Driven Polymer Translocation Through a Narrow Pore
TL;DR: There is a range of polymer lengths in which the system is approximately translationally invariant, and a coarse-grained description of this regime is developed, and general features of the distribution of times for the polymer to pass through the pore may be deduced.
Abstract: Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions. We show that there is a range of polymer lengths in which the system is approximately translationally invariant, and we develop a coarse-grained description of this regime. From this description, general features of the distribution of times for the polymer to pass through the pore may be deduced. We also introduce a more microscopic model. This model provides a physically reasonable scenario in which, as in experiments, the polymer's speed depends sensitively on its chemical composition, and even on its orientation in the channel. Finally, we point out that the experimental distribution of times for the polymer to pass through the pore is much broader than expected from simple estimates, and speculate on why this might be.
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Harvard University1, University of California, Santa Cruz2, University of British Columbia3, University of Oxford4, University of Washington5, University of California, San Diego6, Oak Ridge National Laboratory7, Arizona State University8, Brown University9, Case Western Reserve University10, Boston University11, University of North Carolina at Chapel Hill12, North Carolina State University13, National Institutes of Health14
TL;DR: A nanopore-based device provides single-molecule detection and analytical capabilities that are achieved by electrophoretically driving molecules in solution through a nano-scale pore, a unique analytical capability that makes inexpensive, rapid DNA sequencing a possibility.
Abstract: A nanopore-based device provides single-molecule detection and analytical capabilities that are achieved by electrophoretically driving molecules in solution through a nano-scale pore. The nanopore provides a highly confined space within which single nucleic acid polymers can be analyzed at high throughput by one of a variety of means, and the perfect processivity that can be enforced in a narrow pore ensures that the native order of the nucleobases in a polynucleotide is reflected in the sequence of signals that is detected. Kilobase length polymers (single-stranded genomic DNA or RNA) or small molecules (e.g., nucleosides) can be identified and characterized without amplification or labeling, a unique analytical capability that makes inexpensive, rapid DNA sequencing a possibility. Further research and development to overcome current challenges to nanopore identification of each successive nucleotide in a DNA strand offers the prospect of 'third generation' instruments that will sequence a diploid mammalian genome for ∼$1,000 in ∼24 h.
2,512 citations
TL;DR: In this paper, the authors investigated the transport properties of 50-nm-high 1D nanochannels on a chip and showed that they can be used for the separation and preconcentration of proteins.
Abstract: This thesis explores transport phenomena in nanochannels on a chip. Fundamental nanofluidic ionic studies form the basis for novel separation and preconcentration applications for proteomic purposes. The measurements were performed with 50-nm-high 1D nanochannels, which are easily accessible from both sides by two microchannels. Nanometer characteristic apertures were manufactured in the bonded structure of Pyrex-amorphous silicon – Pyrex, in which the thickness of the amorphous silicon layer serves as a spacer to define the height of the nanochannels. The geometry of the nanometer-sized apertures is well defined, which simplifies the modeling of the transport across them. Compared to biological pores, the present nanochannels in Pyrex offer increased stability. Fundamental characteristics of nanometer-sized apertures were obtained by impedance spectroscopy measurements of the nanochannel at different ionic strengths and pH values. A conductance plateau (on a log-log scale) was modeled and measured, establishing due to the dominance of the surface charge density in the nanochannels, which induces an excess of mobile counterions to maintain electroneutrality. The nanochannel conductance can be regulated at low ionic strengths by pH adjustment, and by an external voltage applied on the chip to change the zeta potential. This field-effect allows the regulation of ionic flow which can be exploited for the fabrication of nanofluidic devices. Fluorescence measurements confirm that 50-nm-high nanochannels show an exclusion of co-ions and an enrichment of counterions at low ionic strengths. This permselectivity is related to the increasing thickness of the electrical double layer (EDL) with decreasing salt concentrations, which results in an EDL overlap in an aperture if the height of the nanochannel and the thickness of the EDL are comparable in size. The diffusive transport of charged species and therefore the exclusion-enrichment effect was described with a simple model based on the Poisson-Boltzmann equation. The negatively charged Pyrex surface of the nanometer characteristic apertures can be inversed with chemical surface pretreatments, resulting in an exclusion of cations and an enrichment of anions. When a pressure gradient is applied across the nanochannels, charged molecules are electrostatically rejected at the entrance of the nanometer-sized apertures, which can be used for separation processes. Proteomic applications