sample), slight differ-ences were observed between autocorrelation curves sequentiallyacquired for FtsZ in the presence of GTP. For this reason and forthe sake of consistency with the other measurements, theenzymatic RS was always added. In all fluorescence fluctuationspectroscopy measurements the coverslips were treated byPEGylation following a procedure described elsewhere [71]. This

B. Monterroso et al. / Methods 59 (2013) 349–362 357

step was critical to avoid adsorption of the biomolecules to thesurface.

3.6.1.1. FCS analysis of FtsZ polymers in the presence of GTP oranalogs. For samples containing unpolymerized FtsZ (in the ab-sence of GTP or the GTP analog), a two species model was fit tothe autocorrelation curves, one assigned to the unassembled pro-tein and a faster one indicating the presence of minor fractions(<20%) of free dye in the samples [45]. The translational diffusioncoefficient corresponding to this fast component was fixed to thevalue independently measured for the free dye in solution. Forthe samples containing FtsZ polymers (i.e. when GTP or GMPCPPwere added to FtsZ at concentrations above the critical concentra-tion of polymerization), a three component model was used: twofast components assigned to the free dye and to unassembled FtsZand a slow component corresponding to the FtsZ polymers, as ex-plained in detail in [45]. The translational diffusion times of freedye and unassembled FtsZ were fixed in the analysis to those inde-pendently measured for the dye in solution and for the fully unas-sembled protein. Translational diffusion coefficients equivalentwithin the error were obtained for the polymer for samples con-taining different amounts of free dye. The contribution of the unas-sembled protein to the autocorrelation function was stronglydependent on the FtsZ concentration in the solution and on thebuffer conditions. The use of tracer amounts of the labeled proteinallowed detection of the unassembled protein in addition to theFtsZ polymers, which otherwise would have masked the unpoly-merized protein due to their higher brightness. While this strategyprovided additional characterization of the system, it increases thenumber of fitting parameters and hence the uncertainty of theanalysis. DLS autocorrelation functions obtained in parallel, onthe other hand, were rather insensitive to the presence of unas-sembled protein, hence providing accurate measurements of thediffusion of the polymer (see above). However, DLS measurementsare highly sensitive to dust and any kind of unwanted aggregatesthat might be present in the solution. The good agreement be-tween DLS and FCS data allowed discarding any artifacts in eachmeasurement [45], also validating the models used for analysisof the corresponding autocorrelation functions and discardingany influence of the dye on the FCS measurements.

3.6.1.2. FCS analysis of Nd-ZipA binding to FtsZ polymers. To measurethe interaction of Nd-ZipA with FtsZ polymers, FCS titrations ofunlabeled FtsZ polymers into solutions containing a fixed amountof lissamine rhodamine B labeled Nd-ZipA (45 nM) with or withoutadditional unlabeled Nd-ZipA (up to 1 lM) were performed [21].The autocorrelation functions recovered from these titrations wereanalyzed using a two-component model:

GðsÞ ¼ 1þ Gð0Þ ð1� fBÞ 1þ ssF

� ��1

1þ sS2sF

� ��1=2"

þfB 1þ ssB

� ��1

1þ sS2sB

� ��1=2#

ð26Þ

where sF and sB are the translational diffusion times of the free andbound labeled nanodisc, respectively, and fB represents the frac-tional abundance of bound nanodisc. The other symbols in theequation have been described above (see section 2.4). The transla-tional diffusion time of free Nd-ZipA was fixed to the value obtainedin the absence of FtsZ. Similar fB values were obtained when this dif-fusion time was floated. The concentration of labeled Nd-ZipA in thesamples was kept low enough to ensure that the complexes withFtsZ did not contain more than 1 molecule of the labeled speciesand hence their brightness was the same as that of the free Nd-ZipA.The lack of changes in the intensity and in the amplitude of the

autocorrelation curves upon hetero-association further ensuredthat the autocorrelation curves obtained could be directly inter-preted in terms of fractional amount of free species and complexes,with no need to correct for differences in brightness. Global analysisof all the curves in the titrations by linking the translational diffu-sion time of the complex or individual analysis of the curves at eachFtsZ concentration produced similar results in terms of fraction ofbound Nd-ZipA. The translational diffusion found for the complexeswas very close to that observed for FtsZ polymers under the samesolution conditions.

