Modified Random Sequential Adsorption Model for Understanding

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Modified Random Sequential Adsorption Model for Understanding Kinetics of Proteins Adsorption at a Liquid-Solid Interface Hwall Min, Eugene Freeman, Weiwei Zhang, Chowdhury Ashraf, David L. Allara, Adri C.T. van Duin, and Srinivas Tadigadapa Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.7b00523 • Publication Date (Web): 27 Jun 2017 Downloaded from http://pubs.acs.org on July 2, 2017

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Modified Random Sequential Adsorption Model for Understanding Kinetics of Proteins Adsorption at a Liquid-Solid Interface Hwall Min a, Eugene Freemana, Weiwei Zhang b, Chowdhury Ashraf b, David Allara d, Adri C T van Duin b,c, Srinivas Tadigadapa a,c,e* a

b

Department of Electrical Engineering, The Pennsylvania State University, University Park, USA

Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, USA c

Materials Research Institute, The Pennsylvania State University, University Park, USA d

e

Department of Chemistry, The Pennsylvania State University, University Park, USA

Department of Biomedical Engineering, The Pennsylvania State University, University Park, USA

Author e-mail address: [email protected] RECEIVED DATE (to be automatically inserted after your manuscript is accepted if required according to the journal that you are submitting your paper to) *

Corresponding

author.

Tel.:

814-865-2730;

fax:

814-865-7065;

E-mail

address:

[email protected]; Address: N-237 Millennium Science Complex, University Park, PA 16802 Keywords: Protein adsorption kinetics, Random Sequential Adsorption (RSA), surface depletion, micromachined quartz crystal resonator (µQCR), human serum albumin (HSA), hydrophobic surface.


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ABSTRACT In this paper we experimentally measure the adsorption kinetics of Human Serum Albumin (HSA) on a hydrophobic hexadecane thiolated gold surface. We use micromachined quartz crystal resonators with fundamental frequency of 83 MHz to accomplish these measurements in real time. In this work, we focus on two key results (i) asymptotic behavior of the sensor responses upon HSA adsorption and (ii) the jamming limit of adsorbed layer formed by both single-injection and multi-injection experiments with the same value of final concentration. We develop a new interface-depletion modified Random Sequential Adsorption (RSA) model to elucidate the adsorption kinetics and the transport properties of the protein molecules. Analysis of the experimentally measured data shows that the results can be explained based upon exponentially depleting interfacial layer RSA model. To better understand the origin of the formation of the interfacial depletion region where the supply of protein molecules is dramatically reduced, we performed a series of molecular dynamics (MD) simulations using the ReaxFF method. These simulations predicts that the resulting adsorption of the protein molecules on the thiolated surface results in a specific orientation at the interface and the diffusion constant of the protein molecules in this layer is significantly reduced. This interplay between the surface adsorption rate and the reduced diffusion coefficient leads to the depletion of the protein molecules in the interfacial layer where the concentration of the protein molecules is much less than the bulk concentration and explains the observed slowdown of the HSA adsorption characteristics on a hydrophobic surface.

INTRODUCTION Interaction between proteins and surfaces are ubiquitous in most biological process. The consequences of such adsorption processes are critical in the regulation of metabolism, and the etiology of several diseases such as dementia. In addition, adsorption of proteins on surfaces is critical for the development of biosensors, stationary phases in chromatographic separations, and design of biocompatible surfaces for implantable devices and structures. Despite the realization of the biological significance, knowledge of protein adsorption mechanisms and kinetics are still not fully understood and


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several important questions remain unanswered1,2. One of the main reasons for this is that most of the protein adsorption phenomenon occurs under non-equilibrium conditions where the protein molecules typically arrive at fast rates as compared to the slower surface bonding and reconformation processes. Typically two empirical observations have been associated with protein adsorption: (i) the adsorption process is not completely reversible especially if the desorption process is not attempted early on

3,4,5

.

On experimental time scales, only a very small amount of the adsorbed protein molecules are exchanged or desorbed from the surface, demonstrating that the adsorption is found to be predominantly irreversible6,,7,8,9, 10. This is explained by strong interactions between the adsorbate and the surface in terms of molecular denaturation. (ii) In spite of this fact, it is found that the maximum amount of adsorbed protein is dependent upon the bulk concentration of the protein in the liquid phase. Langmuir theory has typically provided the most general framework for discussing the adsorption kinetics through the introduction of interactions between surface active sites and adsorbed species. However, it has increasingly become evident that this model for protein adsorption may not be adequate11, 12. For example, the basic requirement of reversibility of adsorbed proteins upon dilution of the protein solutions is consistently found to be violated due to a large barrier to desorption of proteins – leading to the observed irreversibility of the macroscopic adsorption1,13,14,15,16,17, 18. Several extensions of the Langmuir model of protein adsorption have been introduced to explain such observed deviations19, 20, 21, 22, 23, 24

but none are able to fully explain the kinetics of protein adsorption processes. Furthermore,

the Langmuir model does not predict a power-law approach to the jamming limit which is a key feature in protein adsorption phenomena to explain asymptotic behavior. Thus, better models are needed to more precisely predict the kinetics of adsorption and the saturation coverage as a function of concentration. In this paper, we examine modified random sequential adsorption theory to explain the experimental observations relating to protein adsorption at the solid-liquid interface and address the two key features in the adsorption kinetics: (a) the lack of reversibility and (b) the deceleration of adsorption due to surface depletion.


