Alexander Y. Grosberg

Electrostatic focusing of unlabelled DNA into nanoscale pores using a salt gradient.

Solid-state nanopores are sensors capable of analyzing individual unlabelled DNA molecules in solution. While the critical information obtained from nanopores (e.g., DNA sequence) is the signal collected during DNA translocation, the throughput of the method is determined by the rate at which molecules arrive and thread into the pores. Here we study the process of DNA capture into nanofabricated silicon nitride pores of molecular dimensions. For fixed analyte concentrations we find an increase in capture rate as the DNA length increases from 800 to 8,000 basepairs, a length-independent capture rate for longer molecules, and increasing capture rates when ionic gradients are established across the pore. In addition, we show that application of a 20-fold salt gradient enables detection of picomolar DNA concentrations at high throughput. The salt gradients enhance the electric field, focusing more molecules into the pore, thereby advancing the possibility of analyzing unamplified DNA samples using nanopores.

On the transition coordinate for protein folding

To understand the kinetics of protein folding, we introduce the concept of a “transition coordinate” which is defined to be the coordinate along which the system progresses most slowly. As a practical implementation of this concept, we define the transmission coefficient for any conformation to be the probability for a chain with the given conformation to fold before it unfolds. Since the transmission coefficient can serve as the best possible measure of kinetic distance for a system, we present two methods by which we can determine how closely any parameter of the system approximates the transmission coefficient. As we determine that the transmission coefficient for a short-chain heteropolymer system is dominated by entropic factors, we have chosen to illustrate the methods mentioned by applying them to geometrical properties of the system such as the number of native contacts and the looplength distribution. We find that these coordinates are not good approximations of the transmission coefficient and therefore, cannot adequately describe the kinetics of protein folding.

Pathways for protein folding: is a new view needed?

Theoretical studies using simplified models of proteins have shed light on the general heteropolymeric aspects of the folding problem. Recent work has emphasized the statistical aspects of folding pathways. In particular, progress has been made in characterizing the ensemble of transition state conformations and elucidating the role of intermediates. These advances suggest a reconciliation between the new ensemble approaches and the classical view of a folding pathway.

Modeling the conductance and DNA blockade of solid-state nanopores

We present measurements and theoretical modeling of the ionic conductance G of solid-state nanopores with 5-100 nm diameters, with and without DNA inserted into the pore. First, we show that it is essential to include access resistance to describe the conductance, in particular for larger pore diameters. We then present an exact solution for G of an hourglass-shaped pore, which agrees very well with our measurements without any adjustable parameters, and which is an improvement over the cylindrical approximation. Subsequently we discuss the conductance blockade ΔG due to the insertion of a DNA molecule into the pore, which we study experimentally as a function of pore diameter. We find that ΔG decreases with pore diameter, contrary to the predictions of earlier models that forecasted a constant ΔG. We compare three models for ΔG, all of which provide good agreement with our experimental data.

Crumpled Globule Model of the Three-Dimensional Structure of DNA

We argue that in order to maintain the biological function of DNA confined inside the cell nucleus, its spatial structure has to be unknotted, of the so-called crumpled globule type. The fixation of a particular realization of this non-equilibrium structure by attractive interactions between specific units imposes a connection between the spatial structure of DNA and the statistical distribution of these units along the chain contour. This suggests that both primary sequence and spatial structure of native DNA were formed simultaneously by a self-similar evolution process. The predictions of our model are compared with recent observations of long-range correlations in intron-containing genes and non-transcribed regulatory elements and further experimental tests are proposed.

Fast Translocation of Proteins through Solid State Nanopores

Measurements on protein translocation through solid-state nanopores reveal anomalous (non-Smoluchowski) transport behavior, as evidenced by extremely low detected event rates; that is, the capture rates are orders of magnitude smaller than what is theoretically expected. Systematic experimental measurements of the event rate dependence on the diffusion constant are performed by translocating proteins ranging in size from 6 to 660 kDa. The discrepancy is observed to be significantly larger for smaller proteins, which move faster and have a lower signal-to-noise ratio. This is further confirmed by measuring the event rate dependence on the pore size and concentration for a large 540 kDa protein and a small 37 kDa protein, where only the large protein follows the expected behavior. We dismiss various possible causes for this phenomenon and conclude that it is due to a combination of the limited temporal resolution and low signal-to-noise ratio. A one-dimensional first-passage time-distribution model supports this and suggests that the bulk of the proteins translocate on time scales faster than can be detected. We discuss the implications for protein characterization using solid-state nanopores and highlight several possible routes to address this problem.

Equilibrium swelling properties of polyampholytic hydrogels

The role of counter ions and ion dissociation in establishing the equilibrium swelling of balanced and unbalanced polyampholytic hydrogels has been investigated experimentally and theoretically. The swelling dependence on both the net charge offset and the external bath salt concentration has been examined using an acrylamide based polyampholytic hydrogels. By careful consideration of the swelling kinetics, we illustrate the effects of ion dissociation equilibria and counter ion shielding in polyampholytic hydrogels near their balance point where both polyelectrolyte and polyampholyte effects are present. The theory considers a Flory type swelling model where the Coulombic interactions between fixed ions in the hydrogel resemble those of an ionic solid with a Debye screening factor. Theoretical predictions from this model are in qualitative agreement with our experimental results.

Closed loops of nearly standard size: common basic element of protein structure

By screening the crystal protein structure database for close Cα–Cα contacts, a size distribution of the closed loops is generated. The distribution reveals a maximum at 27±5 residues, the same for eukaryotic and prokaryotic proteins. This is apparently a consequence of polymer statistic properties of protein chain trajectory. That is, closure into the loops depends on the flexibility (persistence length) of the chain. The observed preferential loop size is consistent with the theoretical optimal loop closure size. The mapping of the detected unit‐size loops on the sequences of major typical folds reveals an almost regular compact consecutive arrangement of the loops. Thus, a novel basic element of protein architecture is discovered; structurally diverse closed loops of the particular size.

From a melt of rings to chromosome territories: the role of topological constraints in genome folding

We review pro and contra of the hypothesis that generic polymer properties of topological constraints are behind many aspects of chromatin folding in eukaryotic cells. For that purpose, we review, first, recent theoretical and computational findings in polymer physics related to concentrated, topologically simple (unknotted and unlinked) chains or a system of chains. Second, we review recent experimental discoveries related to genome folding. Understanding in these fields is far from complete, but we show how looking at them in parallel sheds new light on both.

Statistics of Knots, Geometry of Conformations, and Evolution of Proteins

Like shoelaces, the backbones of proteins may get entangled and form knots. However, only a few knots in native proteins have been identified so far. To more quantitatively assess the rarity of knots in proteins, we make an explicit comparison between the knotting probabilities in native proteins and in random compact loops. We identify knots in proteins statistically, applying the mathematics of knot invariants to the loops obtained by complementing the protein backbone with an ensemble of random closures, and assigning a certain knot type to a given protein if and only if this knot dominates the closure statistics (which tells us that the knot is determined by the protein and not by a particular method of closure). We also examine the local fractal or geometrical properties of proteins via computational measurements of the end-to-end distance and the degree of interpenetration of its subchains. Although we did identify some rather complex knots, we show that native conformations of proteins have statistically fewer knots than random compact loops, and that the local geometrical properties, such as the crumpled character of the conformations at a certain range of scales, are consistent with the rarity of knots. From these, we may conclude that the known “protein universe” (set of native conformations) avoids knots. However, the precise reason for this is unknown—for instance, if knots were removed by evolution due to their unfavorable effect on protein folding or function or due to some other unidentified property of protein evolution.