Protein Adsorption: Kinetic and Thermodynamic view
Introduction
The mechanism of protein adsorption and resistance can be explained by several factors such as adsorption isotherms, thermodynamic equilibrium and adsorption kinetics. Thermodynamic isotherms can be different from the experimental adsorption isotherms because the adsorbing surface is rapidly saturated and shows the limitation before reaching the true thermodynaimic isotherm.[1] For example, the non spherical protein can show the jump of adsorption isotherms.
Protein adsorption kinetics
(1) approach to interface
(2) attachment to interface
(3) structural rearrangement on the interface
(4) detachment from the interface
(5) transport from the interface
Protein surface interaction
Protein is normally hydrophobic and it is unfavorable in the water. And the polymer surfaces are normally hydrophobic. Hydrophobic interaction between surface and polymer reduces the free energy and dehydration during this hydrophobic interaction increase the entropy. If the protein is in the different ionic strength, electrostatic double layer will be related to the long range interaction however only this ionic charged surface can not explain whole forces. This electrostatic charge can be blocked or reduced by any interference between surface and protein.
Quantification Technique
1. Optical
ellipsometry
variable angle reflectometry,
surface plasmon resonance (most commonly used).
2. spectroscopic techniques:
Infrared absorption
Raman scattering
Fluorescence emission.
3. Other methods
Radioactive isotopes
Solute depletion techniques
Atomic force microscopy: Quantification of the kinetics and thermodynamics of protein adsorption using[2], Isotherm analysis was performed under the basis of AFM image.
Kinetic and thermodynamic control of protein adsorption on the grafted polymer layer on the hydrophobic surface[3]
According to the thermodynamic modeling and comparison with the experimental results by Satulysky et al., the prevention of the protein adsorption is quite more related to the equilibrium (thermodynamic control) than kinetic control. The thermodynamic theoretical model and comparison with experimental result shows the best polymer grafting on the surface, for the kinetic control, is to use non-attractive polymer on surface but for the thermodynamic control, it is better to use the attractive polymer on the surface as shown in figure. This is more realistic for the longer chain.
There are several importance comments on this paper.
(1) “The time scale for adsorption both for the initial adsorption and to reach equilibrium are orders of magnitude faster for surfaces with attractive interactions with polymers”
(2) “The kinetics of protein adsorption on surfaces with grafted polymers involves the competition between the strong bare attractive interactions between the surface and the proteins and the conformational entropy loss that the grafted polymers have to pay to accommodate the proteins.”
(3) In conclusion, on the protein control over finite time scales like drug delivery, kinetic control is more important so it needs relative higher density and long chain of grafting polymer. However for the long term use such as artificial heart or artery, thermo dynamic control would be more important so it needs the attractive polymer on the surface.
Figure (Left) Schematic representation of the ability of grafted polymers to prevent protein adsorption. For polymers attracted to the surface, there is no kinetic barrier but the protein competes with the polymer for adsorption sites. Polymers that are not attracted to the surface present a large steric barrier but not very good thermodynamic prevention because of the ability of the protein to deform the polymer layer. (Right) The curves on the right show the calculated average shapes of two neighboring polymers as a function of time. The shape is defined here (20) by the lateral average radius of gyration of the chains as a function of the distance from the surface. Also, a protein is shown to scale, demonstrating that the deformation of the polymer layer is exactly what is needed for the protein to reach the surface. The black curves correspond to t=0,the green and blue curves are for the times marked by the same color arrows in Fig. 2A, and the red curve is the final equilibrium state.
Here are copied part to thermodynamic modeling in this paper. I need more understanding for this part.
Consider a protein solution of density b that is put into contact with a surface. The surface has polymers that are chemicallyattached to it at one of their ends. The presence of the surfaceinduces a gradient in the chemical potential of the protein. Thisgradient arises from the sudden inhomogeneous environment thatappears in the direction perpendicular to the surface. The proteinsin the close vicinity of the surface feel the bare attractiveinteraction of the surface as well as the repulsions induced bythe polymer molecules. The balance between these interactionswill result in a final equilibrium density profile and amountof proteinadsorbed.
The time evolution from the homogeneous system to the new equilibrium induced by the presence of the modified surface canbe described (in the free-draining limit) with the help of a diffusionequation (15-18) of the form
where we have assumed that the diffusion in the xy plane is faster than the adsorption. This assumption is justified forthe relatively low surface densities that we treat here (19).The time-dependent local chemical potential is defined by µpro(z;t)=,where W is the free-energy density of the system. This free energyincludes the contribution of the grafted polymer molecules, thesolvent, and the surface, under the condition of the fixed proteinconcentration profile given by pro(z;t) at each time t.
The adsorption kinetics can be described with the help of Eq.1, assuming that the time scale of the diffusion of the proteinsis much slower than that of the polymer and solvent rearrangement.This is a physically motivated approximation, because the solventmolecules (water) are much faster than the protein motion, andthe rearrangements of the polymer molecules involve only localmoves, which, for the flexible chains of interest here, are muchfaster than the typical motion of the larger proteinmolecules.