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RANDOM SEQUENTIAL ADSORPTION Random sequential adsorption (RSA) has been extensively applied to the problem of protein adsorption at liquid-solid interfaces to provide insights into the physics of macromolecular adsorption and has gained increasing acceptance as a model of irreversible adsorption of proteins at interfaces25 23 27 28 29 30 31

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. The simplest RSA model related to globular proteins considers the process as irreversible

adsorption of spherical balls32 27 28 30. The model is based on a stochastic process of sequentially adding “hard” spherical ball like particles onto a surface at random locations with the constraint that no added particle is allowed to overlap a previously inserted particle on the surface. The model makes the following assumptions: (i) The molecules are considered as hard spheres and the binding sites are flat and uniform. (ii) The molecules are effectively well-diluted and uniformly distributed to assume that the variations of the concentration do not affect the properties of the fluid. (iii) Once a particle is placed on the surface, it sticks at the same spot, and cannot be removed, i.e., adsorption process is irreversible, (iv) The protein molecules are only adsorbed if they do not overlap a previously adsorbed molecules, and (v) The process continues until the surface reaches its jamming limit or saturation. In this model, the surface is initially filled rapidly, but the more it approaches saturation, the slower the surface is being filled. Based on the description and assumptions above, the number density of the adsorbed particles (), is given in the units of cm-2, as a function of time t can be written as ()

= c′Φ

(1)

where is the adsorption rate in the units of cm-s-1, c′ is the bulk protein number concentration in

#/cm3, and Φ denotes the available fraction of the surface for the insertion of a new particle. In two dimensions the geometrical aspects of the area not occupied by the particles can be quite complicated and does not lend to analytical solutions. Using computer simulations, Feder was able to show that a

jamming limit exists for disks of the same size adsorbing on a plane surface for ( = ∞) = 0.547, where σ is the area of each disk and A is the total area of the surface of adsorption32. Furthermore, the kinetics of the adsorption slows down near the jamming limit and follow (( = ∞)σ − ()σ)~1/√ ACS Paragon Plus Environment

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power law. Schaaf and Talbot23 proposed the kinetic theory specifically applicable to the RSA process on two dimensional surfaces. The adsorption probability, Φ (), for the RSA of circular hard disks onto the surface is given by23 Φ () = 1 − 4 +

!√" #

$ + %

&'√" "#

()!

− "#* + " + ⋯

(2)

$

where = - % + .//, a is the diameter of the disks, . is the adsorbed mass per unit area, and m is the $

mass (= 1.103 × 102(' 34) of a single HSA molecule. Noting that Γ = N(t)m; and substituting eq. (2) into eq. (1), we obtain 5()

$

= c′/ 61 − 4- % + .// + $

!√" #

$

$

7- % + .// 8 + % $

&'√" "#

−

()!

"#

$

"

* + 7- % + . //8 + ⋯ 9 (3)

$

which governs the adsorption process for proteins modeled as spherical disks on a two dimensional surface. RSA gives a more realistic explanation of the adsorption kinetics than Langmuir isotherm as it more accurately incorporates the exclusion effects and geometrical information. At this time, the basic RSA model is well established for the description of the irreversible protein adsorption modeled as hard disks or spheres on a continuum surface. While, the ideal RSA model adequately account for surface saturation, this model has not properly accounted for the transport process of the particles from the bulk to the interface region. Consequently, the current RSA model continue to show inconsistencies with observed experimental results. In this work we will examine the role of time-dependent supply function across the interface boundary layer within the RSA model to explain kinetics of protein adsorption at various protein concentrations.

EXPERIMENTAL SECTION We have chosen human serum albumin (HSA), an extensively investigated protein, to study the kinetics of protein adsorption. Among the common globular proteins, HSA is quite accurately represented as a spherical molecule, and therefore serves as an ideal molecule to investigate RSA model in two dimensions. Furthermore, we use custom designed and fabricated micromachined quartz crystal resonator (µQCR) array to study the adsorption of proteins at the liquid-solid interface. In our previous ACS Paragon Plus Environment