The thermodynamic association constant for Nd-ZipA bindingto FtsZ polymers was obtained by fitting the FCS data with a modelin which it was assumed that, for a given total FtsZ concentration,the protein may exist as a mixture of monomer and a single fibrilwith stoichiometry nolig [21]. The concentration of oligomeric FtsZas a function of the total FtsZ concentration in the solution hadbeen previously measured by hydrodynamic and scattering mea-surements [36,45]. The molar concentration of fibril is equal to:

colig ¼folig ½FtsZ�tot

noligð27Þ

The fraction of Nd-ZipA bound to FtsZ, assuming that a singleFtsZ fibril may bind to Nd-ZipA with a binding constant KAZ, willbe:

fB ¼KAZcolig

1þ KAZcoligð28Þ

In the limit that all the FtsZ exists as the oligomer eqn. [28]reduces to:

fB ¼K 0AZ ½FtsZ�tot

1þ K 0AZ ½FtsZ�tot

ð29Þ

where

K 0AZ ¼ KAZ=nolig ð30Þ

eqs. (29) and (30) were used to model the FCS data and obtain avalid equilibrium association constant.

3.6.2. Steady-state fluorescence anisotropy titrationsFluorescence anisotropy titrations of labeled FtsZ to monitor

GTP-triggered FtsZ assembly under different conditions, includingmacromolecular crowding, were carried out on a PC1 photoncounting steady-state ISS spectrofluorometer as described in [68].The anisotropy binding isotherms were analyzed using a simpletwo-state model compatible with the data, involving assembledand unassembled protein, to obtain the critical concentration ofassembly Cc (Fig. 1):

r ¼ ðCc=CÞðru � rpÞ þ rp ð31Þ

where rp and ru are the anisotropies of the polymerized and unpo-lymerized protein, respectively. r is the fluorescence anisotropymeasured at protein concentration C that is defined as r = fu ru + fp

rp, being fp and fu the molar fractions of assembled and unassembledprotein, respectively. The anisotropy isotherms were fitted usinguser-written scripts and functions in MATLAB (version 7.10, Math-Works, Natick, MA, USA) and in Origin 7.0 with the same result.Thecritical concentration of polymerization is characteristic of cooper-atively assembling systems such as FtsZ and it was routinely deter-mined for all the different batches of labeled protein we prepared toconfirm retention of the polymerization properties. Complementarytime-resolved measurements on assembled and unassembled FtsZindicated that the dye covalently attached to the protein was verymobile, partially explaining why the anisotropy change upon poly-merization remained certainly modest [68].

358 B. Monterroso et al. / Methods 59 (2013) 349–362

3.7. Molar mass estimations of FtsZ polymers from hydrodynamicmeasurements

The apparent molar mass of a single sedimenting solute species,M, may be calculated using independently measured values of thesedimentation coefficient s and the diffusion coefficient D accord-ing to the Svedberg eq. (5) [72]. Since the frictional coefficientsfor sedimentation and diffusion cancel in the derivation of thisexpression, the estimate of molar mass obtained via this relationis valid independently of the structure of the sedimenting/diffusingspecies, and therefore universally applicable to any species and anygeometry (Fig. 2A). At high magnesium concentration, both sedi-mentation and diffusion measurements of FtsZ in the presence ofnucleotide indicate the presence of a narrow size distribution ofoligomeric species [45,60]. We assumed that the Svedberg relationholds approximately for such a distribution [73], and utilize theaverage value of s obtained from analysis of sedimentation velocity

Fig. 3. Illustration of the different behavior of GDP-FtsZ (grey) and GTP-FtsZ oligomers (bsedimentation velocity. (B) Concentration dependence of GDP- and GTP-FtsZ static light(0.5 g/L). Solid lines correspond to the fits of eqn. (3) in [45] to the data and (D) normalizeSolid lines correspond to the fits of eqn. (4) in [45] to the data. Results correspond to me

and the average of the D values obtained from analysis of DLS andFCS for mass calculation [45].

