Understanding Nanoparticle Interaction with Cell Membranes

(left) Sabina Tatur, 
(right) Marco Maccarini











Authors: Sabina Tatur¹, Marco Maccarini²

Affiliation: 
¹Department of Physics, University of Illinois at Chicago, USA 
²CEA Grenoble, France.

Although metallic nanoparticles – small entities with dimensions of just a few nanometers – have already been used for the fabrication of lustre decorations in medieval ceramics from Mesopotamia [1], it took another millennium until Michael Faraday provided a first scientific description of their optical properties in his 1847 lecture [2]. But only the emergence of modern experimental techniques - developed in the past thirty to forty years - triggered a boost in the interdisciplinary area of research, development and industrial activity of nanotechnology and nanoscience [3]. Today, metallic nanoparticles, made of noble metals, magnetic or semiconducting materials are added to many consumer goods to revolutionize the product with unique properties.

The skyrocketing progress in nanotechnology in recent years promises a great benefit for our civilization. Yet, there is, at the same time, an increasing concern about their potential harmful side effects on health and environment, and too little research has been conducted in this field so far. One might suppose that the principal determinants of hazardous materials are the surface properties and the surface area to which organisms are exposed. However, a general extrapolation from known hazardous or non-hazardous materials is impracticable since the physicochemical properties of many nanomaterials and nanoparticles deviate considerably from those of bulk or molecular materials.

The first contact that nanomaterials have with any living organism, is always the plasma membrane, a ~5 nm thick lipid bilayer surrounding each animal or plant cell [4]. Lipid membranes are therefore biologically relevant models to study nanomaterial-cell interactions. Understanding the interaction between nanoparticles and cell membranes has two-fold importance in terms of the evaluation of nanosafety as well as the effectiveness of nanoparticles in medical applications.

In this context, we recently studied the interaction of gold nanoparticles (AuNPs) with model cell membranes and focused our research on the effect of surface charge on AuNP destiny and membrane integrity. Previous research in this field showed that the degree of membrane disruption by AuNPs depend on their concentration, size, surface modification and charge, as well as on the phase state of the lipid bilayer (gel or liquid phase) [5-9]. These studies were, however, only symptomatic and missing the attempt to understand the link between surface characteristics of cell membrane and AuNPs to the final destination of the AuNPs.

To provide insight into the fate of AuNPs and their impact on cell membrane integrity, we analyzed the interaction of cationic ammonium AuNPs and anionic carboxy AuNPs with model membranes of only one lipid component. The single component membranes allowed us to focus on the interaction of the AuNPs with the lipid phases, avoiding complications arising from changes in structure and organization of the lipid membrane as a result of additional components in the membrane. To further bypass the electrostatic interactions between the solid substrate, onto which the lipid membrane was deposited, and the lipid bilayer itself, we prepared double lipid bilayers, in which a second lipid bilayer floats on top of the first one. This kind of membrane system gave us access to a highly hydrated, fluctuating bilayer with dynamic properties comparable to natural cell membranes [10] and was, therefore, our model of choice for the examination of the structural integrity of the model membrane with insight into the fate of the AuNPs by neutron reflectometry.

Figure 1a: The sketch shows structural details of the lipid double bilayer after addition of 1 mg/ml (left) and 0.1 mg/ml (right) of cationic AuNPs. The addition of the higher concentration causes a disruption of the membrane, whereas the addition of the lower one causes the AuNPs to incorporate into the hydrophobic moiety of the membrane.

We found that the AuNPs functionalized with cationic head groups penetrated into the center of the lipid bilayers and caused membrane disruption (see Figure 1a) [11]. In contrast, the AuNPs functionalized with anionic head groups did not permeate through the membrane but rather impeded the disruption of the lipid bilayer at alkaline pH (see Figure 1b).

Figure 1b: The sketch shows structural details of the lipid double bilayer after the addition of 0.01 mg/ml of anionic AuNPs. At alkaline pH, the NPs shield the membrane from disintegration that would usually happen under these conditions.

We are now working on understanding the mechanism of this interaction and hope that our approach can provide a strategy for a prospective nanoparticle risk assessement based on a surface charge evaluation and can contribute to nano-safety considerations during their design.

By understanding how nanoparticles affect our environment and taking precautions accordingly, not only will we revolutionize our products but we will be able to benefit from them yet another millennium.



