Designing new strategy for controlling DNA orientation in biosensors

Orientation controllable DNA biosensors hold great application potentials in recognizing small molecules and detecting DNA hybridization. Though electric field is usually used to control the orientation of DNA molecules, it is also of great importance and significance to seek for other triggered methods to control the DNA orientation. Here, we design a new strategy for controlling DNA orientation in biosensors. The main idea is to copolymerize DNA molecules with responsive polymers that can show swelling/deswelling transitions due to the change of external stimuli, and then graft the copolymers onto an uncharged substrate. In order to highlight the responsive characteristic, we take thermo-responsive polymers as an example, and reveal multi-responsive behavior and the underlying molecular mechanism of the DNA orientation by combining dissipative particle dynamics simulation and molecular theory. Since swelling/deswelling transitions can be also realized by using other stimuli-responsive (like pH and light) polymers, the present strategy is universal, which can enrich the methods of controlling DNA orientation and may assist with the design of the next generation of biosensors.


DPD simulation method
The DPD is a coarse-grained simulation technique with hydrodynamic interaction 1 . The dynamics of the elementary units which are so-called DPD beads, is governed by Newton's equation of motion: Typically, in the DPD, there are three types of pairwise forces acting on bead i by bead j: the conservative force, dissipative force, and random force. In the present work, the electrostatic force is introduced to take into account the electrostatic interactions between charged beads.
The conservative force F C ij is taken as where r ij = r i − r j , r ij = |r ij |, andê ij = r ij /r ij . The parameter r c is the cutoff radius of the conservative force, and a ij represents the maximum repulsion interaction of beads of type i and type j. For any two beads of the same type, we take the repulsive parameter a ii = 25.
In our system, the water (W) and ion (I), DNA (D), plane (N) beads are hydrophilic (the ion concentration is about 0.10 M), thus the interaction parameter between these beads is fixed to be 25, i.e., a W I = a W D = a W I = a W N = a ID = a IN = a DN = 25 1 . In particular, the hydrophilic/hydrophobic property of thermo-responsive polymer (P) is related to external temperature. For the sake of simplicity, here we assume that its hydrophilic/hydrophobic property changes linearly with the temperature, i.e, a P W = a P I = a P D = a P N = 25 + (T − T 0 ) * 500. This relationship shows that when the temperature is low (e.g., T 0 ), the polymer is totally hydrophilic (a P W = 25), while it becomes very hydrophobic (a P W = 75) when the temperature is high (e.g., 1.1T 0 ).
where v ij = v i − v j is relative velocity between beads i and j, and γ is the strength of friction.
Finally, the random force F R ij takes the form of Here, ζ ij is a symmetric random variable with zero mean and unit variance, namely < ). ∆t is the time step of simulation.
Electrostatic interactions were incorporated into the DPD simulations by Groot 2 . Since soft potential in the DPD allows for the overlap between DPD beads, when the charged DPD beads are modeled, this can lead to the formation of artificial ion pairs and cause the divergence of the electrostatic potential. To avoid this problem, Groot chose to spread out the charges using the distribution 2 : where R e is the electrostatic smearing radius, and is typically set as 1.6 r c .
Further, we also use a harmonic bond and l 0 =0.5 r c ) between the neighboring beads to ensure the integrality of polymers. Our simulations apply the velocity-Verlet integration algorithm and the integration time step ∆t=0.015 τ . In addition, we choose the cutoff radius r c , bead mass m, energy k B T 0 as the simulation units. All simulations are performed in the NVT ensembles. The size of the simulation box is 40 r c ×40 r c ×40 r c with the number density of ρ = 3/r 3 c . Similar to previous studies, r c is about 1.0 nm in our system 3,4 . The periodic boundary conditions are adopted in three directions.