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work, we have already shown that µQCRs operate very stably under aqueous loading conditions and exhibit higher frequency shift (sensitivity) as a function of the adsorbed mass per unit area as compared to commercial 5 – 10 MHz quartz resonators 33. The gold electrode of the µQCR is first functionalized using hexadecane thiol to create a thiolated hydrophobic surface. Both the frequency shift and changes in the dissipation factor of µQCR are accurately measured as a function of adsorbing Human Serum Albumin (HSA) layer. A. Micromachined Quartz Crystal Resonator (µ µQCR) array Acoustic wave sensing techniques based on quartz crystal resonators have drawn considerable attention for biotechnology applications because of their high sensitivity to both mass loading and interfacial effects34. In liquid medium applications, the shear wave damps out as it travels through the thickness of the liquid as a consequence of which the quartz resonator typically samples a layer of thickness equivalent to the acoustic wave decay length. For a commercial 5 MHz resonator, this decay length in water is ~ 250 nm, which is large in comparison to the thickness of proteins films which are typically 10 – 50 nm thick. However, for a micromachined 20 µm thick (~83 MHz) resonator, the decay length in water is reduced to ~60 nm which leads to improved resolution of the adsorbed surface mass density. Figure 1(a) shows the optical photograph of the packaged µQCR array consisting of eight resonators placed on the Teflon liquid test cell. The details of the fabrication process can be found elsewhere35. Briefly, the resonators are patterned using photolithographic techniques, and are plasma etched to a thickness of 20 µm to create an inverted mesa resonator design. The creation of an abrupt step in the quartz substrate traps the energy in each pixel and acoustically and energetically isolates each of these for uncoupled, independent shear mode operation34. Each resonator is individually addressed through backside (etched-side) electrodes which are extended to the rim of the sensor array chip. The top electrode is common to all the pixels of the array. In order to effectively confine the acoustic energy in each pixel, the pixel thickness to diameter of the electrodes ratio has been carefully optimized14. For the fabricated 20 µm thick pixels, the fundamental resonance frequency is ~83 MHz. ACS Paragon Plus Environment

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Figure 1. (a) Optical photograph of the packaged quartz resonator array in a 24-pin modified dual-in-line ceramic package placed on the Teflon liquid testing cell. Inset shows the top electrodes of the eight micromachined resonators in close-up. (b) The packaged device is placed in the Teflon liquid-cell and compression fitted to create the reaction chamber for protein solution experiments. Rubber O-ring in the holder acts a seal and prevents leaking. The designed cell can hold up to 800 µl of analyte solution.

B. Measurement Setup The device was packaged in a modified 24 pin, dual-in-line ceramic package in which a 6 mm x 6 mm square hole was cut using water-jet machining, and the fabricated resonator array is attached using silicone adhesive and cured at room temperature for 24 hours to avoid build-up of thermally induced stresses in the quartz. The individual pads of each resonator are wire bonded. Packaged devices were mounted in a specially designed Teflon test cell capable of liquid testing experiments and is shown in Figure 1(b). All measurements were carried out using an Agilent 4395A impedance analyzer inside a special aluminum die-cast enclosure (4.7” x 4.7” x 3.54”) to prevent RF interference and to control the temperature during the experiments. The impedance analyzer was initially calibrated using standard fixtures to obtain accurate resonance parameters and was set to simultaneously measure the magnitude |Z| and phase ψ of impedance as a function of frequency at the first resonance mode. 801 data points were acquired in a specified frequency span around the first resonance frequency mode. Automated data acquisition was accomplished by using a specifically written Labview® program. All experiments were performed at 23 ± 0.1 °C, a pressure of 1 atm, and in a phosphate buffer solution (PBS) at 7.4 pH. ACS Paragon Plus Environment

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C. Materials Human serum albumin (HSA) received from Sigma Aldrich was used as is. Different concentrations of the protein solution ranging from 5 × 10-3 mg/ml to 8 mg/ml were prepared by diluting the 10 mg/ml stock solution into phosphate-buffered saline solution, pH of 7.4 (10 mM PO43−, 137 mM NaCl, and 2.7 mM KCl), Hexadecanethiol (HD) was purchased from Sigma Aldrich and diluted in ethanol to make 1 mM solution. D. Surface Functionalization The QCR surface for each experiment was cleaned thoroughly with UV-ozone treatment three times for 15 minutes each and then rinsed and immersed in ethanol for 1 hour. To form the hydrophobic high density, self-assembled monolayer (HD-SAM), the electrodes were exposed to 1 mM solutions of hexadecanethiol for 24 h. After the formation of SAM, the device was rinsed with ethanol and dried with nitrogen for protein adsorption experiments.

RESULTS The two key results we focus on here are (i) asymptotic behavior of the sensor responses upon HSA adsorption and (ii) the jamming limit of adsorbed layer formed by both single-injection and multiinjection experiments with the same value of final concentration. Initially, the µQCR array was stabilized in pure PBS buffer solution and the baseline frequency was obtained using the impedance analyzer. Thereafter, HSA solution was directly injected into the PBS solution to result in the desired target concentrations. Figure 2 shows a plot of the change in resonance frequency (∆f) upon adsorption of HSA at the fundamental mode as a function of time on the functionalized hydrophobic surface. This is a single injection experiment with bulk HSA concentration of 8 mg/ml. As adsorption proceeds, the resonance frequency decreases, while the dissipation factor increases. From the graph it can be seen that the frequency follows rapid power law decrease in the first 10 minutes followed by a monotonic extended exponential type decrease in frequency. The frequency shift then eventually begins to saturate around ~8660 Hz.


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0

Frequency Shift ∆f (kHz)

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-2

-4

-6

-8

-10 0

0.5

1

1.5

2

2.5

3

3.5

4

Time (h) Figure 2. Shift of µQCR resonance frequency from the adsorption of HSA on hydrophobic surface operated at fundamental mode during a single injection experiment with the concentration of 8 mg/ml. Dashed line follows power law and dotted line follows stretched exponential laws.