are presented such as the separation and preconcentration of proteins. The diffusion of Lectin proteins with different isoelectric points and very similar compositions were controlled by regulating the pH value of the buffer. When the proteins are neutral at their pI value, the diffusion coefficient is maximal because the biomolecules does not interact electrostatically with the charged surfaces of the nanochannel. This led to a fast separation of three Lectin proteins across the nanochannel. The pI values measured in this experiment are slightly shifted compared to the values obtained with isoelectric focusing because of reversible adsorption of proteins on the walls which affects the pH value in the nanochannel. An important application in the proteomic field is the preconcentration of biomolecules. By applying an electric field across the nanochannel, anionic and cationic analytes were preconcentrated on the cathodic side of the nanometer-sized aperture whereas on the anodic side depletion of ions was observed. This is due to concentration polarization, a complex of effects related to the formation of ionic concentration gradients in the electrolyte solution adjacent to an ion-selective interface. It was measured that the preconcentration factor increased with the net charge of the molecule, leading to a preconcentration factor of > 600 for rGFP proteins in 9 minutes. Such preconcentrations are important in micro total analysis systems to achieve increased detection signals of analytes contained in dilute solutions. Compared to cylindrical pores, our fabrication process allows the realization of nanochannels on a chip in which the exclusion-enrichment effect and a big flux across the nanometer-sized aperture can be achieved, showing the interest for possible micro total analysis system applications. The described exclusion-enrichment effect as well as concentration polarization play an important role in transport phenomena in nanofluidics. The appendix includes preliminary investigations in DNA molecule separation and fluorescence correlation spectroscopy measurements, which allows investigating the behavior of molecules in the nanochannel itself.
1,636 citations
TL;DR: The latest generations of sophisticated synthetic molecular machine systems in which the controlled motion of subcomponents is used to perform complex tasks are discussed, paving the way to applications and the realization of a new era of “molecular nanotechnology”.
Abstract: The widespread use of molecular machines in biology has long suggested that great rewards could come from bridging the gap between synthetic molecular systems and the machines of the macroscopic world. In the last two decades, it has proved possible to design synthetic molecular systems with architectures where triggered large amplitude positional changes of submolecular components occur. Perhaps the best way to appreciate the technological potential of controlled molecular-level motion is to recognize that nanomotors and molecular-level machines lie at the heart of every significant biological process. Over billions of years of evolution, nature has not repeatedly chosen this solution for performing complex tasks without good reason. When mankind learns how to build artificial structures that can control and exploit molecular level motion and interface their effects directly with other molecular-level substructures and the outside world, it will potentially impact on every aspect of functional molecule and materials design. An improved understanding of physics and biology will surely follow.
The first steps on the long path to the invention of artificial molecular machines were arguably taken in 1827 when the Scottish botanist Robert Brown observed the haphazard motion of tiny particles under his microscope.1,2 The explanation for Brownian motion, that it is caused by bombardment of the particles by molecules as a consequence of the kinetic theory of matter, was later provided by Einstein, followed by experimental verification by Perrin.3,4 The random thermal motion of molecules and its implications for the laws of thermodynamics in turn inspired Gedankenexperiments (“thought experiments”) that explored the interplay (and apparent paradoxes) of Brownian motion and the Second Law of Thermodynamics. Richard Feynman’s famous 1959 lecture “There’s plenty of room at the bottom” outlined some of the promise that manmade molecular machines might hold.5,6 However, Feynman’s talk came at a time before chemists had the necessary synthetic and analytical tools to make molecular machines. While interest among synthetic chemists began to grow in the 1970s and 1980s, progress accelerated in the 1990s, particularly with the invention of methods to make mechanically interlocked molecular systems (catenanes and rotaxanes) and control and switch the relative positions of their components.7−24
Here, we review triggered large-amplitude motions in molecular structures and the changes in properties these can produce. We concentrate on conformational and configurational changes in wholly covalently bonded molecules and on catenanes and rotaxanes in which switching is brought about by various stimuli (light, electrochemistry, pH, heat, solvent polarity, cation or anion binding, allosteric effects, temperature, reversible covalent bond formation, etc.). Finally, we discuss the latest generations of sophisticated synthetic molecular machine systems in which the controlled motion of subcomponents is used to perform complex tasks, paving the way to applications and the realization of a new era of “molecular nanotechnology”.