References:
[1] Philippe Colomban, “The use of metal nanoparticles to produce yellow, red and iridescent colour, from bronze age to present times in lustre pottery and glass: solid state chemistry, spectroscopy and nanostructure”, Journal of Nano Research, 8, 109-132 (2009). Abstract.
[2] Michael Faraday, “The Bakerian lecture: experimental relations of gold (and other metals) to light”, Philosophical Transactions of the Royal Society of London, 147, 145-181 (1847). Full Text.
[3] Chris Toumey, “The man who understood the Feynman machine”, Nature Nanotechnology, 2, 9-10 (2007). Abstract.
[4] Jeremy M Berg, John L Tymoczko, and Lubert Stryer, “Biochemistry”, W.H.Freeman and Company, 5th edition (2002). [5] Ralph A. Sperling, Pilar Rivera Gil, Feng Zhang, Marco Zanella, Wolfgang J. Parak, “Biological applications of gold nanoparticles”, Chemical Society Reviews, 37, 1896-1908 (2008). Abstract.
[6] Alaaldin M. Alkilany, Pratik K. Nagaria, Cole R. Hexel, Timothy J. Shaw, Catherine J. Murphy, Michael D. Wyatt, “Cellular Uptake and Cytotoxicity of Gold Nanorods: Molecular Origin of Cytotoxicity and Surface Effects”, small, 5, 701-708 (2009). Abstract.
[7] Nikolai Khlebtsov, Lev Dykman, “Biodistribution and toxicity of engineered gold nanoparticles: a review of in vitro and in vivo studies”, Chemical Society Reviews, 40, 1647-1671 (2011). Abstract.
[8] Pakatip Ruenraroengsak, Pavel Novak, Deborah Berhanu, Andrew J. Thorley, Eugenia Valsami-Jones, Julia Gorelik, Yuri E. Korchev, Teresa D. Tetley, “Respiratory epithelial cytotoxicity and membrane damage (holes) caused by amine-modified nanoparticles”, Nanotoxicology, 6, 94-108 (2012). Abstract.
[9] Atsushi Hirano, Hiroki Yoshikawa, Shuhei Matsushita, Yoichi Yamada, and Kentaro Shiraki, “Adsorption and Disruption of Lipid Bilayers by Nanoscale Protein Aggregates”, Langmuir, 28, 3887-3895 (2012). Abstract.
[10] Giovanna Fragneto, Thierry Charitat, Jean Daillant, “Floating lipid bilayers: models for physics and biology”, European Biophysics Journal, 41, 863-874 (2012). Abstract.
[11] Sabina Tatur, Marco Maccarini, Robert Barker, Andrew Nelson, Giovanna Fragneto, “Effect of functionalized gold nanoparticles on floating lipid bilayers”, Langmuir, 29, 6606-6614 (2013). Abstract.

Profiting from Nonlinearity and Interconnectivity to Control Networks

(left) Adilson Motter, (right) Sean Cornelius














Authors: Sean P. Cornelius¹ & Adilson E. Motter^1,2

Affiliation:
¹Department of Physics & Astronomy, Northwestern University, USA.
²Northwestern Institute on Complex Systems, Northwestern University, USA.

The concept of a complex network---a set of “nodes'” connected by “links” that represent interactions between them---pervades science and engineering, describing systems as diverse as food webs, power grids, and cellular metabolism [1]. Due to the interconnected nature of such systems, perturbations that affect one or more nodes can propagate through the network and potentially cause the system as a whole to fail or change behavior. But our study, recently published in Nature Communications [2], shows that this principle can be a blessing in disguise, giving rise to a new strategy to control network behavior.

Past 2Physics article by Adilson E. Motter:
July 01, 2012: "First Material with Longitudinal Negative Compressibility"
by Zachary G. Nicolaou and Adilson E. Motter.

A hallmark of real complex networks, both natural and engineered, is that their dynamics are inherently nonlinear [3]. It is this nonlinearity that permits the coexistence of multiple stable states (some desirable, others not), which correspond to different possible modes of operation of a real network. Because of this, when a network is perturbed, it can spontaneously go to a “bad” state even if there are “good” ones available. The question we asked is: can this principle be applied in reverse? In other words, can we perturb a network that is in (or will approach) a “bad” state in such a way that it spontaneously evolves to a target state with more desirable properties?