We also performed sequential adsorption experiments using solutions of 8 different concentrations of HSA from 0.005 mg/ml to 8 mg/ml and measured the frequency shift at each concentration. Figure 3(a) shows the decrease in frequency upon addition of solution of each higher concentration. In this experiment for the first two, 0.005 mg/ml and 0.05 mg/ml, concentrations we did not obtain any noticeable change in frequency. At low bulk solution concentrations, such as C3 = 0.1 mg/ml and C4 = 0.3 mg/ml, the adsorption process saturates within ~6 minutes of addition of the solution (see Fig. 3(b)). What is surprising is that addition of the next higher concentration solution, initiates another similar frequency shift clearly indicating that the surface of the resonator is not saturated. This observation is contradictory to the predictions of the RSA model where the adsorption process must proceed until the jamming limit. Furthermore, at intermediate concentrations such as C5 = 1 mg/ml and C6 = 3 mg/ml, instead of a saturation behavior, a slow exponential law type decrease in frequency is observed. This is


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eventually followed by very little change in frequency at higher concentrations of C7 = 5 mg/ml and C8

2

0


= 8 mg/ml, indicating that the surface of the resonator is jammed or is completely saturated.

a C2

C3

-2

C4

0.5

b

C3= 0.005 mg/ml

0.25 0 -0.25 -0.5 -0.75 -1 -1.25 -1.5 0

0.1

0.2

0.3

0.4

0.5

Time (h)

-4

C5



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-6 C6

-8

C7

C8

-10 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time (h)

2 Single Injection (8 mg/ml) Sequential Injections (up to 8 mg/ml)

0 -2 -4 -6 -8

c

-10 0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

Time (h)

Figure 3. Measured decrease in frequency, ∆f, upon addition of increasing concentrations of HSA solution. (a) All concentrations are listed in mg/ml and correspond to the following: C1=0.005, C2=0.05, C3=0.1, C4=0.3, C5=1, C6=3, C7=5, C8=8. (b) Shows zoomed-in frequency shift upon addition of solution of concentration C3. (c) Comparison of the results from two experiments: Single-shot experiment with highest concentration (8 mg/ml) in blue and multi-injection sequential experiments with various concentrations (from 0.005 mg/ml to 8 mg/ml) in red. The saturation points are very close in both cases.

In Fig. 3(c), we have plotted the single high concentration adsorption curve along with the curve obtained for sequential concentration adsorption curve for HSA on hydrophobic surface. Although the final frequency shifts, i.e., the adsorbed mass density, of HSA on CH3 surface both in single and sequential adsorption experiments have very similar values, the adsorption process shows distinct differences which will be discussed in greater detail next. What is evident through the following analysis of these experimental results is that at high enough concentrations, the adsorption process initially follows a power law type decay and is consistent with the conventional RSA model described earlier. However, as the process continues the adsorption rate slows down in comparison to the


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conventional RSA model which we believe is due to the formation of surface depletion layer resulting in a stretched exponential type asymptotic behavior to the jamming limit.

DISCUSSION A. Adsorption Kinetics of HSA The main features of the observed protein adsorption kinetics are an asymptotic approach toward saturation, the exponential decay of the rate of surface coverage, and adsorbed mass density. HSA adsorption kinetics on hydrophobic surface was quantitatively studied using µQCR measurements in liquid ambient. Table I summarizes the experimentally measured data analyzed using Sauerbrey mass loading equation for the surface density of adsorbed layer, and the theoretically calculated frequency change under the jamming limit for RSA model and the size and mass of HSA molecule for the same µQCR. The jamming limit for RSA model of 54.7% agrees very well with the measured data implying that HSA protein most likely forms a monolayer in the saturation regime. Table I. The comparison of the measured surface density and frequency shift to theoretical values predicted by the jamming limit of RSA model. Theoretical values are calculated by the Sauerbrey equation.

Parameters

Measured (µQCR)

Theoretical

∆f (Hz)

-8663

-8299

Γ (ng/cm2)

555

532

The surface mass density found in this study can be compared with adsorbed amounts found for HSA on hydrophobic surfaces in the literature. Malmsten studied HSA adsorption on n-butane plasma polymer and observed a surface mass density of 160 ng/cm2 36. Benesch found the adsorbed amount on hydrophobic silicon surface to be 200 – 300 ng/cm2, depending on pH 37. Both Blomberg and Karlsson demonstrated that the surface mass density at the highest initial concentration was 300 ng/cm2 38 39. The adsorbed amounts obtained in our present investigation are higher by about a factor 2 and consistent with our earlier studies on protein adsorption10. These differences can also be accounted for by the fact ACS Paragon Plus Environment

