Single-Particle Plasmon Sensor to Monitor Proteolytic Activity in Real Time

We have established a label-free plasmonic platform that monitors proteolytic activity in real time. The sensor consists of a random array of gold nanorods that are functionalized with a design peptide that is specifically cleaved by thrombin, resulting in a blueshift of the longitudinal plasmon. By monitoring the plasmon of many individual nanorods, we determined thrombin’s proteolytic activity in real time and inferred relevant kinetic parameters. Furthermore, a comparison to a kinetic model revealed that the plasmon shift is dictated by a competition between peptide cleavage and thrombin binding, which have opposing effects on the measured plasmon shift. The dynamic range of the sensor is greater than two orders of magnitude, and it is capable of detecting physiologically relevant levels of active thrombin down to 3 nM in buffered conditions. We expect these plasmon-mediated label-free sensors to open the window to a range of applications stretching from the diagnostic and characterization of bleeding disorders to fundamental proteolytic and pharmacological studies.

Single-particle correlation between peptide loading and response to proteolytic activity Figure S1.Correlation between the plasmons shifts induced by the peptide immobilization and the consequent wnzymatic cleavage (20nM thrombin).Dash line represents a reference line (y = -0.5x).

Intensity-based plasmon sensing
We will derive equations to convert changes in the intensity scattered by a single nanoparticle into a plasmon shift.We assume that the plasmon resonance can be approximated by a Lorentzian function given by Where  is the incident photon energy,   and  are the plasmon energy and linewidth (measured from the scattered spectrum).Note that all units are in eV.In a biosensing experiment this spectrum becomes time dependent due to a timedependent shift of the plasmon resonance.This can be taken into account by considering   to be time-dependent due to a shift   (𝒕).The plasmon resonance is then given by (, ) =  2 1 +   () (2) Herein the factor  has a negative value and describes the increase in scattering cross section in response to a plasmon redshift (i.e. a decrease in cross section with an increase in plasmon energy).The contrast in an intensity-based experiment is probed using a light source with a center energy   .We assume that the linewidth of the source is much narrower than .The contrast is then given by: (3) Provided the value of A is known (either estimated from the asymmetric shape of a typical s-curve, or estimated from a numerical model of the scattering spectrum) this approach can be used to solve analytically for   (𝑡).For  = 0 we can extract   () directly: Where the plus sign holds when   <   and the minus sign when   >   .
For  ≠ 0 we first need to rewrite the equation into: 2   () 2 +  1   () +  0 = 0, Where, From here   () is easily calculated: Where the plus sign holds when   <   and the minus sign when   >   .
Figure S2.Illustration of the quantities used in this derivation.
Thrombin inhibition and adsorption onto the (uncleaved) peptide layer Firstly, it is important to note that due to difficulties from the manufacturing company (CASLO) in reproducing the original peptide (due to Aspartimide formation) the original sequence was slightly modified.The modification involves exchanging part of the aspartic acids (D) for glutamic acid (E) (Figure S3a) aiming to cause minimum interference in the peptide as possible.Consequently, the physicochemical properties of both sequences, such as hydrophobicity, charge and isoelectric point (pI), were estimated using the bioinformatic tool Pepcalc from Innovage.From Figure S3b, as expected, it is possible to observe that both sequences have similar physicochemical properties being the overall net charge of the peptide across the pH values and the hydropathy equal to both peptides and only slight change in the isoelectric point (from 6.32 to 6.45) was expected.Further, we assessed eventual conformation changes between both peptide sequences using the AlphaFold software through COLAB 1 project using ChimeraX software to predict the structures of the peptide sequences.For visual comparison and alignment, the PDB files were imported to Blender v3.3 using the Molecular Nodes add-on from which it can be observed that both peptides present a similar "random coiled" structure (Figure S3c) After comparison of both peptide sequences using bioinformatic tools, we performed an experiment to evaluate how the presence of an well-known inhibitor (Dabigatran; 20µM) would influence the response of our sensor using AuNRs with 25nm width with LSPR at 650nm while probing them at 640nm±15nm.Hence, Figure S3d are provided the timetraces for an experiment using 100nM THRB and 100nM THRB and inhibitor.Here, to provide an accurate and broad impression of both experiments, the timetraces of several particles were averaged before plotting.As expected, in the absence of the inhibitor a quick blue-shift is observed indicating the cleavage of peptide layer by THRB.The consequent red-shift is indicative of THRB to the cleaved layer (later explained in the maintext).Conversely, in the presence of the inhibitor, when THRB enters the chamber (vertical dashed line) the sudden blue-shift is no longer observed and only occurs slowly over a long period of time, which indicates that the enzyme is not fully inhibited under these concentrations of Dabigatran.

