High density monolayers of plasmid protein on latex particles

J

ournal of Statistical Mechanics: Theory and Experiment

Marta Kujda1 , Zbigniew Adamczyk1 , Michal Cie´sla2 and Malgorzata Adamczyk3 1

J Haber Institute of Catalysis and Surface Chemistry Polish Academy of Sciences, Niezapominajek 8, 30-239 Krak´ ow, Poland 2 M Smoluchowski Institute of Physics, Jagiellonian University, L ojasiewicza 11, 30-348 Krak´ ow, Poland 3 Warsaw University of Technology, Faculty of Chemistry, Institute of Biotechnology, Nowakowskiego 3, 00-664, Warszawa, Poland E-mail: [email protected] Received 3 November 2014 Accepted for publication 20 February 2015 Published Online at stacks.iop.org/JSTAT/2015/000000 doi:10.1088/1742-5468/2015/00/000000

Abstract. Monolayers obtained by adsorption of the plasmid protein KfrA on negatively charged polystyrene latex particles under diffusion-controlled conditions at pH 3.5 were interpreted in terms of the random sequential adsorption (RSA) model. A quantitative agreement of the theoretical results derived from these calculations with experimental data was attained for the ionic strength from 0.15 up to 10−2 M. This confirmed the adsorption mechanism of KfrA molecules on latex in the form of tetramers up to 10−2 M. On the other hand, for the ionic strength of 10−3 M the experimental coverage agreed with theoretical predictions under the assumption that screening of electrostatic interaction is enhanced by the presence of counterions and negatively charged polymer chains stemming from latex particles.

J. Stat. Mech. (2015) 000000

High density monolayers of plasmid protein on latex particles: experiments and theoretical modeling

Keywords: thin film deposition (theory), thin film deposition (experiments), structures and conformations (theory), structures and conformations (experiments)

c 2015 IOP Publishing Ltd and SISSA Medialab srl

JNL: JSTAT

PIPS: 510341

TYPE: PAP

1742-5468/15/000000+11$33.00

TS: NEWGEN

DATE: 19/3/2015

EDITOR: AT

SPELLING: UK

High density monolayers of plasmid protein on latex particles

Contents 2

2. Experimental 2.1. Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2. Latex and KfrA characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3. KfrAR751 adsorption on latex particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 3 4 5

3. Theoretical modeling

6

4. Conclusions

10

Acknowledgments

10

References

10

1. Introduction Bacterial alpha-helical proteins play important roles in various cell processes: the organization of chromosome structure (condensation, cohesion), nucleoids and organelles segregation, cytokinesis, gene regulation and signal transduction in prokaryotic organisms [1–6]. KfrA from the broad-host range IncP-1b plasmid R751, the alphahelical protein studied in this work, is engaged in the plasmid inheritance process during cell division, but the molecular mechanism of KfrA action reminds unclear [7– 9]. Despite the major significance of this protein, few quantitative data concerning its physicochemical properties and its interactions with surfaces are available in the literature [10, 11]. The main obstacle in performing thorough experiments is a limited stability of the protein under in vitro conditions because of its aggregation tendency and minor available quantities, usually 100–500 µg. This prohibits the use of ordinary bulk methods, for example dynamic light scattering (DLS) or micro-electrophoretic measurements. In order to overcome these limitations, in previous works [10, 11] an indirect method was developed where KfrA monolayers were formed on colloid carrier particles (polystyrene latex microspheres). Afterwards, electrokinetic properties of such stable monolayers were studied by using the micro-electrophoretic method. However, a proper interpretation of the results obtained by this technique requires a thorough knowledge of protein coverage and molecule orientations in the monolayers for various ionic strengths. Therefore, the main goal of this work is to develop a robust bead model of the KfrA molecule aggregates that facilitates the precise determination of the maximum coverage for various ionic strengths and molecule orientation in the monolayers formed on latex particles. The efficient random sequential adsorption (RSA) modeling is applied in these calculations where, in contrast to previous studies [10, 11], protein interactions are considered via doi:10.1088/1742-5468/2015/00/000000

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1. Introduction


the screened Yukawa-type potential. The modeling is used for the interpretation of experimental data derived by the depletion method previously used for determining the adsorption isotherms of bovine serum albumin [12,13], human serum albumin [14–17] and immunoglobulins [18] on latex particles. However, in order to increase the precision of the method, the residual KfrA concentration in the suspension after the adsorption step is determined via AFM imaging of single molecules adsorbed on mica [19]. These results have significance for basic science, enabling one to determine the mechanisms of protein adsorption on polymeric particles, particularly the role of electrostatic interactions. Also, the range validity of the RSA model for predicting protein adsorption can be quantitatively evaluated.