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that some of the reported investigations were made using optical techniques under dry air conditions which are quite different from our in-situ measurements made under a supernatant PBS solution. Furthermore, the highest bulk concentration of protein solutions used in many of the studies reported in literature use 1 mg/ml concentration which is lower than the concentration required to form a monolayer proven by our experiments which is 8 mg/ml. In our opinion, in several of the reported studies in literature, the observed asymptotic saturation observed using the lower concentration studies arises due to interfacial depletion slowdown which can be easily mistaken for saturation coverage. In fact, in our own studies, we also found the surface mass density saturates around ~350 ng/cm2 when the experiment is performed using a bulk protein solution concentration of 1 mg/ml, which is comparable with the observations in literature. This might also explains the lower surface mass densities in the literature in comparison to our data. To obtain more information on the adsorption process, it is useful to study the response of the sensor from sequential injection experiments in detail. For the experiments at low initial protein concentrations, 0.05, 0.1, and 0.3 mg/ml (c2 – c4), it can be seen that the adsorption process decelerates and saturates well before the expected RSA jamming limit. On the other hand, at higher initial protein concentrations, ≥ 1 mg/ml (c5 – c8), the amount of protein molecules is sufficiently large which leads to incomplete depletion of adsorbate molecules in the interfacial layer and in turn allows for the adsorption process to continue albeit at a slower exponential behavior rather than the expected power law. Furthermore, in the sequential injection experiments, adsorption rate at higher concentrations is also relatively slower than that at lower concentrations since the amount of adsorbing sites are reduced by the preadsorbed molecules from the preceding lower concentration adsorption. On the other hand, in the single injection experiments, shown in Fig. 2, the large amount of analyte in the solution phase initially begins a fast adsorption process following the RSA power law. However, the rapid removal of adsorbate molecules due to the fast initial adsorption rate leads to significant depletion in the interface layer immediately after the initial phase. Thereafter, the interface layer has a lower concentration of available adsorbates


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and along with a continuously decreasing availability of adsorption sites on the surface leads to slower asymptotic exponential accumulation of the molecules on the surface. B. ReaxFF Reactive Molecular Dynamics Simulation of Au-Hexadecane Thiol – Dipeptide in Solutions In order to better understand the origins of the depletion effect in the interfacial layer we set up a model system for ReaxFF simulations. ReaxFF is a bond order based force field for use in molecular dynamic simulations40 which allows for continuous bond formation/breaking. In order to explain the experimental trends and the surface depletion effects, we performed a series of simulations on a hexadecane thiolated Au-surface in contact with water/peptide solution. A merged ReaxFF force field was used with Au/S/O/C/H parameters obtained by combining the Au/S/H parameters from Jarvi et al.41 with the Au-metal and Au/O/H parameters from Keith et al.42 and Joshi et al.43 and were merged with the protein parameters from Monti et al.44. As shown in Figure 4, the model in our ReaxFF simulations contain three layers consisting, from bottom to top, of: (1) Four-layer Au(111) surface with hexadecane thiolate (C16H33S-) molecules placed perpendicular to its surface with one hexadecane thiolate molecule per four Au atoms. There are 576 Au and 36 hexadecane thiolate molecules in this layer. (2) 18 dipeptide molecules and 60 water molecules. We performed our simulation with dipeptide molecules instead of protein to mimic the protein environment and reduce the simulation cost. Here we used aspartame (C12H16N2O3) which has strong hydrophobic (L-phenylalanine) and strong hydrophilic (L-aspartic acid) amino acid residues. We placed them on top of the hexadecane thiolates in 1:2 ratio in such a way that the hydrophobic part of the aspartame molecules is partially inserted between the space of two hexadecane thiolate molecules. In addition, we placed water molecules around hydrophilic part of aspartame molecule to set up specific orientation condition. (3) The top layer is either pure water layer or dipeptide solution layer. We put 750 water molecules or 400 water molecules with 30 dipeptide molecules on the top of the Au-hexadecane thiolate-dipeptide surface for pure water and dipeptide solution cases, respectively. The size of our simulation box is 34.62 x 29.97 x 140.00 Å3. Two separate simulations were conducted before our ACS Paragon Plus Environment

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simulation of the entire system. One is simulation of the surface which contains first and second layers for 100 ps; the second is simulation of the water or dipeptide solution (third layer) for 100 ps. After that, we put them together to simulate entire systems for 400 ps and the last 200 ps results were used for our analyses. All the simulations were performed by ADF code 45, using NVT ensemble with a time step of 0.25 fs. The temperature was controlled to 298.15 K using Berendsen thermostat with a damping constant of 100 fs.

a

b Z

Layer 3

Layer 2

Layer 1

Figure 4. Snapshot of the equilibrated simulation box composed of three layers: Layer 1: Au(111)-C16H33S- ; Layer 2: dipeptide surface/water interface layer; and Layer 3: pure water (a) and dipeptide/water solution (b). Oxygen is shown in red, hydrogen in gray, nitrogen in blue, carbon in cyan, sulfur atoms are in yellow and gold atoms are in mauve.