The free energy of the system is determined by using a molecular mean-field theory. The predictions of the theory for equilibriumsystems have been shown to be in excellent agreement with experimentalobservations for conformational and thermodynamic properties oftethered polymer layers (20, 21) as well as for the adsorptionof proteins on hydrophobic surfaces (11, 14). The basic ideaof the theory is to treat each molecule with all of its intramolecularand surface interactions exactly taken into account (within thechosen model system). The intermolecular interactions are consideredwithin a mean-field approximation. The mean field is determinedby the average properties of all of the molecules in the mixture,and thus the theory is in essence a self-consistentapproach.
We write the free energy of the system in complete analogy with the equilibrium approach (22) but with all of the quantitiesnow assumed to be time-dependent. The explicit expression forthe time-dependent free energy density (per unit area) reads
where the first two terms are the contribution from the tethered polymers, with the first being the conformational entropyof the chains, with P(;t) being the time-dependent probabilitydistribution function (pdf) of chain conformations and the secondbeing the tethered polymers two-dimensional translational entropy.The third term is the solvent entropy, with s(z;t) being thevolume fraction of solvent at distance z from the surface at timet. The last two terms correspond to the translational entropyof the proteins and the protein-surface interaction, respectively,Ups(z) is the bare surface-protein interaction. This interactionis taken from ref. 23 where the potential between lysozyme anda hydrophobic surface was calculated by using atomistic potentials.Note that the solvent and protein contributions are integratedover z to account for all of themolecules.
Eq.2 assumes that the intermolecular attractions between all of the components in the system are the same. This is actuallythe model that we successfully used to compare experimental observationsand the predictions of the theory in early work (14) and inthe comparisons shown below. The excellent agreement between thepredictions of the theory and the experimental observations supportstheassumption.
Eq.2 does not include the repulsive interactions between the molecules. The hard-core repulsions are accounted for by packingconstraints in which the available volume to the molecules, ateach distance z from the surface, is filled by polymer, protein,or solvent molecules. This constraint reads
where the first term is the volume fraction of polymer at z, with ng(z;t)dz=P(;t)ng(z,;t)dz being the averagenumber of polymer segments of volume v0 at time t at distancez from the surface. The second term is the volume fraction ofproteins with v(z;z')dz being the volume that the proteins atdistance z' from the surface contribute to z. The last term isthe volume fraction ofsolvent.
The assumption of solvent and polymer equilibration in the time scale of protein motion implies that the time-dependent pdfof tethered polymer configurations and the solvent-density profileare those that minimize the free energy (Eq.2) subject to thepacking constraint (Eq.3) for fixed protein density profile.Thus, at each time t the density of proteins calculated from thediffusion equation (Eq.1) is given as input to the free energyand this free energy is minimized subject to the packing constraints.This minimization is done by introducing time-dependent Lagrangemultipliers, (z;t). The pdf of chain conformations is
where q(t) is the time-dependent normalization constant. For the solvent-density profile, the expression is
The numerical values of the Lagrange multipliers are obtained by replacing the expression for the pdf, Eq.4, and the solvent-densityprofile, Eq.5, into the constraint equation, Eq.3, where theprotein contribution is given as an input obtained from the diffusionequation, Eq. 1.Once the Lagrange multipliers are obtained,one can calculate the time-dependent protein chemical potentialthat is needed for the time evolution of the adsorption. Thiscalculation is done by differentiating the free-energy densityto obtain
which is readily obtained once the Lagrange multipliers are known. Thus, the time evolution of the system is obtained inthe following way. At time t=0,a tethered polymer layer inequilibrium with pure solvent is brought into contact with a proteinsolution. The initial density profile of proteins enables thecalculation of (z;0) from which µpro(z;0) is obtained by useof Eq.6. From it, the diffusion equation (Eq.1) is iterateda time step. The new density profile of proteins now is givenas input for the calculation of the new Lagrange multipliers fromwhich the chemical potential profile is obtained and the timeevolution is further iterated. This procedure is continued untilthe new equilibrium condition is achieved in which µpro(z;t)=µpro.eq for all z.
Eq.6 shows that the motion of the proteins toward the surface contains three contributions. The first one is the purely diffusivemotion that is found in any ideal system because of the gradientin composition. The second arises from the force exerted to theproteins by the surface. These two terms do not depend on theintermolecular interactions and will lead to a fast approach ofthe proteins to the surface. We refer to them as the purely diffusivemotion (see e.g., Fig. 2 and discussion thereafter). The lastterm is the one arising from the intermolecular (protein-polymerand protein-protein) interactions. This term will be responsiblefor steric barriers and it is expected to lead to regimes in whichthe motion is dominated by kinetic barriers. The interplay betweenthe diffusion and barrier crossing to determine the total adsorptionprocess is discussed in detailbelow.
[1]Quantitative Analysis of Protein Adsorption Kinetics written in collaboration with C.-H. Ho,P.Dryden and D. W. Britt , Department of Bioengineering, University of Utah, Salt Lake City, UT84112, USA,
[2]Robert T. T. et. al., Quantification of the kinetics and thermodynamics of protein adsorption using atomic force microscopy, Journal of Biomedical Research 2005
[3] J. Satulovsky et. al., Kinetic and thermodynamic control of protein adsorption. Biophysics 2000.