Our research was motivated by recent case studies in our research group, which showed how networks damaged by an external perturbation can, counter-intuitively, be healed by intentionally applying additional, compensatory perturbations. For example, bacterial strains left unable to grow in the wake of genetic mutations can be made viable again by the further knockout of specific genes [4], while extinction cascades in ecological networks perturbed by the loss of one species can often be mitigated by the targeted suppression of additional species [5]. However, a systematic extension of such a strategy to general networks remained an open problem, partly due to system-specific constraints that restrict the perturbations one can actually implement. Indeed, in most real networks there are constraints on the potential compensatory perturbations one can implement in the system, and these generally preclude bringing the system directly to the target, or even to a similar state. In food-web networks, for instance, it may only be possible to suppress (but not increase) the populations of certain species (e.g., via hunting, fishing, culling, or non-lethal removals), while some endangered species can't be manipulated at all. Similarly, one can easily knock down one or more genes in a genetic network, but coordinating the upregulation of entire genetic pathways is comparatively difficult.

The critical insight underlying our research is that even when a desired stable state of a dynamical system can't be reached directly, there will exist a set of other states that eventually do evolve to the target---the so-called basin of attraction of that state. If we could only bring the system to one of those states through an eligible perturbation, the system would subsequently reach the target on its own, without any further intervention. A core component of our work is thus the introduction of a scalable algorithm that can locate basins of attraction in a general dynamical system [2] (for a Python implementation of the algorithm, see Ref. [6]). Figure 1 presents a visual illustration of this approach for transitions between patterns stored in an associative memory network, in which the control intervention (downward arrows) causes the network to spontaneously transition to the next pattern under time evolution (diagonal arrows).

Figure 1: Patters representing the letters of the word “NETWORK” are stored as different stable states in an associative memory network. The example shows how our algorithm induces transitions between consecutive letters by only perturbing “off” pixels.

A remarkable aspect of this approach is its robustness. In the example just mentioned, the control procedure succeeds in driving the system to the target or to a similar pattern with a small number of binary errors (gray pixels). Thus, even if the target state cannot be reached by any eligible perturbation, it may nonetheless be possible to drive the network to a similar state using this control procedure. This would not be possible if the dynamics were linear, since in that case the nonlocal nature of the control trajectories may prevent numerical convergence to the desired target even when the initial state is already close to the target [7].

The approach is based on casting the problem as a series of constrained nonlinear optimization problems, which enables systematic construction of compensatory perturbations via small imaginary changes to the state of the network. Prior to the introduction of this technique there were no systematic methods for locating the portions in the attraction basins that can be reached by eligible perturbations in general high-dimensional dynamical systems, short of conservative estimates and brute-force sampling. The latter requires an amount of computation time exponential in the number of dynamical variables of the system, which is notoriously large for complex networks of interest. In contrast, the running time of our approach scales only as the number of variables to the power 2.5.

There are numerous potential applications for the above control approach. As an example, we considered the identification of candidate therapeutic targets in a form of human blood cancer caused by the abnormal survival of cytotoxic T-cells. Here, normal and cancer states correspond to two different types of stable steady states [8]. Potential curative interventions are those that bring the system from a cancerous or pre-cancerous network state to the attraction basin of the normal state, which then leads to programmed cell death. We demonstrate that 2/3 of all such compromised states can be rescued through perturbations limited to network nodes not previously identified as promising candidate targets for therapeutic interventions. Furthermore, we show that perturbing an average of only 3.4 of them suffices to control the entire network. The effectiveness of many approved drugs relies on their being multi-target, temporary, and tunable, which are precisely the characteristics of the type of control interventions introduced by our study, making such predictions attractive for future experimental exploration [9].

This work illustrates how interconnectedness and nonlinearity---unavoidable features of real systems commonly thought to be impediments to their control---can actually be turned to our advantage. This has broad implications and may in particular shed new light on the requirements on the observability of real networks to allow their real-time control (for recent studies on network observability, see Refs. [10, 11]).

Our approach is based on the systematic construction of compensatory perturbations to the network, and, as illustrated in our applications, can account for both rather general constraints on the admissible interventions and the nonlinear dynamics inherent to most real complex networks. These results provide a new foundation for the control and rescue of network dynamics and for the related problems of cascade control, network reprogramming, and transient stability. In particular, we expect these results to have implications for the development of smart traffic and power-grid networks, of new ecosystem and Internet management strategies, and of new interventions to control the fate of living cells.