1.1. The Language Used To Describe Molecular Machines
Terminology needs to be properly and appropriately defined and these meanings used consistently to effectively convey scientific concepts. Nowhere is the need for accurate scientific language more apparent than in the field of molecular machines. Much of the terminology used to describe molecular-level machines has its origins in observations made by biologists and physicists, and their findings and descriptions have often been misinterpreted and misunderstood by chemists. In 2007 we formalized definitions of some common terms used in the field (e.g., “machine”, “switch”, “motor”, “ratchet”, etc.) so that chemists could use them in a manner consistent with the meanings understood by biologists and physicists who study molecular-level machines.14
The word “machine” implies a mechanical movement that accomplishes a useful task. This Review concentrates on systems where a stimulus triggers the controlled, relatively large amplitude (or directional) motion of one molecular or submolecular component relative to another that can potentially result in a net task being performed. Molecular machines can be further categorized into various classes such as “motors” and “switches” whose behavior differs significantly.14 For example, in a rotaxane-based “switch”, the change in position of a macrocycle on the thread of the rotaxane influences the system only as a function of state. Returning the components of a molecular switch to their original position undoes any work done, and so a switch cannot be used repetitively and progressively to do work. A “motor”, on the other hand, influences a system as a function of trajectory, meaning that when the components of a molecular motor return to their original positions, for example, after a 360° directional rotation, any work that has been done is not undone unless the motor is subsequently rotated by 360° in the reverse direction. This difference in behavior is significant; no “switch-based” molecular machine can be used to progressively perform work in the way that biological motors can, such as those from the kinesin, myosin, and dynein superfamilies, unless the switch is part of a larger ratchet mechanism.14
1,434 citations
TL;DR: In nanopore analytics, individual molecules pass through a single nanopore giving rise to detectable temporary blockades in ionic pore current, which ranges from nucleic acids, peptides, proteins, and biomolecular complexes to organic polymers and small molecules.
Abstract: In nanopore analytics, individual molecules pass through a single nanopore giving rise to detectable temporary blockades in ionic pore current. Reflecting its simplicity, nanopore analytics has gained popularity and can be conducted with natural protein as well as man-made polymeric and inorganic pores. The spectrum of detectable analytes ranges from nucleic acids, peptides, proteins, and biomolecular complexes to organic polymers and small molecules. Apart from being an analytical tool, nanopores have developed into a general platform technology to investigate the biophysics, physicochemistry, and chemistry of individual molecules (critical review, 310 references).
1,022 citations
TL;DR: A solid-state nanopore microscope capable of observing individual molecules of double-stranded DNA and their folding behaviour is demonstrated and extensions of the nanopore telescope concept to alternative probing mechanisms and applications are discussed, including the study of molecular structure and sequencing.
Abstract: A nanometre-scale pore in a solid-state membrane provides a new way of electronically probing the structure of single linear polymers, including those of biological interest in their native environments. Previous work with biological protein pores wide enough to let through and sense single-stranded DNA molecules demonstrates the power of using nanopores, but many future tasks and applications call for a robust solidstate pore whose nanometre-scale dimensions and properties may be selected, as one selects the lenses of a microscope. Here we demonstrate a solid-state nanopore microscope capable of observing individual molecules of double-stranded DNA and their folding behaviour. We discuss extensions of the nanopore microscope concept to alternative probing mechanisms and applications, including the study of molecular structure and sequencing.
999 citations
References
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Book•
15 Dec 1979
10,942 citations
"Driven Polymer Translocation Throug..." refers background in this paper
...There exists a considerable literature on the confinement of polymers in channels of diameter significantly larger than the polymers’ persistence length (de Gennes, 1979); well-developed scaling techniques can be used in the theoretical treatment of this regime....
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...ar X iv :p hy si cs /9 90 20 41 v1 [ ph ys ic s. bi oph ] 1 7 Fe b 19 99 Driven Polymer Translocation Through a Narrow Pore David K. Lubensky and David R. Nelson Department of Physics, Harvard University, Cambridge MA 02138 (February 2, 2008) Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an electric field, we study the diffusive motion of a polymer threaded through a narrow channel with which it may have strong interactions....
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...…ic s. bi oph ] 1 7 Fe b 19 99 Driven Polymer Translocation Through a Narrow Pore David K. Lubensky and David R. Nelson Department of Physics, Harvard University, Cambridge MA 02138 (February 2, 2008) Motivated by experiments in which a polynucleotide is driven through a proteinaceous pore by an…...
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...Modern polymer physics has achieved great success with models in which the polymer is regarded as a flexible, uniform “string” whose conformational entropy dominates the system’s behavior (de Gennes, 1979; Doi and Edwards, 1986)....
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...Our arguments assume that the parts of the polynucleotide outside the pore may be described by the theories usually applied to long, flexible polymers (de Gennes, 1979; Doi and Edwards, 1986); we thus ignore, for example, hydrogen-bonding and other specific interactions (Cantor and Schimmel, 1980)....