Since the hexadecane thiolate molecule and one part of dipeptide are hydrophobic while water molecule and the other side of dipeptide are hydrophilic, we expect to observe specific orientation. Therefore, we calculated the atomic density profiles (ADP) of O(H2O) and N(dipeptide) along Zdirection and display them for the pure water case in Figure 5(a). For the pure water model, no peak is seen for ADP of water but two peaks are observed for the ADP of dipeptide around 88.0 Å and 91.0 Å along Z-direction, The bottom layer of Au atoms are located at about 60.0 Å, indicating that all the


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hydrophobic part of dipeptide molecules insert to the space of hexadecane thiolate molecules and the hydrophilic part insert to the bulk water. In order to understand this further, we calculated ADPs of C (carbon on para-position of benzene ring) and O (oxygen of carboxyl) along Z-direction. It is clear that the hydrophobic carbon is much closer to the surface than the hydrophilic oxygen. For the dipeptide solution model, Fig. 5(b), the first peaks of water and dipeptide are located at round 94.0 and 88.0 Å, respectively. This clearly demonstrates the specific orientation with the hydrophilic side farther away from the surface.

Figure 5. (a) The atomic density profile of water and dipeptide molecules along Z-direction for pure water model. In addition to the ADP of peptide N, ADP of hydrophobic C and hydrophilic O along Z-direction is also shown. (b) The atomic density profile of water and dipeptide molecules for the dipeptide solution model. In both (a) and (b), the water ADP values are scaled by 1/6. (c) MSD of water molecules in different layers for pure water and dipeptide solution models. (d) O(H2O)O(H2O) radial distribution functions (solid lines) and their coordination numbers (dash lines) in pure water and dipeptide solution models.


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To investigate the dynamical properties, we calculated the mean squared displacement (MSD) of water in different layers as shown in Figure 5(c). All the plots have near-linear characteristics and the slopes are related to the diffusion constants directly. It is obvious that the slopes of MSD in Layer 2 (80.0-95.0 Å) are much smaller than that in Layer 3 (95.0-105.0 Å) for both pure water and dipeptide solution models. This indicates that the diffusion of water in solution layer is much faster than that at interface. We also note the diffusion of water in pure water model is much faster than that in dipeptide solution model. Such difference comes from the different structure of water in the two models. As shown in Figure 5(d), the intensity of the first peak for O-O radial distribution function (RDF) in dipeptide solution model is much larger than that in pure water model, indicating the less developed hydrogen-bonding network and stronger correlation of water compared to that in the system of pure water model. As a result, the diffusion constant of water becomes smaller. Such findings are consistent with our previous studies for the anion exchange membrane46. For a more clear comparison, the diffusion constants were calculated and are listed in Table II. It is evident that the diffusion of water molecule in Layer 3 is about 2.5 times larger than in Layer 2 for the pure water model and is about 1.7 times larger for the dipeptide solution model. In addition, the diffusion constant of the dipeptide in Layer 3 is also larger than that in Layer 2. These results indicate that the diffusion of water and dipeptide molecules in the solution layer (Layer 3) are much faster than that in interface (Layer 2). This implies that initially, the dipeptide molecules can rapidly diffuse through the water layer to adsorb on to the thiolated surface. Once the specific orientation occurs at the interface, the slow moving water molecules at the interface create a barrier for the dipeptides in the solution to get absorbed on the surface. These predictions are consistent with the experimental findings discussed in Figure 3 and provide a fundamental insight into the formation of the depletion layer at the interface.

Table II. Diffusion constants (cm2/s) of dipeptide and H2O in different layers for pure water and dipeptide solution models at 298.15K.


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Model pure water

solution

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Dipeptide

Water

Layer 2

6.0 x 10-6

Layer 3

15.0 x 10-6

Layer 2

1.3 x 10-7

2.4 x 10-6

Layer 3

2.6 x 10-7

4.1 x 10-6

C. Analysis of the Asymptotic Behavior of Protein Adsorption: RSA + Surface Depletion Model We have already discussed the ideal random sequential adsorption. Clearly, no matter the concentration of the molecules in the supernatant liquid, according to RSA model, the adsorption process should saturate at an ideal surface coverage of 54.7%. Clearly this result is in stark contradiction to the adsorption characteristics obtained in the 0.1 mg/ml – 1 mg/ml concentration range. RSA adsorption assumes molecules striking the surface at a constant rate throughout the adsorption process. However, if the supply function is not a constant and was to decay as function of time, then the kinetics of the adsorption process will be affected. In fact if the supply of molecules, i.e. rate at which molecules strike the surface, was reduced to a negligible rate, then the RSA adsorption process effectively terminates even though the surface is not jammed. The results obtained in our experiments at low protein concentration can now be explained if we postulate the existence of an interfacial layer through which the diffusion of protein molecules is controlled not only by the diffusion constant but also by the molecular and steric interactions between the protein molecules in the adsorbed and solution phases. Equation (3), can be rewritten as dΓ 2  2 2   1 − 4π  a  Γ + 6 3  π  a  Γ  +  40 3 − 176  π   2  m   3π 3π 2 2 m 

3    a  2 Γ   + ⋅ ⋅ ⋅  π     2  m     

= k a cdt

(4)

where c = c'm is the concentration given in mg/ml or mg/cm3. Integrating both sides of eq. (4), assuming m = 1.103x10-10 ng, a = 3.37 nm, and the adsorption rate constant ka and the concentration c = c0 are constants, give a relationship between the mass per unit area or surface coverage Γ and time as


