Observation of branched flow of light.

When waves propagate through a weak disordered potential with correlation length larger than the wavelength, they form channels (branches) of enhanced intensity that keep dividing as the waves propagate1. This fundamental wave phenomenon is known as branched flow. It was first observed for electrons1-6 and for microwave cavities7,8, and it is generally expected for waves with vastly different wavelengths, for example, branched flow has been suggested as a focusing mechanism for ocean waves9-11, and was suggested to occur also in sound waves12 and ultrarelativistic electrons in graphene13. Branched flow may act as a trigger for the formation of extreme nonlinear events14-17 and as a channel through which energy is transmitted in a scattering medium18. Here we present the experimental observation of the branched flow of light. We show that, as light propagates inside a thin soap membrane, smooth thickness variations in the film act as a correlated disordered potential, focusing the light into filaments that display the features of branched flow: scaling of the distance to the first branching point and the probability distribution of the intensity. We find that, counterintuitively, despite the random variations in the medium and the linear nature of the effect, the filaments remain collimated throughout their paths. Bringing branched flow to the field of optics, with its full arsenal of tools, opens the door to the investigation of a plethora of new ideas such as branched flow in nonlinear media, in curved space or in active systems with gain. Furthermore, the labile nature of soap films leads to a regime in which the branched flow of light interacts and affects the underlying disorder through radiation pressure and gradient force.

Effective Stiffness of Hydrated Atomic Force Microscopy Tips.

When generating force curves with atomic force microscopy (AFM), the conventional assumption is that the silicon tip's apex is infinitely stiffer than the force gradient acting between the apex and test object. Although true for measurements in vacuum or at long distances, we show this assumption fails badly at short distances in aqueous environments. In this case, the effective apex is an adsorbed water molecule, bound by a weak O-H···O-H H-bond. At short distances, the magnitude of the force gradient exceeds the stiffness of this bond. This causes conventional AFM measurements to be dominated by the mechanical H-bond stiffness, instead of the force gradient. Here, we introduce a new multifrequency technique that is able to measure the surface force gradient independently from the H-bond. We compare our results to conventional FM-AFM and show that due to the H-bond, FM-AFM can give extremely erroneous measurements and even the wrong force polarity.

Thermodynamics of Charge Regulation near Surface Neutrality.

The interaction between two adjacent charged surfaces immersed in aqueous solution is known to be affected by charge regulation─the modulation of surface charge as two charged surfaces approach each other. This phenomenon is particularly important near surface neutrality where the stability of objects such as colloids or biomolecules is jeopardized. Focusing on this ubiquitous case, we elucidate the underlying thermodynamics and show that charge regulation is governed in this case by surface entropy. We derive explicit expressions for charge regulation and formulate a new universal limiting law for the free energy of ion adsorption to the surfaces. The latter turns out to be proportional to kBT, and independent of the association energy of ions to surface groups. These new results are applied to the analysis of unipolar as well as amphoteric surfaces such as oxides near their point of zero charge or proteins near their isoelectric point.

Sequence-Dependent Deviations of Constrained DNA from Canonical B-Form.

Decades of crystallographic and NMR studies have produced canonical structural models of short DNA. However, no experimental method so far has been able to test these models in vivo, where DNA is long and constrained by interactions with membranes, proteins, and other molecules. Here, we employ high-resolution frequency-modulation AFM to image single long poly(dA)-poly(dT), poly(dG)-poly(dC), and lambda DNA molecules interacting with an underlying substrate that emulates the effect of biological constraints on molecular structure. We find systematic sequence-dependent variations in groove dimensions, indicating that the structure of DNA subject to realistic interactions may differ profoundly from canonical models. These findings highlight the value of AFM as a unique, single molecule characterization tool.

Common Source of Cryoprotection and Osmoprotection by Osmolytes.

While recent studies clarify the effect of osmolytes on Coulomb interaction at elevated concentrations of salt, little is known about the way osmolytes affect the same interaction in cryoprotection. In this Communication we explore the effect of cold on the interaction between two charged surfaces immersed in ternary solution containing salt and osmolyte and find that the effect of cold parallels that of excess salt, i.e., low temperatures increase adsorption of salt counterions to the surface, thus neutralizing it. Two osmolytes, proline and glycine-betaine, are then shown to recharge the surface by releasing the adsorbed counterions. The ability to counteract effects of both cold and excess salt on Coulomb interactions renders these known osmolytes cryoprotectants as well as osmoprotectants, explaining why plants, fish, insects and bacteria accumulate them in response to either drought or cold stress.

