This paper reports the structural behavior and thermodynamics of the complexation of siRNA with poly(amidoamine) (PAMAM) dendrimers of generation 3 (G3) and 4 (G4) through fully atomistic molecular dynamics (MD) simulations accompanied by free energy calculations and inherent structure determination. We have also done simulation with one siRNA and two dendrimers (2×G3 or 2×G4) to get the microscopic picture of various binding modes. Our simulation results reveal the formation of stable siRNA−dendrimer complex over nanosecond time scale. With the increase in dendrimer generation, the charge ratio increases and hence the binding energy between siRNA and dendrimer also increases in accordance with available experimental measurements. Calculated radial distribution functions of amines groups of various subgenerations in a given generation of dendrimer and phosphate in backbone of siRNA reveals that one dendrimer of generation 4 shows better binding with siRNA almost wrapping the dendrimer when compared to the binding with lower generation dendrimer like G3. In contrast, two dendrimers of generation 4 show binding without siRNA wrapping the dendrimer because of repulsion between two dendrimers. The counterion distribution around the complex and the water molecules in the hydration shell of siRNA give microscopic picture of the binding dynamics. We see a clear correlation between water, counterions motions and the complexation i.e. the water molecules and counterions which condensed around siRNA are moved away from the siRNA backbone when dendrimer start binding to the siRNA backbone. As siRNA wraps/bind to the dendrimer counterions originally condensed onto siRNA (Na+) and dendrimer (Cl−) get released. We give a quantitative estimate of the entropy of counterions and show that there is gain in entropy due to counterions release during the complexation. Furthermore, the free energy of complexation of 1G3 and 1G4 at two different salt concentrations shows that increase in salt concentration leads to the weakening of the binding affinity of siRNA and dendrimer.

We study nonlinear dynamics of inhomogeneous DNA double helical chain under dynamic plane-base rotator model by considering angular rotation of bases in a plane normal to the helical axis. The DNA dynamics in this case is found to be governed by a perturbed sine-Gordon equation while taking into account the interstrand hydrogen bonding energy between bases and the intrastrand inhomogeneous stacking energy and by making an analogy with the Heisenberg model of the Hamiltonian of an inhomogeneous anisotropic spin ladder with ferromagnetic legs and antiferromagnetic rung coupling. In the homogeneous limit the dynamics is governed by the kink-antikink soliton of the sine-Gordon equation which represents the formation of open state configuration in DNA double helix. The effect of inhomogeneity in stacking energy in the form of localized and periodic variations on the formation of open states in DNA is studied under perturbation. The perturbed soliton is obtained using a multiple scale soliton perturbation theory by solving the associated linear eigen value problem and by constructing the complete set of eigen functions. The inhomogeneity in stacking energy is found to modulate the width and speed of the soliton depending on the nature of inhomogeneity. Also it introduces fluctuations in the form of train of pulses or periodic oscillations in the open state configuration.

Using all atomistic molecular dynamics (MD) simulations we report the microscopic picture of the nanotube-dendrimer complex for PAMAM dendrimer of generation 2 to 4 and carbon nanotube of chirality (6,5). We find compact wrapping conformations of dendrimer onto the nanotube surface for all the three generations of PAMAM dendrimer. The degree of wrapping is more for non-protonated dendrimer compared to the protonated dendrimer. For comparison we also study the interaction of another dendrimer, poly(propyl ether imine) (PETIM), with nanotube and show that PAMAM dendrimer interacts strongly as compared to PETIM dendrimer as is evident from the distance of closest approach as well as the number of close contacts between the nanotube and dendrimer. We also calculate the binding energy between the nanotube and the dendrimer using MM/PBSA methods and attribute the strong binding to the charge transfer between them. Dendrimer wrapping on CNT will make it soluble and can act as an efficient dispersing agent for nanotube.

The protein-DNA interaction dynamics is studied by modeling the DNA bases as classical spins in a coupled spin system, which are bosonized and coupled to thermal phonons and longitudinal motion of the protein molecule in the nonviscous limit. The nonlinear dynamics of this protein-DNA complex molecular system is governed by the completely integrable nonlinear Schrödinger (NLS) equation which admits N -soliton solutions. The soliton excitations of the DNA bases in the two strands make localized base-pair opening and travel along the DNA chain in the form of a bubble. This may characterize the bubble generated during the transcription process, when an RNA polymerase binds to a promoter site in the DNA double helical chain. When the protein-DNA molecular system interacts with the surrounding viscous solvating water medium, the dynamics is governed by a perturbed NLS equation. This equation is solved using a multiple scale perturbation analysis, by treating the viscous effect as a weak perturbation, and the results show that the viscosity of the solvent medium damps out the soliton as time progresses.