The research was supported by NSF (Grant DMS-1057128), NCI (Grant 1U54CA143869), and a Northwestern-Argonne Early Career Investigator Award.

References:
[1] Mark Newman, "The physics of networks", Physics Today, 61(11), 33 (2008). Full Article.
[2] Sean P. Cornelius, William L. Kath, Adilson E. Motter, "Realistic control of network dynamics", Nature Communications, 4, 1942 (2013). Abstract.
[3] Adilson E. Motter and Réka Albert, "Networks in motion", Physics Today 65(4), 43 (2012). Full Article.
[4] Adilson E Motter, Natali Gulbahce, Eivind Almaas & Albert-László Barabási, "Predicting synthetic rescues in metabolic networks", Molecular Systems Biology, 4, 168 (2008). Full Article.
[5] Sagar Sahasrabudhe & Adilson E. Motter, "Rescuing ecosystems from extinction cascades through compensatory perturbations", Nature Communications, 2, 170 (2011). Abstract.
[6] Sean P. Cornelius & Adilson E. Motter, "NECO - A scalable algorithm for NEtwork COntrol", Protocol Exchange, Nature Protocols (2013), doi:10.1038/protex.2013.063. Link.
[7] Jie Sun and Adilson E. Motter, "Controllability transition and nonlocality in network control", Physical Review Letters, 110, 208701 (2013). Abstract.
[8] Ranran Zhang, Mithun Vinod Shah, Jun Yang, Susan B. Nyland, Xin Liu, Jong K. Yun, Réka Albert, Thomas P. Loughran, Jr. "Network model of survival signaling in large granular lymphocyte leukemia". Proceedings of the National Academy of Sciences of the United States of America, 105, 16308 (2008). Abstract.
[9] Peter Csermely, Tamás Korcsmáros, Huba J.M. Kiss, Gábor London, Ruth Nussinov, "Structure and dynamics of molecular networks: A novel paradigm of drug discovery", Pharmacology & Therapeutics, 138, 333 (2013). Abstract.
[10] Yang Yang, Jianhui Wang, and Adilson E. Motter, "Network observability transitions", Physical Review Letters, 109, 258701 (2012). Abstract.
[11] Yang-Yu Liu, Jean-Jacques Slotine, and Albert-László Barabási, "Observability of complex systems", Proceedings of the National Academy of Sciences of the United States of America, 110, 2460 (2013). Abstract. 

Piezotronic Nanowire “Taxel” Gives Active/Adaptive Sense of Touch

[From Left to Right] Xiaonan Wen, Zhong Lin Wang, Wenzhuo Wu


Authors: Wenzhuo Wu, Xiaonan Wen and Zhong Lin Wang

Affiliation: 
School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, USA.


Emulation of human senses via electronic means has long been a grand challenge in research of artificial intelligence as well as prosthetics, and is of pivotal importance for developing intelligently accessible and natural interfaces between human/environment and machine. Unlike other senses (seeing, hearing, smelling and tasting), capability of skin for touch sensing remains stubbornly difficult to be mimicked, which necessitates the development of large-scale pressure sensor arrays with high spatial-resolution, high-sensitivity and fast response.

Implementations of pressure sensor arrays have been previously reported using assembled nanomaterials or microstructured rubber layers based on the change in capacitance or resistance upon pressure, which have been applied to map strain distribution in a matrix format with resolution in the millimeter-scale [1,2]. In those demonstrations, electronic components like traditional field-effect-transistors (FETs) act as read-out elements for detecting pressure-induced property change in the pressure-sensitive media. Intensive efforts have been devoted to minimize the effect of substrate strain on performance of these electronic components while preserving the deformability of the substrate. This scheme of pressure sensing, whereas, not only requires complicated system integration of heterogeneous components but also lacks proficiency in directly interfacing electronics with mechanical actions in an active way that mechanical straining can be utilized to generate new electronic control/feedback. Therefore, new approaches have to be developed for better mimicking or even competing with the tactile sensing capabilities of human skins.

A direct control over the operation of electronic devices by mechanical action could be advantageous for implementing tactile sensing and realizing direct interfacing between machines and human/ambient. Piezoelectric materials are ideal candidates for this purpose, which produce electrical potential upon variations of applied pressure/stress due to the linear electromechanical coupling/interaction between mechanical and electrical state in materials lacking inversion symmetry. The most well-known piezoelectric material is perovskite-structured Pb(Zr_xTi_1-x)O₃ (PZT), which has been widely used for electromechanical sensing, actuating and energy harvesting. PZT, however, is electrically-insulating and hence less useful for building electronic devices. In addition, the extremely brittle nature of ceramic PZT films and incorporation of lead impose issues such as reliability, durability and safety for long term sustainable operations and hinder its applications in areas such as biomedical devices.