Multiply Modified Repeating DNA Templates for Production of Novel DNA-Based Nanomaterial.

Here, we report synthesis of long (thousands of base pairs), uniform double-stranded (ds) DNA comprising short (6-15 base pairs) tandem repeats. The synthesis method is based on self-assembly of short (6-15 bases) half-complementary 5'-end phosphorylated single-stranded oligonucleotides into long ds polymer molecules and covalent association of the oligonucleotide fragments in the polymer by DNA ligase to yield complete non-nicked ds DNA. The method is very flexible in regard to the sequence of the oligonucleotides and their length. Human telomeric DNA comprising thousands of base pairs as well as methylated, mismatched, and fluorescent dye-modified uniform dsDNA molecules can be synthesized. We have demonstrated by high resolution frequency-modulation atomic force microscopy that the structure of DNA containing mismatches is strongly different from that of the non-mismatched one. The DNA molecules comprising groups capable of anchoring metal particles and other redox active elements along the whole length of the nucleic acid polymer should find use as wires or transistors in future nanoelectronic applications.

Hydration Structure of a Single DNA Molecule Revealed by Frequency-Modulation Atomic Force Microscopy.

Hydration interaction shapes biomolecules and is a dominant intermolecular force. Mapping the hydration patterns of biomolecules is therefore essential for understanding molecular processes in biology. Numerous studies have been devoted to this challenge, but current methods cannot map the hydration of single biomolecules, let alone do so under physiological conditions. Here, we show that frequency-modulation atomic force microscopy (FM-AFM) can fill this gap and generate 3D hydration maps of single DNA molecules under near-physiological conditions. Additionally, we present real-space images of DNA in which the double helix is resolved with unprecedented resolution, clearly revealing individual phosphate groups along the DNA backbone. FM-AFM therefore emerges as a powerful enabling tool in the study of individual biomolecules and their hydration under physiological conditions.

Three-Dimensional Characterization of Layers of Condensed Gas Molecules Forming Universally on Hydrophobic Surfaces.

Understanding the solvation layer of hydrophobic surfaces is essential for elucidating the interaction between hydrophobic surfaces in aqueous solutions. Despite their importance, little is known on these layers due to the lack of lateral resolution in spectroscopic or scattering experiments and probe instability in the static scanning probe methods used in most experiments. Using a high-resolution FM-AFM with stiff cantilevers and hydrophilic tips, we overcome this instability to provide the first detailed 3d maps of the solvation/hydration layer of two archetypal hydrophobic surfaces: graphite (HOPG) and self-assembled fluoro-alkane monolayer (FDTS). In degassed solutions we find different tip-surface interactions for the two surfaces; hydration oscillations superimposed on van der Waals attraction with HOPG and electrostatic repulsion with FDTS. Both are similar to interactions observed with hydrophilic surfaces. In solutions equilibrated with atmospheric air or high-pressure nitrogen, the tip-surface interaction changes dramatically, disclosing the formation of a 2-5 nm thick layer of condensed gas molecules adsorbed to the hydrophobic surfaces. This layer leads to strikingly similar tip-surface interactions for HOPG and FDTS with only weak dependence upon the concentration of dissolved gas molecules, indicating universality in the way hydrophobic surfaces present themselves to nondegassed aqueous solutions. Measurements at low cantilever oscillation amplitudes reveal the inner structure of the layer of condensed gas molecules with an average distance between its constituents, 0.5-0.8 nm, agreeing with recent molecular dynamics calculations. In addition to the uniform condensed layers, we probe sparse nanobubbles found on the surface. Those show distinct interaction with the tip, different from that with the flat layer.

Zwitterionic Osmolytes Resurrect Electrostatic Interactions Screened by Salt.