A pseudo-first order kinetic model for protease adsorption and cleavage
The kinetic model described in the main text comprises 3 stages: (I) the enzyme adsorption onto the peptide layer; (II) the enzyme binding to the cleavage site and peptide cutting; (III) the enzyme adsorption onto cleaved regions in the peptide layer.The first and third stages are modeled as pseudo-first order reversible reactions for the adsorption/desorption equilibrium, whereas the second stage is modeled as two consecutive irreversible steps, where  0 and  0 represent the intact peptide before and after enzyme adsorption, respectively,  0 is the peptide with an enzyme specifically bound to its cleavage site, and  1 and  1 are the cleaved peptide without and with an enzyme (nonspecifically) adsorbed, respectively.The pseudo-first order rate constants are indicated in the reaction scheme of eq. 9, where  0 is the protease bulk concentration.When solving the kinetic equations, it was assumed that the peptide cutting rate constant   is much larger than the binding rate constant   , so that  0 converts almost instantaneously into  1 .The typically large values of   for thrombin make this assumption reasonable.Whereas enzyme binding rates   should be fast in bulk solution because the species involved are freely diffusing, the same does not necessarily apply at the particle's surface due to molecular crowding in the peptide layer.Under these assumptions, the set of differential equations from the reaction scheme of eq. 9 gives the following solution for the time evolution of cleaved peptide, where   is the average number of peptides per particle.The following definitions were introduced for grouping the rate constants, The plasmon shift is roughly proportional to the number of cleaved peptides that are solvent exposed ( 1 ), because it is assumed that the plasmon shift associated with stage I is negligible and that the magnitudes of blue-and red-shift from stages II and III are comparable to each other.The kinetic law of eq. 1 in the main text was derived from eq. 10 by further assuming that   ≪    0 ,   which, despite the loss of generality, still affords a good description of our experimental results.The preexponential factors of eq. 1 from the main text (  ) are then given by,  Above some concentration  0 , the simulated kinetic curves display a local maximum, which is also observed in the experimental time traces.The instant  max at which this local maximum occurs can be approximately found from, In the example of Figure S3, this concentration limit is  0 * = 28.6 nM.Instead of using the approximation of eq.16, the values of  max were numerically calculated using the method of Newton-Raphson.In order to replicate the experimental results, the model estimates of plasmon shift were calculated from  1 ( max ), when  max <  w , when  max occurs before the end point of the measurement window which was set at  w = 2400 s.Otherwise at low  0 values, when a local maximum is not observed, the plasmon shifts were calculated at the end point of kinetic curves, i.e. from  1 ( w ).This calculation afforded the model curve shown below in Figure S5, from which it was calculated the normalized plasmon shift shown in Figure 5 of the main text (red dashed curve).
Another parameter from the kinetic curves that was assessed both experimentally and theoretically was the reaction halftime  1 2 ⁄ , which is defined as, When using eq. 10 to solve eq. 18, it yields an equation that does not have an exact algebraic solution, so it was again numerically calculated using the method of Newton-Raphson.The main result is shown as a dashed red curve in Figure 5a of the main text.[Thrombin] (nM)

Figure S3 .
Figure S3.Comparison between peptide sequences and the effect of inhibition.(a) Modifications in the peptide sequence; (b) Calculation of the physicochemical properties of both sequences (pepcal from Innovagen); (c) Graphical representation of both peptides' structure.(d) The effect of inhibitor in sensor' response.
model, a set of kinetic curves were simulated for the values of thrombin concentration used in the experiments, as shown in fig.S1.

Figure S4 .
Figure S4.Illustration of the molecular phenomena underlying the performance of the sensor and the parameters included in the model.(a) and (b) Kinetic curves simulated from eq. 1 of the main text using   = 210 5 M -1 s -1 ,   = 0.01 s - 1 ,   = 2.510 4 M -1 s -1 ,   = 0.005 s -1 ,  •   = 0.8 and 8, respectively, and assuming an average shift of  = 0.08 nm per peptide.(C) Kinetic curves simulated varying  •   values for the same concentration of active enzyme (50nM)

Figure S5 .
Figure S5.Reaction Half-time determination a) Illustration of the determination of the half-time t1/2; b) Histogram of t1/2 for two thrombin concentrations.
Figure S6.Quantification of active enzyme.Non-trivial response from plasmon shift vs concentration of active enzyme -experimental and modeled results.