4. FtsZ self-association and assembly

4.1. FtsZ oligomerization in the presence of GDP

Analysis of the dependence of the molar mass of FtsZ in GDP-containing buffers at neutral pH upon protein and Mg2+ concentra-tion measured by SE revealed that GDP-FtsZ self-associates frommonomer to form oligomers following a Mg2+ -linked non-cooper-ative (isodesmic-like) association mechanism in which each mono-mer binds to any oligomeric species with almost the same affinity.The oligomerization process is coupled to the binding of anadditional Mg2+ for each FtsZ monomer added to the growing oli-gomer. FtsZ self-association was also modulated by ionic strength,and the tendency of FtsZ to form oligomers decreases as the salt

lack) as determined by different biophysical methods. (A) GDP- and GTP-FtsZ (1 g/L)scattering at 90�. (C) Normalized DLS autocorrelation curves of GDP- and GTP-FtsZ

d FCS profiles of GDP- and GTP-FtsZ (0.5 g/L) with a tracer amount of FtsZ-Alexa 488.asurements in 5 mM MgCl2, 500 mM KCl and pH 7.5. Figures modified from [45,60].

B. Monterroso et al. / Methods 59 (2013) 349–362 359

concentration increases, with hexamers being the larger speciesdetectable in buffer containing 0.5 M K+. The SV analysis of FtsZin the presence of GDP was compatible with the proposed associ-ation behavior and with its modulation by Mg2+ and salt; the sed-imentation coefficient distribution of GDP-FtsZ at 500 mM KClshowed two main species, most probably monomers and dimers,and a certain amount of higher order oligomeric species (Fig. 3A)[35,60]. The mechanism of ligand-linked self-association of GDP-FtsZ was further confirmed by the analysis of the compositionand time-dependence of scattering of GDP-FtsZ as measured bythe CG-SLS method [43] (Fig. 3B). The quantitative agreement ofthe thermodynamic parameters describing the association processderived from SE and CG-SLS is quite remarkable [36]. These results,taking into account the concentration in the E. coli cytosol of thesmall ligands modulating FtsZ self-association (1–2 mM Mg2+ and0.1–1.0 M K+), suggest that FtsZ in its GDP-form has a relativelylow tendency to form high-order oligomers in vivo.

4.2. FtsZ assembly and size-distribution of protein polymers in thepresence of GTP or GMPCPP

The assembly of FtsZ in the presence of constantly replenishedGTP was studied, at neutral pH and 0.5 M potassium, under steady-state conditions [45] by SV, CG-SLS, FCS, and DLS (Fig. 3). This studyconfirmed previous results indicating cooperative appearance of anarrow size distribution of finite oligomers with increasing proteinconcentration [60] (Fig. 4). Parallel experiments on solutions con-

Fig. 4. FtsZ sedimentation velocity data and analysis. Dependence of the deriveddistribution of sedimentation coefficients upon total FtsZ concentration in thepresence of GTP. From top to bottom, 0.05, 0.1, 0.2, 0.4, 1 and 1.5 g/L FtsZ.Figure modified from [60].

taining GMPCPP, a slowly hydrolysable analogue of GTP, in placeof GTP, likewise indicated the concerted formation of a narrow sizedistribution of fibrillar oligomers. The mass of the two kinds ofpolymers was calculated via Svedberg equation [72] using theaverage of the normalized diffusion values obtained by FCS andDLS together with the s-values. This estimation rendered a lowernumber of FtsZ monomers for GTP- than for GMPCPP-FtsZ poly-mers (85 ± 5 vs. 150 ± 15). An independent estimation of the massof the polymers was obtained by MALLS that, in this particularcase, required taking into account the dependence of the intensityof the scattered light with the protein concentration and the detec-tion angle to analyze the experimental data. The obtained values,113 ± 8 and 160 ± 18 monomers for GTP-FtsZ and GMPCPP-FtsZpolymers, are in good agreement within error with the Svedbergvalues. c(M) analysis was also consistent with these results. Thecharacterization of the scattering angular dependence of FtsZ poly-mers also allowed getting an estimate of their dimensions by thecalculation of the radius of gyration [46]. The values obtained,around 1000 and 1100 Å for GTP- and GMPCPP-FtsZ polymers,respectively, are fairly close to the theoretical upper limits esti-mated assuming a planar cyclic geometry, around 900 and1300 Å [46], compatible with the cyclic structures proposed to de-scribe the concentration dependence and size-distribution of FtsZfibers under the same experimental conditions [60].