Many cells synthesize significant quantities of zwitterionic osmolytes to cope with the osmotic stress induced by excess salt. In addition to their primary role in balancing osmotic pressure, these osmolytes also help stabilize protein structure and restore enzymatic activity compromised by high ionic strength. This osmoprotective effect has been studied extensively, but its electrostatic aspects have somehow escaped the mainstream. Here, we report that, despite their overall neutrality, zwitterions may dramatically affect electrostatic interactions in saline solutions of biological relevance. Using atomic force microscopy, we study the combined effect of osmolytes and salts on electrostatic interactions between two negatively charged silica surfaces in mixtures of five salts (NaCl, KCl, CsCl, MgCl2, and CaCl2) and five zwitterionic osmolytes (betaine, proline, trimethylamine N-oxide, glycine, and sarcosine) as a function of solutes concentration and pH. All osmolytes are found to counteract the screening effect of salt on electrostatic repulsion, albeit to a different extent. They do so by both increasing the screening length shortened by added salts and by desorbing bound protons and cations, hence enhancing the negative surface charge. Both effects are traced to the osmolytes' higher molecular polarizability compared with water. In addition to this direct effect on the solution's dielectric constant, we identify an osmolytic Hofmeister effect with the more hydrophobic osmolytes more efficiently desorbing weakly hydrated cations from weakly hydrated silica and the less hydrophobic osmolytes better desorbing strongly hydrated cations from strongly hydrated silica. The combined results shed light on Coulomb interactions in a more realistic model of the cytosol, a relatively unexplored territory.

Regulation of Surface Charge by Biological Osmolytes.

Osmolytes, small molecules synthesized by all organisms, play a crucial role in tuning protein stability and function under variable external conditions. Despite their electrical neutrality, osmolyte action is entwined with that of cellular salts and protons in a mechanism only partially understood. To elucidate this mechanism, we utilize an ultrahigh-resolution frequency modulation-AFM for measuring the effect of two biological osmolytes, urea and glycerol, on the surface charge of silica, an archetype protic surface with a pK value similar to that of acidic amino acids. We find that addition of urea, a known protein destabilizer, enhances silica's surface charge by more than 50%, an effect equivalent to a 4-unit increase of pH. Conversely, addition of glycerol, a protein stabilizer, practically neutralizes the silica surface, an effect equivalent to 2-units' reduction of pH. Simultaneous measurements of the interfacial liquid viscosity indicate that urea accumulates extensively near the silica surface, while glycerol depletes there. Comparison between the measured surface charge and Gouy-Chapman-Stern model for the silica surface shows that the modification of surface charge is 4 times too large to be explained by the change in dielectric constant upon addition of urea or glycerol. The model hence leads to the conclusion that surface charge is chiefly governed by the effect of osmolytes on the surface reaction constants, namely, on silanol deprotonation and on cation binding. These findings highlight the unexpectedly large effect that neutral osmolytes may have on surface charging and Coulomb interactions.

New Information on the Hydrophobic Interaction Revealed by Frequency Modulation AFM.

Using ultrahigh resolution atomic force microscopy (AFM) operated in frequency modulation mode, we extend existing measurements of the force acting between hydrophobic surfaces immersed in water in three essential ways. (1) The measurement range, which was previously limited to distances longer than 2-3 nm, is extended to cover all distances, down to contact. The measurements disclose that the long-range attraction observed also by conventional techniques, turns at distances shorter than 1-2 nm into pronounced repulsion. (2) Simultaneous measurements of the dissipative component of the tip-surface interaction reveal an anomalously large dissipation commencing abruptly at the point where attraction begins. The dissipation is more than 2 orders of magnitude larger than expected from bulk water viscosity or from similar measurements between hydrophilic surfaces. (3) The short-range repulsion is oscillatory, indicating molecular ordering of the medium as the hydrophobic surfaces approach each other. The oscillation period, ∼0.5 nm, is larger than the ∼0.3 nm period observed with hydrophilic surfaces. Their range, ∼1.5 nm, is longer as well. These observations are consistent with a conspicuous change in the properties of the surrounding medium, taking place simultaneously with the onset of attraction as the two surfaces approach each other.

On the limited recognition of inorganic surfaces by short peptides compared with antibodies.

The vast potential applications of biomolecules that bind inorganic surfaces led mostly to the isolation of short peptides that target selectively specific materials. The demonstrated differential affinity toward certain surfaces created the impression that the recognition capacity of short peptides may match that of rigid biomolecules. In the following, we challenge this view by comparing the capacity of antibody molecules to discriminate between the (100) and (111A) facets of a gallium arsenide semiconductor crystal with the capacity of short peptides to do the same. Applying selection from several peptide and single chain phage display libraries, we find a number of antibody molecules that bind preferentially a given crystal facet but fail to isolate, in dozens of attempts, a single peptide capable of such recognition. The experiments underscore the importance of rigidity to the recognition of inorganic flat targets and therefore set limitations on potential applications of short peptides in biomimetics.