Figure 1: [click on image to view higher resolution] Piezopotential in Wurtzite crystal. (a) Atomic model of the Wurtzite-structured ZnO. (b) Distribution of piezopotential along a ZnO NW under axial strain calculated by numerical methods. The growth direction of the NW is along c-axis. The color gradient represents the distribution of piezopotential in which red indicates positive piezopotential and blue indicates negative piezopotential.

Due to the polarization of ions in a crystal that has non-center symmetry, a piezoelectric potential (piezopotential) is created in the crystal by applying a stress [3] (Figure 1). For piezoelectric semiconductor materials such as ZnO, GaN, InN and CdS, the effect of piezopotential on the transport behavior of charge carriers is significant due to their multiple functionalities of piezoelectricity, semiconductor and photon excitation. One of the important effects of piezopotential on p-n junction and metal-semiconductor contact is to tune/control the charge transport across the interface, which is the basis of piezotronic effect (Figure 2) [3,4]. Electronics fabricated by using inner-crystal piezopotential as a “gate” voltage to tune/control the charge transport behavior is called piezotronic device. Our group initiated the research in piezotronics back to 2007 [5]. Since then we have investigated the piezotronic effect for realizing novel applications such as strain-gated piezotronic logic nanodevices [6] and piezotronic strain memory device [7]. In contrast to conventional CMOS units, the strain-gated electronics is driven by mechanical agitation. A brief comparison between piezotronic transistor and field effect transistor (FET) is shown in Figure 3.

Figure 2: [click on image to view higher resolution] Schematic of energy diagram illustrating the effect of piezopotential on modulating the metal-semiconductor contact and p-n junctions. (a) With compressive strain applied, the negative piezoelectric polarization ionic charges induced near the interface (symbols with “-”) increases the local Schottky barrier height (SBH). (b) With tensile strain applied, the positive piezoelectric polarization ionic charges induced near the interface (symbols with “+”) decreases the local SBH. (c) and (d) With strain applied, the piezoelectric polarization ionic charges are induced near the junction interface.

Figure 3: [click on image to view higher resolution] Comparison between traditional FET and Strain-gated piezotronic transistor (SGT).

Designing, fabricating and integrating arrays of nanodevices into a functional system is the key for transferring nano-scale science into applicable nanotechnology. In our latest work [8], we report the first and by far the largest 3D array integration of vertical NW piezotronic transistors circuitry (92 x 92 taxels with 234 taxels per inch) as active/adaptive taxel-addressable pressure-sensor matrix for tactile imaging. Here “taxel” is short for tactile pixel, which is the unit in our array device. We combined the top-down microfabrication processes for fabricating device structure with the bottom-up synthesis of ZnO NWs at low-temperature (85^oC).

The taxel area density of SGVPT (strain-gated vertical piezotronic transistor) array is 8464/cm², which is higher than the number of tactile sensors in recent reports (~ 6-27/cm²) [1,2,9] and mechanoreceptors embedded in the human fingertip skins (~ 240/cm²) [10]. The fabricated sensors are capable of mapping spatial profiles of small pressure changes (< 10 kPa). The spatial resolution with taxel dimension (20 x 20 μm²) and pitch size (100 μm) as well as the tactile sensitivity (2.1 μs∙kPa^-1) have been demonstrated, enabling a 15-to-25-fold increase in number of taxels and 300-to-1000-fold increase in taxel area density compared to recent reports.

Each taxel in the array device is made of a strain-gated vertical piezotronic transistor (SGVPT) based on vertically-aligned n-ZnO nanowires (NWs) (Figure 4a, d). SGVPT operates based on modulation of local contact characteristics and charge carrier transport by strain-induced ionic polarization charges at the interface of metal-semiconductor contact, which is the fundamental of piezotronics. Using the piezoelectric polarization charges created at metal-semiconductor interface under strain to gate/modulate transport process of local charge carriers, piezotronic effect has been applied to design independently addressable two-terminal transistor arrays, which convert mechanical stimuli applied on the devices into local electronic controlling signals (Figure 4b-c). Figure 4c shows the equivalent circuit to present the operation scheme of SGVPT array.