The behavior described here for FtsZ polymers induced by GTPor GMPCPP at 5 mM MgCl2 and 500 mM KCl was maintainedthrough the broad protein concentration interval studied [45,60].Within this range, the polymers displayed s- and D-values corre-sponding to almost the same mass for each specific nucleotide,suggesting a concerted formation of preferred FtsZ fibril sizesand highlighting the qualitatively similar self-association schemesfor GTP and GMPCPP polymers (under these conditions) despite ofthe different size of the final assembly product. The response ofGTP and GMPCPP-FtsZ polymers to changes in Mg2+ concentrationis remarkably different. Thus, when GMPCPP (allegedly equivalentto GTP) is the nucleotide ruling the assembly, the polymers formedexisted as a defined species whose size is not sensitive to Mg2+ con-centration, in contrast with the notable decrease in the size of theGTP-FtsZ polymers below 250 lM Mg2+ [45]. Besides, reduction ofMg2+ concentration enhances the critical concentration of assem-bly of both GTP-FtsZ and GMPCPP-FtsZ polymers, being the effectmore dramatic in the presence of GTP [45,68].

We do not think it is worthwhile, at present, to speculate on thepossible functional significance of the narrow size distribution ofGTP-FtsZ oligomeric species, obtained under this specific set ofin vitro conditions (neutral pH, 0.5 M potassium) since the systemstudied here is highly simplified and lacks the companion proteinsand surfaces required to assemble the division ring in vivo. More-over, the reactivity of the plastic GTP-FtsZ fibers is greatly affectedby solution conditions [10,11], thus affecting their size-distribu-tion. Interestingly salt concentration controls in opposite mannerthe tendency of the GTP- and GDP-bound FtsZ species to self-assemble forming polymers and oligomers, respectively (Rivasand coworkers, unpublished results and [10,11]). The establish-ment of possible relationships between this variability on FtsZbehavior and non-equilibrium processes, such as nucleotide hydro-lysis and subunit exchange, seems premature since the data onthese biochemical reactions is very limited and controversial atpresent [10,11]. However, it is worth to emphasize that the dataderived from these studies must be taken into account in any fu-ture attempt to formulate a mechanistic scheme for FtsZ self-assembly, which will ultimately be integrated into more complexschemes describing systems containing the additional division-specific elements referred to above.

Table 1 summarizes main properties of FtsZ species at high salt,with and without magnesium with different nucleotides.

Table 1Properties of GDP-FtsZ oligomers and GTP- or GMPCPP-FtsZ polymers at close to physiological buffer conditionsa.

Propertyb GDP-FtsZ GTP-FtsZ GMPCPP-FtsZ Reference

Maver/M1 1.9 ± 0.2c na na [35,36][1.2 ± 0.1]c,d

S20,w (S) 4.2 ± 0.1 �14–15 �19–20 [35,45,60][3.4 ± 0.1] [2.8 ± 0.1]d [2.8 ± 0.1]d

D (cm2/s) (48 ± 4) � 10�8 (4.2 ± 0.4) � 10�8 (3.2 ± 0.4) � 10�8 [45,68][(62 ± 2) � 10�8] d

MS,D/M1 2.1 ± 0.1 85 ± 7 150 ± 10 [45][1.4 ± 0.1]d

M/M1 �2.1 115 ± 8 160 ± 15 [36,45][�1.7] [�1.5] [�1.5]

RG (Å) — 1000 ± 100 1100 ± 110 [46]Size (n) na 103 ± 26 (AFM) 137 ± 32 (AFM) [76]

125–200 (EM) — [60]

na, not applicable.a 50 mM Tris–HCl, pH 7.4, 500 mM KCl, 5 mM magnesium; values in brackets correspond to the species in the presence of EDTA.b Species properties as determined by the techniques in parenthesis: Average number of monomers, Maver/M1 (SE); sedimentation coefficient, s (SV); diffusion coefficient, D

(DLS and FCS, average value), Svedberg Mass from s and D (MS,D/M1); number of monomers, M/M1 and radius of gyration, RG (MALLS); and size, in number of monomers n, asdetermined by electron microscopy (EM) or atomic force microscopy (AFM).

c Average value from data analysis with an isodesmic association model at 1 G/L FtsZ.d Rivas and coworkers, unpublished.