The governing role of surface hydration in ion specific adsorption to silica: an AFM-based account of the Hofmeister universality and its reversal.

AFM measurements of the force acting between silica surfaces in the presence of varied alkali chloride salts and pH's elucidate the origin of the Hofmeister adsorption series and its reversal. At low pH, electrostatics is shown to be insignificant. The preferential adsorption of Cs(+) to the silica surface is traced to the weak hydration of neutral silanols and the resulting hydrophobic expulsion of weakly hydrated ions from bulk solution to the interface. The same interactions keep the strongly hydrated Na(+) and Li(+) in solution. As pH is increased, a tightly bound hydration layer forms on deprotonating silanols. Cs(+) is correspondingly expelled from the surface, and adsorption of small ions is encouraged. The deduced role of surface hydration is corroborated by hydration repulsion observed at high pH, surface overcharging at low pH, and data in other oxides.

Mixed alkanethiol monolayers on submicrometric gold patterns: a controlled platform for studying cell-ligand interactions.

Nanoscale organization of surface ligands often has a critical effect on cell-surface interactions. We have developed an experimental system that allows a high degree of control over the 2-D spatial distribution of ligands. As a proof of concept, we used the developed system to study how T-cell activation is independently affected by antigen density and antigen amount per cell. Arrays of submicrometer gold islands at varying surface coverage were defined on silicon by electron beam lithography (EBL). The gold islands were functionalized with alkanethiol self-assembled monolayers (SAMs) containing a small antigen, 2,4,6-trinotrophenyl (TNP), at various densities. Genetically engineered T-cell hybridomas expressing TNP-specific chimeric T-cell antigen receptor (CAR) were cultured on the SAMs, and their activation was assessed by IL-2 secretion and CD69 expression. It was found that, at constant antigen density, activation increased monotonically with the amount of antigen, while at constant antigen amount activation was maximal at an intermediate antigen density, whose value was independent of the amount of antigen.

Charge regulation indicates water expulsion from silica surface by cesium cations.

HYPOTHESIS: Since the discovery of the Hofmeister effect in 1888, the varied propensity of ions to proteins, DNA and other surfaces has motivated research aimed at deciphering the underlying ion specific adsorption mechanism. Experimental and numerical studies have shown that in agreement with Collins' heuristic law of matching water affinity, weakly hydrated (chaotropic) ions adsorb preferentially to hydrophobic surfaces. Here, we show that this preference is driven by expulsion of bound water molecules from the surface by the adsorbing ions. EXPERIMENTS: Using AFM spectroscopy of the force acting between two silica surfaces, we characterize surface charge regulation by adsorbed Na+ and Cs+ ions at different salt concentrations, pH values and temperatures. These data are analyzed in the framework of a recent theory of charge regulation, relating it to change in surface entropy. FINDINGS: Upon binding to the silica, cesium cations expel water molecules from the surface to create additional adsorption sites for more ions. Cs+ adsorption is thus driven by the release of hydrating water molecules and the resulting increased surface entropy. The model indicates that on average, the binding of three cesium cations releases enough water molecules to make room for two additional bound cations. Na+ does not exhibit such behavior.

Electrically controlled molecular recognition harnessed to activate a cellular response.

Seamless embedment of electronic devices in biological systems is expected to add the outstanding computing power, memory, and speed of electronics to the biochemical toolbox of nature. Such amalgamation requires transduction of electronic signals into biochemical cues that affect cells. Inspired by biology, where pathways are directed by molecular recognition, we propose and demonstrate a generic electrical-to-biological transducer comprising a two-state electronic antigen and a chimeric cell receptor engineered to bind the antigen exclusively in its "on" state. T-cells expressing these receptors remain inactivated with the antigen in its "off" state. Switching the antigen to its "on" state by an electrical signal leads to its recognition by the T-cells and correspondingly to cell activation.

Effect of cation size and charge on the interaction between silica surfaces in 1:1, 2:1, and 3:1 aqueous electrolytes.