Molecular theory
We use a molecular theory to model temperature-sensitive DNA-b-PNIPAm copolymers which are end-grafted to a planar substrate and immersed in an aqueous solution of salt ions (0.10 M, which is close to physiological salt concentration). The theory was previously used to study the thermodynamics and structural properties of end-tethered neutral and charged polymers with the consideration of the conformation, size, and shape of each molecule [5][6][7] , and was shown to be in quantitative agreement with simulations and experimental observations [8][9][10] . More explicitly, the Helmholtz free energy for the system in Fig. 1 of the main text is where β = 1/k B T is the inverse absolute temperature.
The first term in the right-hand side of Eq. 6 is the conformational entropy of copolymer chains, which is written as: where σ is the surface coverage of copolymer and p(α) is the probability distribution function (pdf) of finding a copolymer in conformation α, and we can utilize it to calculate any thermodynamical and structural quantity of the copolymer as well as the orientation of DNA. For example, the polymer volume fraction is expressed by Here n i (α, z)dz denotes the number of segments of type i that a copolymer chain in conformation α contributes in the layer between z and z + dz (i = n, D represent PNIPAm and DNA, respectively). v i is the volume of each segment of type i.
The second term of Eq. 6 represents the effective intermolecular interactions between PNIPAm segments and water, which is where χ nw (z) describe the strength of the PNIPAm-water effective repulsions as well as the association among PNIPAm monomers with the increase of temperature. The water volume fraction is given by ϕ w (z) = ρ w (z)v w , with the density of water molecules ρ w (z) in the layer between z and z + dz and volume of water molecule v w , which is used as the unit of volume.
The third term in free energy expression is the translational (mixing) entropy of small molecules, including the cations, anions and water. It is given by where ρ i (z) is the density of molecule of species i.
The fourth term in Eq. 6 describes the anisotropic interactions for DNA in Mayer-Saupe self-consistent field approximation [11][12][13] , which is as follows: where s 2 (z) is the order parameter defined through an averaged value of the DNA orientation with respect to the director(i.e., z axis), and it is given by where θ(α, z) is the orientation of the DNA in conformation α in the layer from z to z + dz with respect to z axis.
The last term in Eq. 6 accounts for the electrostatic contribution to the free energy, which is given by where ψ(z) is the local electrostatic potential, and ε is the dielectric constant of water.
⟨ρ q (z)⟩ is the average charge density at z including contributions coming from all the charged species, which is given by where e is the elementary charge. Here we consider all charged small molecules, that is, N a + , Cl − . The last term comes from the contribution of DNA and each base pair with a charge of −e.
For an equilibrium state of the system, two constraints should be satisfied. One is the packing or incompressibility constraint, which reflects the intermolecular repulsions at each layer, namely The other constraint is the global electroneutrality, given by: The packing and electroneutrality constraints are fulfilled by introducing the Lagrange multipliers π(z) and λ into the free energy. Notice that the system is in contact with a bath of all the other species and therefore the calculations have to be performed in the semigrand canonical ensemble. By including two constraints, we write down the semigrand potential density: where the chemical potentials for N a + and Cl − are in reality exchange chemical potentials.
To find equilibrium solutions, we minimize the semigrand potential with respect to different variables. It turns out that the probability distribution function p(α) is expressed as: The volume fraction of water is given by: The densities of N a + and Cl − are: For the electrostatic potential, it gives rise to a generalized Poisson-Boltzmann equation: with the boundary conditions: For the neutral surface, it becomes: Given the fact that the system is immersed in the bulk solution, the chemical potentials of N a + , Cl − and the Lagrange multiplier λ can be transformed as functions of the bulk concentration. Unknown parameters in the above equations are the lateral pressure βπ(z) and electrostatic potential ψ(z). These quantities can be determined by substituting Eq.
In practice, we convert the integral equations into a set of coupled nonlinear equations by discretizing the space, whereas details on the discretization and numerical methodology and how the chains are generated can be found in the following.

Numerical solution
Here we present an outline of the numerical method used to solve the equations derived from the molecular theory. This is done by dividing the z-axis into parallel spherical layers of thickness δ. Functions are assumed to be constant within a layer; hence integrations can be replaced by summations. The ith layer is defined as the region between (i − 1)δ ≤ r < iδ.
The packing constraints, Eq. 15, in a discrete form for layer i is: The volume fraction of PNIPAM and DNA equals Here the discretized probability distribution functions p(α) is The volume fractions of cations, anions and water are given by: The generalized Poisson equation is described as follows: Here ⟨ρ q (i)⟩ is the total charge density in layer i, which is where ρ D (i) is The discrete boundary conditions are and ψ(n + 1) = 0.
The discretized packing constraint and Poisson equation constitute a set of coupled nonlinear equations for π(i) and ψ(i). These coupled equations can be solved with standard numerical techniques.
The chain model for PNIPAm is the three-state RIS model 14 . In this model, each bond has three different isoenergetic states. The DNA is treated as rod, whose orientations are generated randomly. The conformations of DNA-b-PNIPAm are generated by a simple sampling method and all the accepted conformations are self-avoiding. We generate 10 6 independent conformations. In our calculations, each segment of PNIPAM has the volume of v n =0.16 nm 3 , which was chosen according to the partial specific volume of PNIPAM in water, and for water v w =0.03 nm 3 as we use before 15 . the DNA is consisted of 12 base pair, each one has a negative charge (-e) and a volume of 1.0 nm 3 . The layer thickness was σ=0.6 nm.
The interaction parameter χ wn (i) = (g 00 + g 02 T ) + (g 10 + g 12 T )ϕ n (i) + (g 20 + g 22 T )ϕ 2 n (i) between water and PNIPAM comes from the experiment of Afroze et al 18   Supplementary Fig. 5 shows the further investigation of DNA orientation as a function of temperature in the presence of proteins, which are treated as nanospheres in our system for the sake of simplicity 19 . Here we choose ubiquitin (Ub) with a diameter of 2 nm as an example, which is usually used in protein detection 20 . Both the DPD simulation and molecular theory results show that the DNA order parameter is larger than that in the absence of ubiquitin. Considering that the variation of DNA orientation can be detected experimentally by fluorescence energy transfer 21 , thus the detection of protein can be achieved.