Theory of end‐labeled free‐solution electrophoresis: Is the end effect important?

Abstract

In the theory of free-solution electrophoresis of a polyelectrolyte (such as the DNA) conjugated with a "drag-tag," the conjugate is divided into segments of equal hydrodynamic friction and its electrophoretic mobility is calculated as a weighted average of the mobilities of individual segments. If all the weights are assumed equal, then for an electrically neutral drag-tag, the elution time t is predicted to depend linearly on the inverse DNA length 1/M. While it is well-known that the equal-weights assumption is approximate and in reality the weights increase toward the ends, this "end effect" has been assumed to be small, since in experiments the t(1/M) dependence seems to be nearly perfectly linear. We challenge this assumption pointing out that some experimental linear fits do not extrapolate to the free (i.e. untagged) DNA elution time in the limit 1/M→0, indicating nonlinearity outside the fitting range. We show that a theory for a flexible polymer taking the end effect into account produces a nonlinear curve that, however, can be fitted with a straight line over a limited range of 1/M typical of experiments, but with a "wrong" intercept, which explains the experimental results without additional assumptions. We also study the influence of the flexibilities of the charged and neutral parts.

Electrophoresis of Heteropolymers. Effect of Stiffness

“…The optimal value of the bead radius was found to be a ≈ 0.25b for a Gaussian chain. 28 For a freely jointed chain with a constant segment length equal to b, we find the optimal a ≈ 0.20b.…”

“…The results of the mobility calculation should depend, at least in principle, on the choice of the bead radius a (which enters the equation for the diagonal element of the HI tensor, eq 3) and the distance b between the beads along the chain. The issue of choosing a and b was discussed in ref 28; here, we summarize that discussion, but also offer some additional considerations.…”

“…We recently applied the approach of Long et al to a perfectly stiff rodlike polymer. 28 We found that while the weights still diverge at the ends, this divergence is only logarithmic and, in fact, the end effect decreases as the polymer gets longer (see eq 26 below). This demonstrated that the effect of stiffness can be significant; but, of course, real polymers are semif lexible and in many cases of interest the persistence length, while non-negligible, is much smaller than the polymer length.…”

“…The average ⟨1/r ij ⟩ can be calculated analytically in simple cases (such as Gaussian chains and rigid rods 26,28 ), or numerically by sampling the conformational space of the polymer (the approach taken in this paper). Note that using a more complicated Rotne−Prager−Yamakawa (RPY) expression, 37 (22) which only differs from eq 19 when r ij < 2a, that is, when the beads i and j overlap.…”

Electrophoretic Mobility of Polyelectrolytes within a Confining Well

“…If the mechanical force acts only on the monomers and not on the counterions then the net force on the fluid does not cancel, long-ranged flows are possible and the chain is no longer free-draining [15]. This concept has been applied to many situations [12] including tethered polyelectrolytes [16] and end-labeled freesolution electrophoresis [17]. One oft-given example is the electrophoretic motion of a deformed polyelectrolyte through a nanofluidic channel [18][19][20] …”