Figure 4: [click on image to view higher resolution] (a) Comparison between three-terminal voltage-gated NW FET (left) and two-terminal strain-gated vertical piezotronic transistor (right). (b) Schematic illustration of a 3D SGVPT array with taxel density of 92 × 92 and scheme for spatial profile imaging of local stress. (c) Equivalent circuit diagram of the 3D SGVPT array. (d) SEM image of SGVPT array taken after etching-back the SU 8 layer and exposing top portions (~ 20 μm) of the ZnO NWs. Inset, 30^o-tilt view of the exposed ZnO NWs for single taxel. (e) Optical image of the transparent 3D SGVPT array on flexible substrate. (f) Current responses for single taxel under different pressures, presenting the gate modulation effect of applied pressure on the electrical characteristics of SGVPT.

The elimination of wrap gate offers a new approach for 3D structuring. The local contact profile and carrier transport across the Schottky barriers, formed between ZnO NW and metal electrodes, can be effectively controlled by the polarization-charge-induced potential. Electrical characteristics of the two-terminal SGVPT are therefore directly modulated by external mechanical actions induced strain, which essentially functions as a gate signal for controlling carrier transport in SGVPT. The modulation effect of applied pressure is shown from the plot of current variations against pressure changes (Figure 4f). Cross-bar electrodes have been configured for multiplexed data acquisition and the spatial profiles of applied stress can be recorded and imaged. The output signal is current response so that it is easy to integrate SGVPT array with back-end interface circuits for fast data processing, recording and transmission.

Three unique capabilities of SGVPT array device, which are not readily available in previous reports, have been demonstrated in this work:
1. The capability of using SGVPT array for multi-dimensional signature recording, which not only records the calligraphy or signature patterns, when people write, but also registers the corresponding pressure/force applied at each location/pixel by the person and the speed or writing. This augmented capability can essentially provide means for realizing personal signature recognition with unique identity and enhanced security.
2. The shape-adaptive sensing capability of SGVPT array, which provides means for detecting the shape change of device in situ in real-time and feeding-back the sensed changes in shape for calibration of other functionalities as well as corresponding control/response performed by the system. The real time detection of shape changes caused by stretching or twisting is a desirable feature for sensors embedded in an artificial tissue or prosthetic device. This unique capability enables the potential integration of SGVPT device for applications in artificial/prosthetic skin in smart biomedical treatments and intelligent robotics.
3. Additionally, the SGVPT devices can also function as self-powered active tactile sensors by converting mechanical stimulations into electrical signals utilizing the piezopotential without applied bias, which emulates the physiological operations of mechanoreceptors in biological entities, such as human hair follicles and hair cells in the cochlea.

Table 1: Comparison between piezoresistive effect and piezotronic effect.

Our approach is based on a completely different mechanism from the traditional designs based on piezoresistive effect. A comparison between piezotronic effect and commonly recognized piezoresistive effect is listed in Table 1. This technology eliminates the wrap-gate electrode for fabricating 3D vertical NW based transistor, taking advantage of piezotronic effect. The structural transformation from three-terminal configuration into two-terminal configuration significantly simplifies the layout design and circuitry fabrication while maintains effective control over individual devices. The approach presented has the potential to be integrated with silicon-based CMOS technology for achieving augmented functionalities in smart systems in the era of “More Than Moore”, such as artificial skin, personal electronics and potential integration with compliant energy harvesting modules for self-powered flexible functional systems [11]. The scalability of this platform in integrating in-place synthesized single-crystalline NWs in controllable manners together with its demonstrated compatibility with state-of-the-art microfabrication techniques enables future large-scale implementation of wurtzite NWs for practical applications in human-electronics interfacing, smart skin and micro/nano-electromechanical systems.

