Web-based calculator for voltage-driven transport of polypeptides through nanopores
Voltage-driven transport of charged polyelectrolytes through nanopores perforating thin membranes is of contemporary technical importance due to its role in next-generation DNA sequencing. The forces governing voltage-driven transport of homogeneously charged polyelectrolytes such as DNA are reasonably well understood, because a constant transmembrane potential acts unidirectionally on a polyelectrolyte captured in a nanopore. In most practical situations, the electrostatic forces overwhelm thermal fluctuations on the time scales governing whole-polymer movements, and the polymer translocates with essentially unity probability.
When a heterogeneous linear charge density is introduced, the situation becomes much more complex. Translocation across the membrane (as opposed to retraction to the side from which molecule was captured) is no longer assured. Diffusion plays a much larger role, particularly when the voltage-derived forces are balanced by others, such as membrane adhesion, electrokinetic flow, and entropic forces.
This calculator derives from the modeling work given in the references, in which a fairly straightforward theory of polypeptide diffusion is optimized to measurements of the voltage-dependent interaction of α-synuclein with the Voltage-Dependent Anion Channel (VDAC). The theory involves building up a quasi-potential from the various forces in play:
Other forces, such as localized barriers or binding potential wells, could also be present. The current calculator includes barriers (error functions), Gaussians, and constant forces, but can easily be extended to include any contribution to the diffusion potential.
The escape times and probabilities are calculated by applying the Smoluchowski equation to the diffusion potential, assuming a position-independent diffusion constant.
The default calculator view is shown here:
The charge density plot shows the linear charge density of the polyelectrolyte, which determines its interaction with the transmembrane potential. The two curves show the sequence-dependent charge density (determined by the sequence controls) and the effective charge density (shown after modification with the pore characteristics, as set by the pore parameters controls). Use the “export” button to export these curves to a tab-separated text file.
The quasipotential plot shows the diffusion potential that serves as input to the Smoluchowski treatment for estimating first passage (escape) times. One curve is shown for each voltage calculated. Use the “export” button to export these curves to a tab-separated text file. Use the “Show injection points” checkbox to toggle a draggable slider that displays and controls the window used to search for injection points (see General parameters for more details), as shown here:
The results graphic shows the results of the Smoluchowski equation calculation. The controls on the bottom of the panel select the quantity to be plotted. The average escape time is what is typically measured in experiments. Using salt gradients (see references), the conditional escape times for retraction and translocation events can also be determined (the “average retraction time” or “average translocation time”). The retraction and translocation probabilities can also be plotted.
The results graphic can allow direct comparison of experimental data (given in a three-column format: voltage, average time, and uncertainty in the average time) to the calculated values. Use the “reverse polarity” button to reverse the polarity of the voltage axis for the loaded data to allow direct comparison to the calculation, which has a fixed polarity (positive voltages are relative to the trans side of the membrane).
Contains all of the controls for the quasipotential and calculation. Use the “Save” configuration button to export the entire configuration in a JSON format that can be re-loaded using the “Load” button. Experimental data loaded through the load data function are saved in the configuration file, but are not linked to the original experimental data file.
The calculation and quasipotential controls are divided into panels. The description of each follows.
The entropy controls extend the calculator to treat tethered polyelectrolytes (i.e. when translocation is known to be impossible).
The “Add new: “ button allows custom elements to be added to the quasipotential. These include barrier (error function), gaussian, and constant force elements. The fields are self-explanatory, so only “barrier” is shown here.
Each custom element can be removed from the calculation using the “delete” button.
A barrier element adds an error function of the given height (negative reduces the direction of the barrier), width (sigma), and position along the polypeptide. This is useful for membrane tethering. Two of them with equal and opposite heights can be combined to create a potential plateau.
A gaussian element adds a gaussian function of the specified height and width (sigma) at the specified position. Note that this is an unnormalized Gaussian; the height of the Gaussian will be equal to the height of the barrier at its maximum point.
A constant force element adds a constant slope to the quasipotential. The beginning and ending positions of the slope are specified by the controls, as is the magnitude of the force in pN. The conversion is 4.11 pN = 1 kT/nm at room temperature.