Cooperative colloidal self-assembly of metal-protein superlattice wires

Material properties depend critically on the packing and order of constituent units throughout length scales. Beyond classically explored molecular self-assembly, structure formation in the nanoparticle and colloidal length scales have recently been actively explored for new functions. Structure of colloidal assemblies depends strongly on the assembly process, and higher structural control can be reliably achieved only if the process is deterministic. Here we show that self-assembly of cationic spherical metal nanoparticles and anionic rod-like viruses yields well-defined binary superlattice wires. The superlattice structures are explained by a cooperative assembly pathway that proceeds in a zipper-like manner after nucleation. Curiously, the formed superstructure shows right-handed helical twisting due to the right-handed structure of the virus. This leads to structure-dependent chiral plasmonic function of the material. The work highlights the importance of well-defined colloidal units when pursuing unforeseen and complex assemblies.

to small values. c, The helicity of the average bending moment is magnified at lower ionic strengths (corresponding to high ) due to stronger electrostatic interaction. different cNaCl for the sample series with nAuNP/nTMV 10-25 (indicated in the legend). The differences in the SAXS profiles (and hence the nanostructures) is more sensitive to the cNaCl than to the nAuNP/nTMV. Some evaporation of water might occur from the samples during the measurement regardless of careful sealing. Therefore the nominal cNaCl might be an underestimation of the actual cNaCl. The dispersed AuNPs ("AuNP free" in (c)) are measured at a low ionic strength.

Supplementary Note
Bending and torsional forces exerted on a helical line charge by a point charge in a static configuration.
To get qualitative insight of the forces exerted on a TMV due to the close vicinity of a AuNP, let us simplify the situation to include only a rigid rod with a negative helical charge distribution and an opposite point charge. We approach the problem by assuming a static configuration. Physically this would mean that all forces and torques are counteracted by reaction forces, which allows us to inspect the configuration without the complications included in elastic deformation or relative motion of the configuration. The static approach is also motivated by the observation that TMV, which corresponds to the rod with a negative helical charge distribution, is relatively rigid and undergoes only a minor deformation when incorporated to the helical assemblies.
The point charge is located on the z axis at a constant distance from the origo O. Let us define an oppositely charged helix having its center at O and with a rotation axis defined by the y axis. Every point on the helix is now defined by the vector ( ) that rotates about the y axis, i.e.
where is the helical pitch and = 2 Δ / according to Fig. S5.
The distance from ( ) to the point charge is The electrostatic force exerted on the helix by the point charge is ≡̂.
= [ 2 sin 2 (2 − ) + 2 + 2 − 2 cos (2 − ) + 2 cos 2 (2 − )] In order to inspect the torsional forces exerted on the helix we may divide the helix into infinitesimal segments and inspect the net torsional forces on the right hand side and the left hand side of the point charge ( Fig. S5b, S5c).
We can observe that due to the point charge, any segment of the helix is subject to a bending moment about the x axis and a torque It is important to recognize that a rod can be deformed into a helix by applying simultaneous bending and torsion. The handedness of the torsion defines the handedness of the formed helix (right handed torsion yields a right handed helix, Fig. S6). Therefore we estimate the net effect of the bending moments exerted on the helix by inspecting the helicity ( ) of the forces. The convention is that positive helicity denotes a right handed structure, and thus a positive helicity of forces denotes forces that drives a right handed deformation.
We start by inspecting the effect of all torsional and bending forces acting on a segment at , ≥ 0. (The same arguments can similarly be applied to the case ≤ 0.) As we are considering a static configuration, we are allowed to make the assumption that the total of all forces and torques exerted on any segment equals to zero. Physically this implies that any force is counteracted by a reaction force. The abovementioned ′ variables result from the attractive force acting on an infinitesimal segment by the point charge. It needs to be pointed out that ′( ) is infinitesimally small, and becomes significant only when integrated over an interval.
The significant bending and torque that acts on a segment is that which is transmitted from other parts of the helix (Fig. S6). Therefore, to avoid misinterpretation we now define the variables to describe the (by internal stress) transmitted bending and torque acting on a segment. The bending moments about x and z axes acting on a segment at ′ on the y axis are and and the torque about the y axis acting on the segment at 0 is , ( ) and , ( ) are the z and x components of ( ). , ( ) is periodically alternating between positive and negative values and ( 0 ) is hence small in comparison to ( 0 ) and is thus not taken into consideration.
The used definition of helicity ( 0 ) in this configuration is ambiguous and requires careful treatment. The definition should yield a positive value for net internal forces striving to bend the structure in a right handed manner. Here we choose to define ( 0 ) as in line with the abovementioned identification that helicity here arises from simultaneous bending ( ( )) and torsion ( ( )). The connection between and the formation of a helical structure can be understood in terms of deflection from the initial main axis (y axis). Axial torsion alone does not cause a round rod to deflect from its initial main axis. Bending does cause deflection from the initial main axis, but does not include any component of helical torsion. If bending and right handed torsion are applied simultaneously, the structure strives to deform in a helical manner. Furthermore, for small deflections (in the elastic regime) the deflection caused by local bending is directly proportional to ( ) as the deflection caused by local torsion is directly proportional to ( ), yielding helicity as the product of these two.
We can now calculate the total helicity ,total as We know from experiments that in the experimental system consisting of TMVs and AuNPs, the AuNPs are allowed to move with respect to the TMV. Therefore it is meaningful in this consideration to evaluate the average helicity 〈 ,total 〉 , which can be evaluated as For this we use the screened Coulomb potential for a point charge where is the Debye length which gives an electric field and an electrostatic force = 1/(4 0 r ), 0 is the vacuum permittivity, and r is the relative permittivity for the media. The This consideration shows that a point charge can exert both bending and torsional forces on a helical charge distribution. The asymmetric electrostatic interaction is the most probable explanation for the formed helical superstructure, because when torsion and bending are applied on an elastic rod simultaneously, the rod deforms in a helical manner. The handedness of the applied torsion yields the handedness of the helical deformation (right handed torsion together with bending yields a right handed helix). In this inspection we observe that the helicity is either right handed or left handed, depending on the relative position of the point charge, but the -average (= Δ -average) helicity remains positive, corresponding to an average right handed twist. To compare this simplified charge configuration with that of a cationic nanoparticle and TMV is far from trivial. However, our experimental data shows that the strong electrostatic interaction dominates the self-assembly, leading to the conclusion that the right handed helical structures result from the asymmetric electrostatic interaction between a cationic spherical nanoparticle and TMV, which carry a helical charge distribution. As said, merely the symmetric attraction can explain the formation of helical superlattices, but an asymmetric interaction is needed to explain the preferred handedness. The details of the electrostatic potential map of TMV is on sub nanometer level, whereas the observed pitch of the helical superlattices is in micrometer scale. We believe that a complete understanding of the formation of the observed helical superlattice structures would require detailed, but large scale molecular simulations that are beyond the state of the art.