References:
[1] Kuniharu Takei, Toshitake Takahashi, Johnny C. Ho, Hyunhyub Ko, Andrew G. Gillies, Paul W. Leu, Ronald S. Fearing & Ali Javey. "Nanowire active-matrix circuitry for low-voltage macroscale artificial skin". Nature Materials, 9: 821-826 (2010). Abstract.
[2] Stefan C. B. Mannsfeld, Benjamin C-K. Tee, Randall M. Stoltenberg, Christopher V. H-H. Chen, Soumendra Barman, Beinn V. O. Muir, Anatoliy N. Sokolov, Colin Reese & Zhenan Bao. "Highly sensitive flexible pressure sensors with microstructured rubber dielectric layers". Nature Materials, 9: 859-864 (2010). Abstract.
[3] Zhong Lin Wang. "Progress in piezotronics and piezo-phototronics". Advanced Materials, 24: 4632-4646 (2012). Abstract.
[4] Zhong Lin Wang. "Piezotronics and piezo-phototronics" (Springer, 2013).
[5] Zhong Lin Wang. "Nanopiezotronics". Advanced Materials, 19: 889-892 (2007). Abstract.
[6] Wenzhuo Wu, Yaguang Wei, Zhong Lin Wang. "Strain-gated piezotronic logic nanodevices". Advanced Materials, 22: 4711-4715 (2010). Abstract.
[7] Wenzhuo Wu and Zhong Lin Wang. "Piezotronic nanowire-based resistive switches as programmable electromechanical memories". Nano Letters, 11: 2779-2785 (2011). Abstract.
[8] Wenzhuo Wu, Xiaonan Wen, Zhong Lin Wang. "Taxel-addressable matrix of vertical-nanowire piezotronic transistors for active/adaptive tactile imaging". Science, 340: 952-957 (2013). Abstract.
[9] Tsuyoshi Sekitani, Tomoyuki Yokota, Ute Zschieschang, Hagen Klauk, Siegfried Bauer, Ken Takeuchi, Makoto Takamiya, Takayasu Sakurai, Takao Someya. "Organic nonvolatile memory transistors for flexible sensor arrays". Science, 326: 1516-1519 (2009). Abstract.
[10] R.S. Johansson, A.B. Vallbo. "Tactile sensibility in the human hand - relative and absolute densities of 4 types of mechanoreceptive units in glabrous skin". Journal of Physiology, 286: 283-300 (1979). Article.
[11] Zhong Lin Wang, Wenzhuo Wu. "Nanotechnology-enabled energy harvesting for self-powered micro-/nanosystems". Angewandte Chemie International Edition, 51: 11700-11721 (2012). Abstract.

Inspiration from Nature: Ultralight Fractal Designs for High Mechanical Efficiency

[From Left to Right] Daniel Rayneau-Kirkhope, Robert Farr, Yong Mao



Authors: Daniel Rayneau-Kirkhope¹, Robert Farr^2,3, Yong Mao⁴

Affiliation:
¹Open Innovation House, School of Science, Aalto University, Finland,
²Unilever R&D, Colworth House, Sharnbrook, Bedford, UK
³London Institute for Mathematical Sciences, Mayfair, London, UK
⁴School of Physics and Astronomy, University of Nottingham, UK

Hierarchical design is ubiquitous in nature [1]. Material properties can be tailored by having structural features on many length scales. The gecko, a lizard ranging from 2 to 60 cm in length, has a remarkable ability to walk on vertical walls and even upside-down on ceilings. This ability is brought about through the repeated splitting of the keratinous fibres on the bottom of the gecko’s foot, which increases the contact area so effectively that even the very weak van der Waals interactions can support the entire weight of the gecko [2].

A more specific form of hierarchical design is self-similar design, where one structural feature is found to be repeated on a number of different length scales. A natural example is the trabecular or spongy bone found around the joints in animals [3]. Here, a series of small beams are arranged in such a way that the stiffness and strength requirements are met while using minimal material. Regardless of the level of magnification, the same patterns are found in the structure. Interestingly, the exact configuration of the constituent beams in the trabecular bone is constantly changing: it is the result of a continuous opitimisation process that goes on throughout the lifetime of the bone and responds to change in stress levels [4]. It is found that when the animal’s bones support only small loads, many very slender pillars are present, and when the loading increases, fewer but stouter pillars are employed [5].

In our recently published work [6], we demonstrate that through the use of hierarchical, self-similar design principles, advantageous structural properties can be obtained. We show that the scaling of the amount of material required for stability against the loading can be altered in a systematic manner. A particular structure is fabricated through rapid prototyping, and we obtain the optimal generation number (for our specific structure) for any given value of loading.

