We demonstrate the use of individual semiconducting single-wall carbon nanotubes as versatile biosensors. Controlled attachment of the redox enzyme glucose oxidase (GOx) to the nanotube sidewall is achieved through a linking molecule and is found to induce a clear change of the conductance. The enzyme-coated tube is found to act as a pH sensor with large and reversible changes in conductance upon changes in pH. Upon addition of glucose, the substrate of GOx, a steplike response can be monitored in real time, indicating that our sensor is also capable of measuring enzymatic activity at the level of a single nanotube. This first demonstration of nanotube-based biosensors provides a new tool for enzymatic studies and opens the way to biomolecular diagnostics.

We report charge inversion, the sign reversal of the effective surface charge in the presence of multivalent counterions, for the biologically relevant regimes of divalent ions and mixtures of monovalent and multivalent ions. Using streaming currents, the pressure-driven transport of countercharges in the diffuse layer, we find that charge inversion occurs in rectangular silica nanochannels at high concentrations of divalent ions. Strong monovalent screening is found to cancel charge inversion, restoring the original surface charge polarity. An analytical model based on ion correlations successfully describes our observations. DOI: 10.1103/PhysRevLett.96.224502 PACS numbers: 47.57.jd, 66.90.+r, 68.08.ÿp Screening by counterions is of fundamental importance in mediating electrostatic interactions in liquids. For multivalent counterions (Z ions, where Z is the ion valency including the sign), a counterintuitive phenomenon is observed: Screening not only reduces the effective surface charge, but it can also actually cause it to flip sign. This socalled charge inversion (CI) has been proposed to be biologically relevant in, e.g., DNA condensation, viral packaging, and drug delivery [1]. CI is not explained by conventional mean-field theories of screening. Recently, an analytical model was proposed that assumes that Z ions form a two-dimensional strongly correlated liquid (SCL) at charged surfaces [2]. This effect is particularly strong for high Z, and was confirmed experimentally for Z 3 and 4 [3]. Experimental evidence has remained inconclusive for the cases Z 2 and mixtures of Z ions with monovalent ions [4], both of which are biologically relevant given that K , Na , and Mg 2 are the most abundant cations in the cell. The main difficulty is that existing experimental probes become unreliable at high concentrations (*10 mM): Electrophoretic mobility measurements suffer from increasingly low signal to noise at higher salt, whereas surface force measurements are complicated by short-range forces.In this Letter, we investigate CI in individual silica nanochannels at high ionic strength by employing streaming currents as a new method. A streaming current is an ionic current that results from the pressure-driven transport of counterions in the diffuse part of the double layer [5], as illustrated in Fig. 1(b). The Stern layer, where the SCL is formed, is generally accepted to be immobile [6]. Consequently, streaming currents provide a direct measurement of the effective surface charge at the diffuse layer boundary. The well-defined rectangular channel geometry allows for straightforward interpretation. Contrary to other methods, streaming currents remain a reliable probe of the surface charge at high salt, up to 1 M in our experiments. We report unambiguous CI by divalent ions at concentrations above 400 mM. Additionally, we resolve the effect of screening by monovalent salt. We find that monovalent ions reduce CI by high-Z ions, and even cancel CI entirely at sufficiently high monovalent ion concentrations. We succ...

We have directly observed reversal of the polarity of charged surfaces in water upon the addition of trivalent and quadrivalent ions using atomic force microscopy. The bulk concentration of multivalent ions at which charge inversion reversibly occurs depends only very weakly on the chemical composition, surface structure, size, and lipophilicity of the ions, but is very sensitive to their valence. These results support the theoretical proposal that spatial correlations between ions are the driving mechanism behind charge inversion.

The condensation of stiff, highly charged DNA molecules into compact structures by condensing agents ranging from multivalent ions 1 to small cationic proteins 2,3 is of major biological and therapeutic importance 4,5 , yet the underlying microscopic mechanism remains poorly understood 1,6-9 . It has been proposed 7,10 that DNA condensation is a purely electrostatic phenomenon driven by the existence of a strongly correlated liquid (SCL) of counterions at the DNA surface. The same theoretical argument predicts that multivalent counterions overcompensate the DNA charge when present at high concentration 11 , in turn destabilizing the condensates 12 . Here, we demonstrate the occurrence of DNA charge inversion by multivalent ions through measurements of the electrophoretic mobility of condensed DNA. By observing the multivalent-ioninduced condensation of a single DNA molecule using magnetic tweezers, we further show that charge inversion influences condensation by modulating the barrier for condensate nucleation in a manner consistent with the SCL mechanism.The role played by spatial correlations of screening ions in biological systems remains poorly understood. Definitive experimental evidence is particularly difficult to obtain because of the short length scales involved. The strongly correlated liquid (SCL) mechanism predicts that charge inversion necessarily accompanies and influences counter-ion-induced like-charge attraction 12 , thus providing a unique opportunity to test this mechanism. We concentrate on DNA because of its high charge density, the level of experimental control that it provides and the direct relevance of condensation to genome packaging.To verify the existence of DNA charge inversion, we measured the electrophoretic mobility, µ, of DNA condensates in solution using dynamic light scattering (DLS). The mobility, µ, reflects the bare charge of DNA plus that of counterions at its surface, and its sign is expected to reverse on charge inversion [13][14][15] . In DLS, the phase of laser light scattered from the condensates is monitored over time; condensates drifting at constant velocity in an electric field yield a phase that evolves linearly in time at a rate proportional to their mobility. Figure 1a shows the measured phase for concentrations c = 0.1 and 3 mM of the quadrivalent cation spermine ([C 10 N 4 H 30 ] 4+ ). The two signals have opposite slopes, indicating a sign reversal of µ (negative for c = 0.1 mM and positive for c = 3 mM). This is to our knowledge the first experimental report of DNA charge inversion induced solely by simple multivalent ions. Figure 1b shows the measured mobility of condensed DNA as a function of the concentration of spermine and buffer conditions. In 1 mM TRIS buffer, the mobility is positive for spermine concentrations greater than the charge-inversion concentration c 0 = 0.5 mM. Increasing the TRIS buffer concentration to 10 mM hinders charge inversion, causing c 0 to increase to 1 mM. Further adding 50 mM monovalent KCl salt causes charge inversion to disa...

Charge inversion occurs when the effective charge of a surface exposed to solution reverses polarity due to an excess of counterions accumulating in the immediate vicinity of the surface. Using atomic force spectroscopy, we have directly measured the effect on charge inversion of changing the dielectric constant of the solvent and the surface-charge density. Both decreasing the dielectric constant and increasing the bare surfacecharge density lower the charge-inversion concentration. These observations are consistent with the theoretical proposal that spatial correlations between ions are the dominant driving mechanism for charge inversion.