2.1. Materials and methods

Recombinant KfrA protein from IncP-1β plasmid R751 was used in this work. The molar mass of the protein and its purity were checked by SDS-PAGE electrophoresis in the Laemmli system using reducing sample buffer and 12% polyacrylamide gel [20]. The bulk concentration of KfrA was determined using standard BCA (bicinchoninic acid) Protein Assays [21]. These concentrated stock solutions of KfrA were diluted to a desired bulk concentration prior to each experiment. The diffusion coefficient of KfrA molecules was determined by DLS, using the Zetasizer Nano ZS Malvern, instrument. The micro-cuvette having the volume of 12 microliters (ZEN2112) provided by Malvern was used in these measurements. Negatively charged polystyrene latex suspensions from Invitrogen were used for KfrA adsorption measurements. The stock suspension was diluted to 240 mg L−1 (0.024%) prior to the KfrA adsorption. The electrophoretic mobility of the bare and protein covered latex was measured with the Laser Doppler Velocimetry (LDV) technique using the Malvern device. The diffusion coefficient of latex was also determined by DLS. The experimental temperature was thermostated at 298 ± 0.1 K. After adsorption on latex, the residual concentration of the protein was determined by using the concentration depletion procedure, previously developed in order to study human serum albumin adsorption on latex particles [19]. Briefly, the latex particle suspensions, after the KfrA adsorption step, were transferred to the diffusion cell (see figure 1). Freshly cleaved mica sheets were immersed vertically in the suspension. KfrA was adsorbed under diffusion conditions over a fixed time period (typically 30 min). Afterwards, the mica sheets covered by KfrA monolayers were rinsed and imaged by AFM imaging under dry conditions, using the NT-MDT Solver device with the SMENA B scanning head. The measurements were performed in a semi-contact mode using a silicon probe (poly-silicon cantilevers NSG-03). The average number of protein molecules adsorbed over equal sized areas, randomly chosen over the mica sheets was determined. The relative precision of these measurements was ±3%. In this way, the dependence of the surface concentration of KfrA molecules adsorbed at the mica on the initial concentration of protein in the mixture was determined quantitatively. The lack of proteins on the mica suggests that all KfrA molecules adsorbed on the latex particles. The bulk concentration of protein, at which KfrA starts to appear on mica, corresponds to the maximum adsorbed doi:10.1088/1742-5468/2015/00/000000

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2. Experimental


Figure 1. The experimental procedure for producing KfrAR751 monolayers on latex particles and determining their maximum coverage.

amount of KfrA on the latex particles. Knowing this and the specific area of the latex one can calculate the coverage of irreversibly adsorbed protein. 2.2. Latex and KfrA characteristics

The size of the latex for various ionic strengths was determined via the DLS measurements of the diffusion coefficient. Given the diffusion coefficient, the hydrodynamic diameter of particles was calculated using the Stokes–Einstein dependence [22]. The hydrodynamic diameter of latex particles varied between 840 ± 15 nm, for ionic strength I = 10−3 M and 810 ± 10 nm for I = 0.15 M. A typical AFM micrograph of KfrA monolayer on mica (adsorption conditions: pH 3.5, I = 10−3 M NaCl, bulk concentration of the protein cb = 0.2 mg L−1 ) is shown in the inset of figure 2. As can be seen, KfrA aggregates appear as isolated entities, which facilitate a precise determination of their size by minimizing tip convolution artefacts. The histogram of aggregate sizes obtained from such measurements is shown in figure 2. The average value of the aggregate diameter determined from the histogram was 10.6 ± 1 nm. This exceeds the predicted dimensions of a tetramer in the regular configuration (see doi:10.1088/1742-5468/2015/00/000000

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Figure 2. The histogram of adsorbed protein aggregate sizes determined by AFM. The inset shows the 1 × 1 µm micrograph of the KfrAR751 monolayer at the mica surface. Adsorption conditions: pH 3.5, I = 10−3 M NaCl, cb = 0.2 mg L−1 .