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Book•
01 Jan 1986
TL;DR: In this article, the viscoelasticity of polymeric liquids was studied in the context of rigid rod-like polymers and concentrated solutions of rigid rods like polymers.
Abstract: Introduction Static properties of polymers Brownian motion Dynamics of flexible polymers in dilute solution Many chain systems Dynamics of a polymer in a fixed network Molecular theory for the viscoelasticity of polymeric liquids Dilute solutions of rigid rodlike polymers Semidilute solutions of rigid rodlike polymers Concentrated solutions of rigid rodlike polymers Index.
10,225 citations
"Driven Polymer Translocation Throug..." refers background or methods in this paper
...Modern polymer physics has achieved great success with models in which the polymer is regarded as a flexible, uniform “string” whose conformational entropy dominates the system’s behavior (de Gennes, 1979; Doi and Edwards, 1986)....
[...]
...Our arguments assume that the parts of the polynucleotide outside the pore may be described by the theories usually applied to long, flexible polymers (de Gennes, 1979; Doi and Edwards, 1986); we thus ignore, for example, hydrogen-bonding and other specific interactions (Cantor and Schimmel, 1980)....
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...However, even with the longest available chains, ν is never observed experimentally to be larger than 0.55 (Doi and Edwards, 1986), so we use this value for specific numerical calculations....
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01 Jan 1992
Abstract: Preface to the first edition. Preface to the second edition. Abbreviated references. I. Stochastic variables. II. Random events. III. Stochastic processes. IV. Markov processes. V. The master equation. VI. One-step processes. VII. Chemical reactions. VIII. The Fokker-Planck equation. IX. The Langevin approach. X. The expansion of the master equation. XI. The diffusion type. XII. First-passage problems. XIII. Unstable systems. XIV. Fluctuations in continuous systems. XV. The statistics of jump events. XVI. Stochastic differential equations. XVII. Stochastic behavior of quantum systems.
6,887 citations
"Driven Polymer Translocation Throug..." refers background or methods in this paper
...This calculation can be formulated as one of a wellstudied class of problems known as first-passage problems (Risken, 1984; van Kampen, 1992)....
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...Approximate formulas based on the Kramers escape rate (van Kampen, 1992) should then apply....
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TL;DR: In this article, the authors consider the specific effects of a bias on anomalous diffusion, and discuss the generalizations of Einstein's relation in the presence of disorder, and illustrate the theoretical models by describing many physical situations where anomalous (non-Brownian) diffusion laws have been observed or could be observed.
3,383 citations
"Driven Polymer Translocation Throug..." refers background in this paper
...Such a random force, however small, would in principle result in anomalous diffusion on sufficiently long length scales (Bouchaud and Georges, 1990; Fisher et al., 1998)....
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...It is known that one-dimensional diffusion becomes anomalous when [U(x) − U(0)]2 → ∞ as x→ ∞, where the overbar indicates an average with respect to the random distribution of bases (Bouchaud and Georges, 1990; le Doussal and Vinokur, 1995; Scheidl, 1995)....
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...Once all four possible situations have been explored experimentally, however, it should be possible, for example, to estimate the value of α by comparing data for the appropriate pairs of situations....
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...Since it is known that diffusion in random media can be qualitatively different from diffusion in ordered systems (Bouchaud and Georges, 1990), it is worth asking whether we expect any important changes when the homopolymer is replaced by a random heteropolymer....
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TL;DR: It is shown that an electric field can drive single-stranded RNA and DNA molecules through a 2.6-nm diameter ion channel in a lipid bilayer membrane, which could in principle provide direct, high-speed detection of the sequence of bases in single molecules of DNA or RNA.
Abstract: We show that an electric field can drive single-stranded RNA and DNA molecules through a 2.6-nm diameter ion channel in a lipid bilayer membrane. Because the channel diameter can accommodate only a single strand of RNA or DNA, each polymer traverses the membrane as an extended chain that partially blocks the channel. The passage of each molecule is detected as a transient decrease of ionic current whose duration is proportional to polymer length. Channel blockades can therefore be used to measure polynucleotide length. With further improvements, the method could in principle provide direct, high-speed detection of the sequence of bases in single molecules of DNA or RNA.
3,251 citations
"Driven Polymer Translocation Throug..." refers background in this paper
...For example, Kasianowicz, Brandin, Branton, and Deamer (hereafter KBBD) have recently detected single strands of RNA (polyuridylic acid) passing through a 1.5 nm pore formed by a membrane-bound protein (Kasianowicz et al., 1996)....
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