Application of two complementary AFM measurements, force vs separation and adhesion force, reveals the combined effects of cation size and charge (valency) on the interaction between silica surfaces in three 1:1, three 2:1, and three 3:1 metal chloride aqueous solutions of different concentrations. The interaction between the silica surfaces in 1:1 and 2:1 salt solutions is fully accounted for by ion-independent van der Waals (vdW) attraction and electric double-layer repulsion modified by cation specific adsorption to the silica surfaces. The deduced ranking of mono- and divalent cation adsorption capacity (adsorbability) to silica, Mg(2+) < Ca(2+) < Na(+) < Sr(2+) < K(+) < Cs(+), follows cation bare size as well as cation solvation energy but does not correlate with hydrated ionic radius or with volume or surface ionic charge density. In the presence of 3:1 salts, the coarse phenomenology of the force between the silica surfaces as a function of salt concentration resembles that in 1:1 and 2:1 electrolytes. Nevertheless, two fundamental differences should be noticed. First, the attraction between the silica surfaces is too large to be attributed solely to vdW force, hence implying an additional attraction mechanism or gross modification of the conventional vdW attraction. Second, neutralization of the silica surfaces occurs at trivalent cation concentrations that are 3 orders of magnitude smaller than those characterizing surface neutralization by mono- and divalent cations. Consequently, when trivalent cations are added to our cation adsorbability series the correlation with bare ion size breaks down abruptly. The strong adsorbability of trivalent cations to silica contrasts straightforward expectations based on ranking of the cationic solvation energies, thus suggesting a different adsorption mechanism which is inoperative or weak for mono- and divalent cations.

A constant-frequency feedback loop for non-contact frequency-modulated atomic force microscopy via root locus: Implemented on a single-board field-programmable gate array device.

Non-contact, frequency modulated atomic force microscopy is often operated in the constant-frequency mode to obtain a height map of the sample's surface. Once linearized, the dynamics of the constant-frequency closed-loop system are reduced to a single transfer function. By modifying the bandwidth of this transfer function, a tradeoff is achieved between image noise and imaging speed. In this article, a new constant-frequency feedback loop is developed, utilizing the self-excitation technique for resonating the cantilever. Along with the proposed controller, it will be shown with the root locus that one needs to vary a single parameter, the loop gain, to modify the closed-loop bandwidth. The result is a robust, low-order, real-poled, feedback loop that is very easy to tune. The methodology is validated experimentally on a single-board field-programmable gate array device.

Accurate, explicit formulae for higher harmonic force spectroscopy by frequency modulation-AFM.

The nonlinear interaction between an AFM tip and a sample gives rise to oscillations of the cantilever at integral multiples (harmonics) of the fundamental resonance frequency. The higher order harmonics have long been recognized to hold invaluable information on short range interactions but their utilization has thus far been relatively limited due to theoretical and experimental complexities. In particular, existing approximations of the interaction force in terms of higher harmonic amplitudes generally require simultaneous measurements of multiple harmonics to achieve satisfactory accuracy. In the present letter we address the mathematical challenge and derive accurate, explicit formulae for both conservative and dissipative forces in terms of an arbitrary single harmonic. Additionally, we show that in frequency modulation-AFM (FM-AFM) each harmonic carries complete information on the force, obviating the need for multi-harmonic analysis. Finally, we show that higher harmonics may indeed be used to reconstruct short range forces more accurately than the fundamental harmonic when the oscillation amplitude is small compared with the interaction range.

Autopilot for frequency-modulation atomic force microscopy.

One of the most challenging aspects of operating an atomic force microscope (AFM) is finding optimal feedback parameters. This statement applies particularly to frequency-modulation AFM (FM-AFM), which utilizes three feedback loops to control the cantilever excitation amplitude, cantilever excitation frequency, and z-piezo extension. These loops are regulated by a set of feedback parameters, tuned by the user to optimize stability, sensitivity, and noise in the imaging process. Optimization of these parameters is difficult due to the coupling between the frequency and z-piezo feedback loops by the non-linear tip-sample interaction. Four proportional-integral (PI) parameters and two lock-in parameters regulating these loops require simultaneous optimization in the presence of a varying unknown tip-sample coupling. Presently, this optimization is done manually in a tedious process of trial and error. Here, we report on the development and implementation of an algorithm that computes the control parameters automatically. The algorithm reads the unperturbed cantilever resonance frequency, its quality factor, and the z-piezo driving signal power spectral density. It analyzes the poles and zeros of the total closed loop transfer function, extracts the unknown tip-sample transfer function, and finds four PI parameters and two lock-in parameters for the frequency and z-piezo control loops that optimize the bandwidth and step response of the total system. Implementation of the algorithm in a home-built AFM shows that the calculated parameters are consistently excellent and rarely require further tweaking by the user. The new algorithm saves the precious time of experienced users, facilitates utilization of FM-AFM by casual users, and removes the main hurdle on the way to fully automated FM-AFM.