figure 3(a)) equal to 9 × 9 nm and agrees with the predicted dimensions of a tetramer in the hexagonal configuration (see figure 3(b)) equal to 12.3 × 9 nm (average value 10.6 nm). Hence, these AFM results suggest that KfrA molecules at pH 3.5 appear as a tetramer in the hexagonal configuration. 2.3. KfrAR751 adsorption on latex particles

KfrA adsorption on latex particles was performed according to the procedure shown schematically in figure 1. First, equal volumes of the protein solutions of an appropriate concentration cb (0.25 mg L−1 ) were mixed with the latex suspension of the concentration cl (240 mg L−1 ). The adsorption time was 900 s. The electrophoretic mobility of KfrA covered latex particles was precisely measured using the micro-electrophoretic technique. Afterwards, the residual concentration of KfrA in the suspension after the adsorption step was determined by AFM imaging as described above. This procedure enabled a direct evaluation of the electrophoretic mobility variations as a function of the bulk concentration of protein added to the latex suspension. It should also be mentioned that the estimated relaxation time of KfrAR751 monolayer formation on latex particles, was ca. one second for the final latex concentration of 120 mg L−1 [11]. Therefore, the adsorption time of 900 s ensured that all protein molecules could adsorb on the latex particles. In a few series of experiments it was confirmed that KfrA adsorption on latex was irreversible for pH 3.5 and an NaCl concentration up to I = 0.15 M. The saturated coverage was evaluated using the AFM imaging procedure of residual KfrA adsorption on mica, described in detail in [19] and shown schematically in figure 1. By applying this method, the average number of KfrA molecules per unit area of mica, adsorbed after a fixed time, was determined. It should be mentioned that the deposition of latex particles on mica was negligible over the time of these experiments (30 min) because of their low bulk concentration and low diffusion coefficients compared to KfrA molecules. It was determined that the maximum coverages of KfrA on latex were 1.2, 1.5 and 2.0 mg m−2 for NaCl concentrations of 10−3 , 10−2 and 0.15 M, respectively. As can be deduced, the maximum coverage of KfrA on latex monotonically increases with the ionic strength due to the decreasing range of the lateral electrostatic interactions [11]. doi:10.1088/1742-5468/2015/00/000000

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Figure 3. A schematic representation of KfrA tetramers: (a) in the regular configuration and (b) in the hexagonal configuration. The tetramers are composed of identical spheres of diameter d = 4.5 nm.


Table 1. Experimental data for KfrAR751 adsorption on latex for various ionic strengths. Ionic strength [M NaCl]

Q [e]

Γ [mg m−2 ]

0.15 10−2 10−3

8 14 16

2.0 ± 0.1 1.5 ± 0.1 1.2 ± 0.1

3. Theoretical modeling The theoretical modeling of KfrAR751 monolayer formation on latex particles was performed in terms of the random sequential adsorption (RSA) approach developed in [23,24] for quantifying irreversible adsorption proteins (ferritin) on flat interfaces. It should be mentioned that in these calculations the specific interactions among protein molecules were neglected and their shape was approximated by a circular disk. Afterwards, the RSA model was used for calculating the kinetics, the saturated (jamming) coverage and the monolayer structure of non-spherical anisotropic particles [25–27]. In recent publications [28–31], RSA calculations were also applied for predicting the jamming coverage of protein molecules that were approximated by bead models. In particular, in the paper [31] a regular and hexagonal tetramer adsorption was studied. However, in these works the effect of the electrostatic interactions among adsorbed particles is neglected. This factor is considered quantitatively in the simulations performed in this work. The general rules of the Monte Carlo simulation scheme based on the RSA concept are as follows: (i) a virtual particle (molecule) is created, the position of which within the simulation domain and its orientation are selected randomly with a probability depending on the interaction energy, (ii) if the particle fulfills the predefined adsorption criteria it becomes irreversibly deposited and its position remains unchanged during the entire simulation process, (iii) if the deposition criteria are violated, a new attempt, uncorrelated with previous attempts, is made. doi:10.1088/1742-5468/2015/00/000000

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In order to obtain the total uncompensated (electrokinetic) charge (expressed in number of elementary charges) on the KfrAR751 aggregate the following relationship was used [11]: (1) Q = 18.7πηda µ where the tetramer hydrodynamic radius da is expressed in nm, the dynamic viscosity of the medium η is expressed in g (cm s)−1 and electrophoretic mobility µ in µm cm s−1 V−1 . Methods used for the measurement of these parameters have been described in detail in [10]. Here, the uncompensated charges varied from 8e for I = 0.15 M to 16e for I = 10−3 M. The elektrokinetic charge Q and maximum coverage of KfrA on latex particles Γ are summarized in table 1.


