Alternation of regular and chaotic dynamics in a simple two-degree-of-freedom system with nonlinear inertial coupling.

We show that nonlinear inertial coupling between a linear oscillator and an eccentric rotator can lead to very interesting interchanges between regular and chaotic dynamical behavior. Indeed, we show that this model demonstrates rather unusual behavior from the viewpoint of nonlinear dynamics. Specifically, at a discrete set of values of the total energy, the Hamiltonian system exhibits non-conventional nonlinear normal modes, whose shape is determined by phase locking of rotatory and oscillatory motions of the rotator at integer ratios of characteristic frequencies. Considering the weakly damped system, resonance capture of the dynamics into the vicinity of these modes brings about regular motion of the system. For energy levels far from these discrete values, the motion of the system is chaotic. Thus, the succession of resonance captures and escapes by a discrete set of the normal modes causes a sequence of transitions between regular and chaotic behavior, provided that the damping is sufficiently small. We begin from the Hamiltonian system and present a series of Poincaré sections manifesting the complex structure of the phase space of the considered system with inertial nonlinear coupling. Then an approximate analytical description is presented for the non-conventional nonlinear normal modes. We confirm the analytical results by numerical simulation and demonstrate the alternate transitions between regular and chaotic dynamics mentioned above. The origin of the chaotic behavior is also discussed.

Analyzing the forces binding a restriction endonuclease to DNA using a synthetic nanopore.

Restriction endonucleases are used prevalently in recombinant DNA technology because they bind so stably to a specific target sequence and, in the presence of cofactors, cleave double-helical DNA specifically at a target sequence at a high rate. Using synthetic nanopores along with molecular dynamics (MD), we have analyzed with atomic resolution how a prototypical restriction endonuclease, EcoRI, binds to the DNA target sequence--GAATTC--in the absence of a Mg(2+) ion cofactor. We have previously shown that there is a voltage threshold for permeation of DNA bound to restriction enzymes through a nanopore that is associated with a nanonewton force required to rupture the complex. By introducing mutations in the DNA, we now show that this threshold depends on the recognition sequence and scales linearly with the dissociation energy, independent of the pore geometry. To predict the effect of mutation in a base pair on the free energy of dissociation, MD is used to qualitatively rank the stability of bonds in the EcoRI-DNA complex. We find that the second base in the target sequence exhibits the strongest binding to the protein, followed by the third and first bases, with even the flanking sequence affecting the binding, corroborating our experiments.

Detecting SNPs using a synthetic nanopore.

We have discovered a voltage threshold for permeation through a synthetic nanopore of dsDNA bound to a restriction enzyme that depends on the sequence. Molecular dynamic simulations reveal that the threshold is associated with a nanonewton force required to rupture the DNA-protein complex. A single mutation in the recognition site for the restriction enzyme, i.e., a single nucleotide polymorphism (SNP), can easily be detected as a change in the threshold voltage. Consequently, by measuring the threshold voltage in a synthetic nanopore, it may be possible to discriminate between two variants of the same gene (alleles) that differ in one base.