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4666.72 ln(607.17 − Γ ) − 4729.27 ln (545.44 − Γ ) + 62.54 ln(4060.75 − Γ ) = k a c0 t + Const

(5)

and corresponds to the ideal RSA based adsorption kinetics. However, if the concentration c is not considered to be a constant but an exponentially decaying function of time i.e., c = c0exp(-k't), then eq. (4) can be written as dΓ  2 2   1 − 4π  a  Γ + 6 3  π  a  Γ  +  40 3 − 176  π   2  m   3π 3π 2 2 m  2

3    a  2 Γ   + ⋅ ⋅ ⋅  π     2  m     

= k a c0 exp(− k ′t )dt

(6)

Once again integrating both sides gives the modified RSA model relationship between the surface coverage Γ and time t as 4666.72 ln (607.17 − Γ ) − 4729.27 ln (545.44 − Γ ) + 62.54 ln (4060.75 − Γ ) = −

ka c0 exp(− k ′t ) + Const k′

(7)

Figure (6) shows the experimental data for concentrations c3 of 0.1 mg/ml and c5 of 1 mg/ml fitted using eq. (7) with ka and k' as parameters and shows that a good fit with the experimental data can be obtained. Typical values of ka and k' from these fits were determined to be ~6 x 10-5 cm/s and 0.008 s-1 respectively. The value of ka agrees well with that reported in literature of 3.5 x 10-5 cm/s 47. For both concentrations, the adsorption process terminates earlier than the ideal RSA jamming limit since the supply function begins to exponentially approach to zero as a function of time. Figure 6 also shows the ideal RSA adsorption kinetics and the jamming limit as being much higher than that obtained at the lower concentrations. Inset in Fig. (6) shows the ideal RSA eq. (5) fitted to the experimental data for the concentration of c8 of 8 mg/ml and the cumulative all concentrations mass density adsorption data. This model is generic and does not specifically invoke detailed solution of the continuity equation for the interfacial layer but emphasizes that this interfacial layer is critical to the observations reported here.


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Figure 6. Shows the experimentally measured and modified RSA fit to the real-time adsorption of HSA on thiolated gold electrode for concentration of c3 = 0.1 mg/ml and c5 = 1 mg/ml. The ideal RSA adsorption, calculated using eq. (5), is also shown. Inset shows the ideal RSA overlaid with c8 = 8 mg/ml and all concentrations adsorbed mass data. Mass density data is obtained by multiplying the frequency shift data shown in Fig. (2) and (3) by the Sauerbrey constant of -0.0641 ng cm-2Hz1

for the 83 MHz resonator.

The model presented here can be broadly justified by postulating the existence of an interfacial layer immediately above the thiolated resonator surface at a different protein concentration than the bulk protein solution concentration c0. Addition of each successively increasing concentration of protein molecules results in an increased flux of the protein molecules into this interfacial layer and a subsequent increase in the adsorbed mass. In other words, the addition of each higher concentration protein solution initially sets-up a transient situation which suddenly provides copious amounts of protein molecules in the interface layer with a high diffusion coefficient and thereby fulfilling the supply function of the proteins required for the standard RSA model. This results in the fast power-law type initial adsorption behavior seen in both Fig. 2 and Fig. 3(a). After the initial transient, the resulting adsorption of the protein molecules on the thiolated surface results in a specific orientation at the ACS Paragon Plus Environment

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interface. The steady state diffusion time constant for the protein molecules into the interface layer now becomes lower due to the specific orientation and thereby sets-up a depletion zone in the layer immediately adjacent to the surface. This slowdown of the protein diffusion through the interfacial water layer dominates the supply function of the molecules especially at low concentrations. Thus, depending upon the coverage of the thiolated surface of the resonator, the concentration of the protein molecules in the interfacial depletion layer is either much lower than the concentration of the bulk protein solution (Layer 3) or can be fully depleted leading to a saturated behavior as seen in Fig. 3(b). Hence, in the sequential injection experiments, for the concentrations c3 – c4 (Fig. 3(a)), the rapidly decaying curves quickly turn into the saturation regime in spite of the fact that the surface is not jammed. Thus, for large t, in this case the right hand side of eq. (5) exponentially approaches zero and the adsorption process essentially ceases even prior to reaching the surface jamming limit. It is obvious that this saturation behavior does not indicate actual surface saturation (jamming) since the next injection of higher concentration adsorbate solution results in another frequency decrease. Figure 7 plots d./dt vs ., the concentration of c3, c5, and c8 for HSA on thiolated gold surface. From these, it can be readily seen that the value of dΓ/dt is smaller for c5 solution than for c3 solution. A smaller value of dΓ/dt in the initial adsorption region implies a lower value of ka i.e., lower probability that the protein would adsorb upon impact with the surface. This somewhat counter intuitive observation of a lower value of ka at a higher adsorbate solution concentration is a consequence of the sequential nature of the adsorption experiment. Since the c5 adsorption experiment follows the c3 adsorption experiment, the surface has already some adsorbed HSA molecules and the interaction of the oncoming protein molecules from the bulk results in specific orientation resulting and the apparent reduction in the ka value now reflects reduced availability of adsorption sites. In contrast, experiment performed on a clean surface at concentration c8 in the single-concentration experiment clearly shows that the obtained ka value is higher than that at c3 concentration.