360 B. Monterroso et al. / Methods 59 (2013) 349–362

5. Hetero-association between ftsz and zipa proteins in solution

5.1. Interaction of soluble ZipA with GDP-FtsZ oligomers

The hetero-association of GDP-FtsZ with a soluble recombinantZipA mutant (sZipA) was studied by means of CG-SLS and SE [36].At physiological ionic strength and in the presence of 5 mM Mg2+,CG-SLS experiments show that the interaction between FtsZ (thatunder this experimental conditions is, as mentioned above, anensemble of monomer to hexamer species) and sZipA (a monomer)is quantitatively described by an equilibrium model that takes intoaccount significant scattering contributions from the isolated pro-teins (i.e. the species characterized in solutions containing one orthe other) plus complexes, formed by only one sZipA and FtsZ olig-omers with a length of six at most. The association model that bestdescribed the CG-SLS data was in good agreement with the sedi-mentation data, which allows concluding that the binding of sZipAto GDP-FtsZ is of moderate affinity and does not significantly affectthe interactions between FtsZ monomers.

5.2. Dynamic interaction of ZipA inserted in nanodiscs with FtsZoligomers and polymers

We have studied the interaction of Nd-ZipA with FtsZ both inGTP and GDP bound states at neutral pH [21]. The produced Nd-ZipA was found to be a homogeneous species containing a singleZipA molecule as determined by SE. This stoichiometry is indeedthe same observed for the soluble mutant, sZipA, which remainsmonomeric in solution (see above) [36]. SE was used to measurethe binding of GDP-FtsZ to ZipA inserted in nanodiscs (Fig. 5). Aspreviously observed for sZipA [36], Nd-ZipA also interacts withGDP-FtsZ oligomers with moderate affinity (micromolar range).This means that the presence of the N-terminal transmembranedomain and the fact that it is surrounded by lipids, like in the nat-ural membrane, do not have any influence on the complexes estab-lished with FtsZ through the C-terminal globular domain of ZipA.

To analyze the interaction of Nd-ZipA with the FtsZ polymers acombination of SV and FCS methods was used (Fig. 5). No influenceof the nucleotide eliciting FtsZ polymerization (GTP or GMPCPP)was observed on the binding to Nd-ZipA. As for GDP-FtsZ,the equivalence between the interaction of sZipA and Nd-ZipAwith polymeric FtsZ further confirms the lack of influence of the

transmembrane domain of ZipA on the interaction with FtsZ [21].The energetic analysis of the complexes showed that the thermo-dynamic equilibrium constant of Nd-ZipA binding was the samefor GDP-FtsZ oligomers and for GTP (or GMPCPP) induced poly-mers. Therefore, polymerization does not stabilize the FtsZ�ZipAcomplexes supporting that ZipA may act as a passive anchor forthe proto-ring without any major implication in its assembly reg-ulation. The moderate affinity of the interaction between ZipA andFtsZ may help in the modulation of complex formation during thedifferent stages of the cell cycle to favor the assembly at midcellduring septation.

6. Concluding remarks

In this review we have summarized the recent attempts to char-acterize functionally relevant self- and hetero-association reac-tions of the bacterial division protein FtsZ by means of thecombination of hydrodynamic and thermodynamic techniques, to-gether with complementary mechanistic biochemical approaches.This orthogonal strategy allowed overcoming the specific weak-nesses of each method and a better discrimination between alter-native interpretations of a particular experimental result. Besides,potentially misleading information related to experimental perfor-mance (for instance non ideality, as different criteria apply) ormethodological limitations (as individual contributions in non-fractionated polydisperse samples or influence of labeling) couldbe avoided. This quantitative characterization is essential to anunderstanding of the functional energetics of macromolecularcomplexes involving multiple modes of association, such as theassemblies of the bacterial division machinery.

