Buffer Influence on the Amino Acid Silica Interaction

Abstract Protein‐surface interactions are exploited in various processes in life sciences and biotechnology. Many of such processes are performed in presence of a buffer system, which is generally believed to have an influence on the protein‐surface interaction but is rarely investigated systematically. Combining experimental and theoretical methodologies, we herein demonstrate the strong influence of the buffer type on protein‐surface interactions. Using state of the art chromatographic experiments, we measure the interaction between individual amino acids and silica, as a reference to understand protein‐surface interactions. Among all the 20 proteinogenic amino acids studied, we found that arginine (R) and lysine (K) bind most strongly to silica, a finding validated by free energy calculations. We further measured the binding of R and K at different pH in presence of two different buffers, MOPS (3‐(N‐morpholino)propanesulfonic acid) and TRIS (tris(hydroxymethyl)aminomethane), and find dramatically different behavior. In presence of TRIS, the binding affinity of R/K increases with pH, whereas we observe an opposite trend for MOPS. These results can be understood using a multiscale modelling framework combining molecular dynamics simulation and Langmuir adsorption model. The modelling approach helps to optimize buffer conditions in various fields like biosensors, drug delivery or bio separation engineering prior to the experiment.


Supporting Information
. PMF profile of R and K and the buffer species.  TRIS(Neutral) -3 5 *interaction energies are reported at a separation of 8Å between the species

Derivation of Cooperative Langmuir Model
Let's assume there are two different adsorbate species A and B. The species are assumed to be in the ideal gas phase unless these are adsorbed on the surface adsorption sites (shown as the black parabola in the schematic in Fig. S2) of the adsorbent. Each adsorption site can accommodate a maximum of two molecules where the adsorption phenomenon is governed by adsorbate-adsorbent interaction as well as adsorbateadsorbate interaction. Figure S2. Schematic diagram representing a cooperative adsorption model of two different species A and B. The black semi circles are the adsorption sites, which can accommodate up to two molecules.
To formulate the statistical mechanics of this adsorption processes we first enumerate the different number of microstates for a single adsorption site (see the schematic in Fig.S3) as follows: 1. Adsorption site is empty. 2. Occupied by one A molecules and an empty spot. 3. Occupied by two A molecules. 4. Occupied by one B molecules and an empty spot. 5. Occupied by two B molecules.

Figure S3. Different microstates for a single adsorption site (capable of holding two adsorbate molecules) in the presence of two adsorbates A and B.
and are the potential energy of the molecule A and B due to interaction with the adsorbent upon adsorption. is the interaction energy between two molecules when both of these two are adsorbed on a single adsorption site.
is the corresponding interaction energy for the B molecules and is the interaction energy between A and B in case the adsorption site is occupied by one A and one B molecule respectively.
The grand canonical partition function for the single adsorption site is then given by and are the thermal de Broglie wavelength of the adsorbate molecule A and B respectively. is the free volume offered by half of the adsorption site. Here, the terms −3 and −3 come from the configurational part of the partition function. and are the chemical potential of the molecular A and B respectively. Here, = 1/ . is the Boltzmann constant and is the temperature. Now, if there are independent adsorption sites, the total grand canonical partition function of the system is = The expectation value of the number of adsorbed molecule A is then given by Now, at equilibrium, the chemical potential of the molecular species A and B are related to their partial pressure according to following thermodynamic condition And the Langmuir Binding Constant for the molecular species A and B defined as Using equations (4) and (5), equation (3) can be rewritten in the following form Similarly, we can write another equation for the expectation value of adsorbed molecule B. The equation (6) above is written in terms of the partial pressure of the adsorbates. Alternatively, it can be rewritten in terms of the equilibrium concentration of the adsorbates. If and are the concentration of the species A and B in equilibrium then, is proportionality constant relating the pressure of an ideal gas with its concentration. Now, let's define scaled Langmuir constant as, The equation (6) can therefore be alternatively written as, When there are no interactions between the molecules A and B, instead of invoking the cooperative adsorption model, we employ the non-cooperative Langmuir Adsorption model as shown schematically in Figure S4 below.

Figure S4. Schematic diagram representing non-cooperative competitive Langmuir adsorption model of two different species A and B. The black semi circles are the adsorption sites which can accommodate only one molecule.
In that case, the expectation value for the number of adsorbed A molecules is

Figure S6: (a/b) Experimentally measured Henry coefficient of K/R as a function of pH in presence of MOPS buffer. (c/d) Fraction of K/R bound to silica for different values of the interaction energy (
) between K/R and MOPS (Negative) as a function of pH as calculated using multiscale modelling. The experimental Henry coefficient and calculated bounded fraction show qualitatively same behavior for | | > 7 kJ/mol (or | | > 11 kJ/mol ) for K (or R). The chromatographic column was operated on an Agilent 1100 HPLC system with an UV/Vis detector. Amino acids (AAs) were measured at 210 nm, aromatic AAs additionally at 280 nm. The flow rate was ~12 cm min -1 for every run and the injection volume for every AA was 20 µL. The Henry coefficient H was determined with H = k' / φ. Where k' is the retention factor of the AA and φ is the phase ratio of the column. The retention factor is calculated as k' = (tR -t0)/t0. Here tR stands for the retention time of the AA and t0 for the retention time of a noninteracting tracer in this case 1 g L -1 uracil. The phase ratio of the column is calculated with φ = (1-ε t )/ ε t . Here ε t is the total porosity of the column calculated with the flow rate V = 2 mL min -1 : ε t = (t0 * V ) / Vcolumn. The volume of the column is 0.55 mL.