Figure 4. Various models of KfrA aggregates: dimer, tetramer (hexagonal, regular, tetrahedron) and hexamer (regular), studied in RSA simulations. All of them are composed of identical spheres of the diameter of d = 4.5 nm.

φ=

Nag Nag N

φ11 (|ri − rj |) ,

(4)

i=1 j=1

where Nag is the number of beads in the aggregate and N is the number of aggregates adsorbed on the latex surface. Knowing the net interaction energy, the probability of the model molecule adsorption was calculated from the Boltzmann distribution p(φ) = exp(−φ/kB T ) [32]. Here, T = 298 K and 1/(4π) ≈ 0.714 kB T nm/e2 . doi:10.1088/1742-5468/2015/00/000000

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Usually, two major deposition criteria are defined: (i) there should be no overlapping of the virtual particle with any previously adsorbed particles and (ii) there should be a physical contact of the particle with the interface. Despite the simplicity of the governing rules, the RSA method is a powerful tool for producing efficient populations of a high number of molecules (often exceeding 106 ). In addition, this method is flexible since interacting molecules of anisotropic shapes, adsorbing at the interface of finite geometries (for example spheres), can be efficiently considered. Specifically, in the present case, the true shape of the KfrAR751 molecule was approximated in terms of equal sized beads having the diameter d and forming various configurations (see figures 3 and 4). These model molecules were adsorbed, according to the above RSA scheme, on a homogeneous sphere whose diameter dl was equal to 820 nm, which exactly matches the average dimension of the latex particles used in experiments. The lateral interactions among two beads (belonging to different molecules) were accounted for by using the Yukawa pair potential φ11 physically derived from the screened Coulomb interactions q 2 − r−d (2) e Le , φ11 = 4πr where q is the electric charge per bead, is the electric permittivity of the medium, r is the distance between two bead centres and Le is the electrical double-layer thickness given by kB T , (3) Le = 2e2 I where kB is the Boltzmann constant, e is the elementary charge and I is the ionic strength of the electrolyte solution. It should be mentioned that by formulating equation (2) it is assumed that the electric charge is equal for all beads. By considering equation (2) one can express the net interaction potential φ of a model molecule approaching the latex surface covered by other molecules using the formula


A single RSA simulation run was stopped after the number of random addition steps n exceeded 104 t0 where t0 = nSp /S is a dimensionless time unit, Sp = (Nag /4)πd2 and S = πd2l is the surface area of a latex particle. Typically, in one simulation run, the adsorption layers consisting of 4000 to 16 000 molecules was generated, depending on the ionic strength. Therefore, in order to improve the statistics, averages from ca. 50 independent runs were taken. This ensures the relative statistical precision of the simulation better than 0.1%. However, it should be mentioned that the largest contribution to the total error stems from finite simulation time. Based on a few longer simulations (up to 106 t0 ) we estimated that the relative error amount to 3%. The surface concentration of the protein is Np /S and the KfrA mass coverage is calculated from the formula Nag Np mKfrA , (5) Γ= S where mKfrA = 6.51 · 10−17 mg is the mass of a single KfrA bead. Snapshots of saturated KfrA monolayers on latex particles derived from these simulations are shown in figure 5 for NaCl concentrations of 10−3 , 10−2 and 0.15 M. These and other theoretical data derived from RSA simulations for various aggregates shown in figure 4 are collected in table 2. As can be seen, the best agreement with experimental results (table 1) is observed for the aggregate composed of four beads forming a tetrahedron where the predicted coverage equals 2.00 mg m−2 and 1.57 mg m−2 doi:10.1088/1742-5468/2015/00/000000

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Figure 5. Jamming (saturated) KfrA tetramer monolayers on latex particles derived from the RSA simulations for various electrolyte concentrations: (a) 10−3 , (b) 10−2 and (c) 0.15 M.