The combined – and self-consistent – results described herehave allowed formulating a quantitative description of 1) theself-association of FtsZ in GDP-containing solutions to form a broadrange of oligomeric species (whose relative abundance decreasesas the ionic strength increases) in a Mg2+-linked non-cooperativeprocess, and 2) the self-assembly of FtsZ in the presence of GTPto form a narrow size distribution of high molecular weight spe-cies, by means of a concerted process resembling a second-orderphase transition reaction. In addition, a good estimate of the num-ber of FtsZ monomers that form part of these polymers have beenobtained. The results on FtsZ�ZipA complex formation, namely thatZipA in nanodiscs moderately binds FtsZ oligomers and polymers,

Fig. 5. Interaction of GTP- and GDP-FtsZ with Nd-ZipA as measured by AUC and FCS methods. (A) Binding of labeled Nd-ZipA to GTP-FtsZ polymers: SV of Nd-ZipA (5 lM) inthe absence (grey) and in the presence (black) of FtsZ (25 lM); normalized FCS autocorrelation profiles of Nd-ZipA (45 nM) in the absence (grey) and in the presence (black) ofincreasing concentration of FtsZ (up to 50 lM). For FCS curves, lines correspond to the best fit of eqn. (S2) and (S3) in [21] to the data. (B) SE gradients of labeled Nd-ZipA(10 lM) in the absence (grey) or presence (black) of GDP-FtsZ (50 lM). Solid lines indicate the best-fit gradients of a single species at equilibrium as described in [21]. (C)Molar fractions of bound Nd-ZipA (1 lM) as a function of the concentration of the average FtsZ oligomer for GDP (dashed line) and GTP (solid line), assuming 2 and 100 FtsZmolecules per GDP- or GTP- oligomer, respectively. The distributions were calculated using the best-fit parameters values given in figure legends 3B (GDP) and 5B (GTP) in[21]. To facilitate the comparative analysis, the fraction of bound Nd⁄-ZipA to FtsZ-GDP represents the sum of all the species of Nd-ZipA containing FtsZ with significantabundance. Results correspond to measurements in 5 mM MgCl2, 500 mM KCl and pH 7.5. Figures modified from [21].

B. Monterroso et al. / Methods 59 (2013) 349–362 361

provide some hints on the mechanism of structural remodeling ofthe division ring during septation: the binding of FtsZ to the mem-brane through ZipA is plastic enough to allow FtsZ relocation tomidcell when required for division. This minimal synthetic systempartially reproduced assembly reactions of the cell division ele-ments that will ultimately help to define their precise functionsin vivo. In addition, these reconstituted systems were used togenerate fluorescence-based assays that can be exploited forsystematic screening of inhibitors of essential division proteininteractions.

Given the current trends it is reasonable to imagine that, usingreconstituted systems of increasing complexity, the coordinatedreactions involved in a complex biological process, such as bacte-rial division, will be eventually reproduced in an artificial cell-likeenvironment. However, in many instances, the analysis of molecu-lar interaction events by, among other approaches, the combinedused of orthogonal quantitative techniques as the ones described

here, will remain one of the limiting factors decisive for future pro-gress [74,75].

Acknowledgements

We thank all the members of our laboratory contributing to theworks here reviewed. This work was supported by the Spanishgovernment through grants BIO2008-04478-C03 and BIO2011-28941-C03-03 to GR, BFU2010-14910 and BIO2011-28941-C03-02 to SZ; by the European Commission through contractHEALTH-F3-2009-223432, by Human Frontiers Science Programthrough grant RGP0050/2010-C102, and Comunidad de Madridthrough grant S-BIO-0260/2006 to GR; and by the CSIC throughgrants 200980I186 and 201020I001 to SZ and CA, respectively.BM is a JAE postdoctoral associate from the European Social Fundand the Spanish Consejo Superior de Investigaciones Científicas(CSIC).

362 B. Monterroso et al. / Methods 59 (2013) 349–362

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