Detection of Single Molecules Using Stochastic Resonance of Bistable Oligomers

Ultra-sensitive elements for nanoscale devices capable of detecting single molecules are in demand for many important applications. It is generally accepted that the inevitable stochastic disturbance of a sensing element by its surroundings will limit detection at the molecular level. However, a phenomenon exists (stochastic resonance) in which the environmental noise acts abnormally: it amplifies, rather than distorts, a weak signal. Stochastic resonance is inherent in non-linear bistable systems with criticality at which the bistability emerges. Our computer simulations have shown that the large-scale conformational dynamics of a short oligomeric fragment of thermosrespective polymer, poly-N-isopropylmethacrylamid, resemble the mechanical movement of nonlinear bistable systems. The oligomers we have studied demonstrate spontaneous vibrations and stochastic resonance activated by conventional thermal noise. We have observed reasonable shifts of the spontaneous vibrations and stochastic resonance modes when attaching an analyte molecule to the oligomer. Our simulations have shown that spontaneous vibrations and stochastic resonance of the bistable thermoresponsive oligomers are sensitive to both the analyte molecular mass and the binding affinity. All these effects indicate that the oligomers with mechanic-like bistability may be utilized as ultrasensitive operational units capable of detecting single molecules.


S1. Simulation protocol
Morphology simulations were performed using the GROMACS simulation package. Details of the parameters used for non-bonded interactions are presented in Figure S1a. Long-range electrostatic interactions were treated using a smooth particle mesh Ewald technique. All calculations were performed in the NVT ensemble using the canonical velocity-rescaling thermostat, as implemented in the GROMACS simulation package.
A random initial configuration was used to start the simulation. To reach an equilibrated morphology, the simulation was initialized using 16,742 water molecules and one NIPMAm oligomer in a syndiotactic configuration 30 monomeric units long. These molecules were modeled inside a box measuring 5.0 × 3.0 × 3.0 nm first exposed to a thermal bath at 290 K for 50 ns with a simulated time step of 0.001 ps (n = 5 independent trajectories). The simulation was repeated in a larger box (8.0 × 8.0 × 8.0 nm), confirming that results were not influenced by box size. An image of the larger simulation box (8.0 × 8.0 × 8.0 nm) is shown in Figure S1b.
To study how the oligomers respond to a power load, system simulation was continued for an additional 150 ns (n = 2 independent trajectories). Model error was estimated using the full width at 50% of the distribution curve maximum. Various water models (SPCE, TIP3P, TIP4P) were used, showing that results are independent of the model applied. Significant differences in the spontaneous oscillations of the end-to-end distance e R under the critical load ( 400 F pN = Figure S1c) were not found. Figure S1. Simulation details. a) Non-bonded interaction parameters from the OPLS-AA force field used in the simulation; b) the YZ-plane of the simulation box (8.0 × 8.0 × 8.0 nm; 50,888 particles); and c) oscillations of the end-to-end distance e R for various water models (SPCE, TIP3P, and TIP4P).
The simulation workflow consisted of the following: 1) An "open" conformation of oligo-30s-NIPMAm was obtained by equilibrating the oligomer at 290 K. This configuration of oligo-30s-NIPMAm was oriented in the YZ-plane and fixed in the X dimension.
2) The center of mass for the first monomeric unit in the oligomeric chain was fixed using a spring potential of 2 100 / k kJ molnm = . No other specific constraints for bond length or atom position were applied.
3) The longitudinal (compressing) load F was applied to the center of mass of the last monomer unit and directed toward the attraction point, located at the center of mass of the first monomeric unit along the vector connecting the left and right ends of the molecule. Note that the orientation of this vector changed over time because the first monomeric unit was fixed while the 30 th monomeric unit was mobile. 4) To study stochastic resonance, an oscillating force was realized by setting a charge (+1) at one end of the oligomer and a compensative charge (-1) at the other end. An external oscillating electrical field 0 cos E E t  = was directed along the compressive force F . The period of the harmonic electrical field was close to the period of random fluctuation ns T 5 = , and the amplitude 5) The lateral load G was applied to the center of mass of the 16 th monomer unit (the middle part of the oligo-NIPMAm). Hysteresis (Figure 4a) was observed when a lateral load was added to the system under critical compression. In this case, the vibration region (stochastic resonance) depended on increasing or decreasing the lateral load. 6) To represent stochastic resonance, the end-to-end distance under a compressing force F and a lateral force G that were fixed near their critical values was plotted against time. To apply an additional load to the system, the following workflow was used: 1) An "open" conformation of oligo-30s-NIPMAm at a temperature of 290 K was oriented in the YZ-plane and fixed in the X dimension (See Figures S2a and b).

S2. Sensing regime
2) Small molecules (one, two, or three) were placed in the vicinity of the oligo-NIPMAm molecule. After ~10 ns of equilibration, the small molecule was absorbed on the oligo-NIPMAm (see Figure S3 for minimum distances for various types of molecules).
3) The longitudinal load applied to the oligomer was then bent as described in the simulation protocol. Alternatively, the oligomer can be placed in a closed state, equilibrated at 320 K, then loaded in opposite directions. Results were not qualitatively different in this scenario.

S3. Sensitivity
The sensing regime is sensitive to the mass of the binding small molecule and its binding affinity (see Figure S7). The number of sites and the hydrogen binding affinity differed between the small molecules. Binding energies were obtained using an umbrella sampling technique. Figure S7. Binding energies and the number of hydrogen bonds in each molecule studied. The molar mass, critical force for spontaneous vibrations, critical force normalized to molar mass, binding energy, and number hydrogen bonds is shown for each molecule.