Table 2. The mass coverage of KfrAR751 monolayers on latex for various ionic strengths and aggregate models derived from the RSA modeling T = 298 K. Model

Dimer

Tetramer (hexagonal)

Tetramer (tetrahedron)

Hexamer (regular)

Γ [mg m−2 ]

∞ 0.15 10−2 10−3

2.24∗ ± 0.01 1.95 ± 0.06 0.86 ± 0.03 0.27 ± 0.01

∞ 0.15 10−2 3 · 10−3 10−3

2.01∗ ± 0.01 1.91 ± 0.06 1.30 ± 0.04 1.07 ± 0.1 0.50 ± 0.02

∞ 0.15 10−2 3 · 10−3 10−3

2.14∗ ± 0.01 2.00 ± 0.06 1.32 ± 0.04 1.08 ± 0.1 0.50 ± 0.02

∞ 0.15 10−2 3 · 10−3 10−3

2.14∗ ± 0.01 2.00 ± 0.06 1.57 ± 0.05 1.23 ± 0.1 0.52 ± 0.02

0.15 10−2 3 · 10−3 10−3

1.95 ± 0.06 1.56 ± 0.04 1.35 ± 0.1 0.70 ± 0.02

Note: The relative error of the above values is approximately 3%. Results with asterisks (∗ ) were calculated using the maximum coverage previously calculated in the [30, 31].

for an NaCl concentration of 0.15 and 10−2 M, respectively. A significantly larger deviation is observed for the lowest NaCl concentration of 10−3 M where the predicted coverage for the tetrahedron equals 0.52 mg m−2 and 0.70 mg m−2 for the hexamer compared to the experimental value of 1.2 mg m−2 . It is interesting to mention that a similar effect was previously reported for the recombinant human serum albumin adsorption on latex particles [19] where the maximum coverage at 10−3 M NaCl exceeded almost twice the theoretically predicted value. Analogously, as in the above-cited work, we assume that a plausible explanation of this deviation should be sought in an increased screening of the lateral electrostatic interactions among adsorbed KfrA aggregates. This hypothesis is justified by the fact that the anion concentration in the vicinity of the latex surface can be increased because of the appearance of polymeric chains protruding from the core. In order to verify this prediction, additional modeling was performed for various ionic strengths. It was found that by assuming an effective ionic strength of 3 · 10−3 , one obtains in the case of the tetrahedron 1.23 mg m−2 , which agrees with the experimental value of 1.2 mg m−2 . doi:10.1088/1742-5468/2015/00/000000

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Tetramer (regular)

I [M]


4. Conclusions Electrokinetic measurements supplemented by AFM determination of residual protein concentration enabled a quantitative analysis of the adsorption mechanism of KfrA on latex particles. It was confirmed that the maximum coverage of the protein increases systematically with the ionic strength up to 2.0 mg m−2 for 0.15 M of NaCl. These results were interpreted in terms of the random sequential adsorption (RSA) model of soft particles interacting via the screened Yukawa potential. A quantitative agreement of the theoretical results derived from these calculations with experimental data was attained for the ionic strength above 10−3 M. The deviation occurring for ionic strength of 10−3 M was explained in terms of an increased screening of electrostatic interaction among adsorbed molecules due to the presence of polymeric chains stemming from the latex. Besides the significance for basic science, the results obtained in this work can be exploited for developing a robust procedure of preparing KfrA monolayers on latex particles having well-defined coverage and structure. Such immobilised protein monolayers exhibit considerably higher stability compared to native bulk solutions. In this way, interactions of KfrA with various ligands can be studied over a long period of time.

Acknowledgments This work was financially supported by the Ministry of Science and Higher Education grants: UMO-2012/07/B/ST4/00559 and by The Warsaw University of Technology, Faculty of Chemistry.

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Analogously, in the case of the hexamer one obtains 1.35 mg m−2 that deviates more from the experimental value. Although these results support the hypothesis that KfrA adsorbs on latex in the form of tetramers (most likely tetrahedron), this is not completely unequivocal because other aggregates can give similar results. However, the prevailing tetramer configuration of KfrA molecules was previously confirmed in [10] via the precise adsorption kinetic measurements. Apart from the aggregation issue, our results proved that for higher electrolyte concentrations one can adsorb uniform KfrA monolayers on latex particles characterized by high density. Such monolayers can be used for thorough electrokinetic characteristics of the protein and for studying their interactions with various ligands, such as other proteins and DNA.

High density monolayers of plasmid protein on latex particles [5] [6] [7] [8] [9] [10]

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