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Figure 7: Adsorption kinetics for HSA adsorbing on hydrophobic surface measured by µQCM. (a) For concentration c3 of 0.1 mg/ml (b) For concentration c5 of 1 mg/ml in sequential injection experiments. (c) For concentration c8 of 8 mg/ml in single injection experiment.

In summary, the experimental results show that in the initial stages and at high enough concentrations, the adsorption process initially follows a power law type decay and is consistent with the standard RSA model. However, as the process continues the adsorption rate slows down in comparison to the predicted adsorption rate predicted by the standard RSA model due to the formation of the interfacial depletion layer resulting in a stretched exponential type asymptotic behavior to the jamming limit. We found similar behavior for two additional proteins, Immunoglobulin G (IgG) and Fibrinogen (Fib), adsorbed on a thiolated hydrophobic surface. It must be pointed out that IgG and Fibrinogen are not strictly globular in structure and must involve a much more complicated adsorption and specific orientation processes at the interface. IgG has Y-shaped arrangement of the peptide chains and Fibrinogen is an extremely elongated molecule. Using a modified probability function to include anisotropic protein adsorption mechanism, we might be able to more accurately investigate the kinetics of IgG and Fibrinogen.

CONCLUSIONS In-situ, real time monitoring of HSA adsorption using µQCR measurements have been used to analyze protein adsorption process and the protein-surface interaction kinetics on a hydrophobic surface. We have demonstrated that the obtained results can be interpreted by postulating an exponential decay in the supply function of the protein molecules with the RSA model and is able explain the observed adsorption features and kinetics in sequentially increasing concentration loading as well as a single high ACS Paragon Plus Environment

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concentration loading µQCR measurements. Using ReaxFF based molecular dynamics simulations of the gold/thiolate/peptide/water system we found that the interaction of the hydrophobic and hydrophilic ends of the peptide molecules with the thiolated surface on one side and water molecules on the other leads to a specific orientation and creates an interfacial layer with much reduced diffusion coefficients for the protein molecules. The interplay between the surface adsorption rate and the reduced diffusion coefficient leads to the depletion of the protein molecules in the interfacial layer where the concentration of the protein molecules is much less than the bulk concentration and explains the observed slowdown of the HSA adsorption characteristics on a hydrophobic surface.

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38. Blomberg, E.; Claesson, P. M.; Tilton, R. D. Short-Range Interaction between Adsorbed Layers of Human Serum-Albumin. J Colloid Interf Sci 1994, 166 (2), 427-436. 39. Karlsson, L. M.; Tengvall, R.; Lundstrom, I.; Arwin, H. Penetration and loading of human serum albumin in porous silicon layers with different pore sizes and thicknesses. J Colloid Interf Sci 2003, 266 (1), 40-47. 40. van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A. ReaxFF: A Reactive Force Field for Hydrocarbons. The Journal of Physical Chemistry A 2001, 105 (41), 9396-9409. 41. Järvi, T. T.; van Duin, A. C. T.; Nordlund, K.; Goddard, W. A. Development of Interatomic ReaxFF Potentials for Au–S–C–H Systems. The Journal of Physical Chemistry A 2011, 115 (37), 10315-10322. 42. Keith, J. A.; Fantauzzi, D.; Jacob, T.; van Duin, A. C. T. Reactive forcefield for simulating gold surfaces and nanoparticles. Physical Review B 2010, 81 (23), 235404. 43. Joshi, K.; van Duin, A. C. T.; Jacob, T. Development of a ReaxFF description of gold oxides and initial application to cold welding of partially oxidized gold surfaces. J Mater Chem 2010, 20 (46), 10431-10437. 44. Monti, S.; Corozzi, A.; Fristrup, P.; Joshi, K. L.; Shin, Y. K.; Oelschlaeger, P.; van Duin, A. C. T.; Barone, V. Exploring the conformational and reactive dynamics of biomolecules in solution using an extended version of the glycine reactive force field. Phys Chem Chem Phys 2013, 15 (36), 15062-15077. 45. te Velde, G.; Bickelhaupt, F. M.; Baerends, E. J.; Fonseca Guerra, C.; van Gisbergen, S. J. A.; Snijders, J. G.; Ziegler, T. Chemistry with ADF. Journal of Computational Chemistry 2001, 22 (9), 931967. 46. Zhang, W.; van Duin, A. C. T. ReaxFF Reactive Molecular Dynamics Simulation of Functionalized Poly(phenylene oxide) Anion Exchange Membrane. The Journal of Physical Chemistry C 2015, 119 (49), 27727-27736. 47. Kurrat, R.; Ramsden, J. J.; Prenosil, J. E. Kinetic-Model for Serum-Albumin Adsorption Experimental-Verification. J Chem Soc Faraday T 1994, 90 (4), 587-590.


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TABLE OF CONTENT GRAPHIC


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Modified Random Sequential Adsorption Model for Understanding

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