Scaling

The volume of material required for stability can be related to the loading through a simple power law relationship. That is, the volume required is given by a dimensionless loading parameter raised to some power with a pre-factor (that is dependent only on material properties and specifics of the geometry). When the loading is small, it is the scaling (power) of the loading that dominates the relationship. Under tension, this power is one and a structure requires an amount of material that is proportional to the loading it must withstand; for a solid beam under compression, due to elastic buckling, the power is one-half. Given, for all realistic applications, the non-dimensional loading parameter is much less than 1, this means more material is required to support compressive than tensional loads. This one-half power law has direct consequences when one considers optimal structure: if a beam is bearing a compressive load, it is more efficient to use one beam rather than two, whereas in the case of tension, due to the linear relationship, splitting a tension member into more than one piece has no effect on the volume required for stability.

Fractal design

Our work centers on a very simple, iterative procedure that can be used to create designs of great complexity. The “generation” of a structure describes the number of iterations used to create the geometry. The simplest compression bearing structure is a solid slender beam. When loaded with a gradually increasing force, the beam will eventually buckle into a sinusoidal shape known as an “Euler buckling mode”. We can suppress this by using a hollow tube, but we introduce a second mode of a local failure of the tube wall – Koiter buckling. After optimizing for tube diameter and thickness, it is found that the scaling power increases to two-thirds, and the volume of material required for stability is reduced.

Figure 1: Showing the iterative process from low generation numbers to higher for structures bearing compression along their longest axis. At each step, all beams that are compressively loaded are replaced by a (scaled) generation-1 frame.

The next step is to replace the hollow beam with a space frame of hollow beams. The space frame used here is made up of n octahedra and two end tetrahedra. Optimising the number of octahedra, the radius and the wall thickness of the component beams (which are all assumed be identical) we find a new power law, and again, an improvement over the hollow beam design.

Continuing this procedure of replacing all beams under compressive load with (scaled) space frames constructed from hollow beams (figure 1), we find that the scaling law is always improved by the increased level of hierarchy. In general, the scaling is described by a (G+2)/(G+3) power-law relating non-dimensional volume to non-dimensional loading. Thus, as the generation number tends to infinity, the scaling relating material required for stability to loading approaches that of the tension member.

3D Printing

Working with Joel Segal, of the University of Nottingham, we fabricated an example of a generation-2 structure with solid beams, shown in figure 2. This was done through rapid prototyping technologies: micrometer-layer-by-micrometer-layer the structure was printed in a photosensitive polymer with each beam a fraction of a millimeter in radius. This structure shows the plausibility of the design and the extent to which modern manufacturing techniques allow for an increased creativity in design geometry. Through a process of 3-d printing and electro less deposition, it is believed that a metallic, hollow tubed structure could be created.

Figure 2: Showing a structure fabricated through rapid prototyping techniques. The inset shows the layering effect of the 3D printing technique. The structure shown in constructed in RC25 (Nanocure) material from envisionTEC on an envisionTEC perfactory machine.

Optimal generations

Although the scaling is always improved by increasing the generation number of the structure, the prefactor isn’t. The optimal structure is then obtained by balancing the scaling relationship with the prefactor in the expression. Generally, as the loading decreases (or the size of the structure increases), the scaling becomes more important and the optimal generation number increases. For large loads (or small structures) it can even be the case a simple, solid, beam is optimal.

Our work also formalises this relationship, for a long time engineers have created chair legs from hollow tubes or cranes out of space frames, Gustave Eiffel used three levels of structural hierarchy in designing the Eiffel tower. We show formally, that the optimal generation number has a set dependence on the loading conditions and allow future structures to be designed with this in mind. A further consequence of the alteration of the scaling law is that the higher the generations, the less difference it makes as to whether you have one structure holding a given load or two structures holding half the load each.

Reference:
[1] Robert Lakes, "Materials with structural hierarchy", Nature, 361, 511 (1993). Abstract.
[2] Haimin Yao, Huajian Gao, "Mechanics of robust and releasable adhesion in biology: Bottom–up designed hierarchical structures of gecko", Journal of the Mechanics and Physics of Solids, 54,1120 (2006). Abstract.
[3] Rachid Jennanea, Rachid Harbaa, Gérald Lemineura, Stéphanie Bretteila, Anne Estradeb, Claude Laurent Benhamouc, "Estimation of the 3D self-similarity parameter of trabecular bone from its 2D projection", Medical Image Analysis, 11, 91 (2007). Abstract.
[4] Rik Huiskes, Ronald Ruimerman, G. Harry van Lenthe, Jan D. Janssen, "Effects of mechanical forces on maintenance and adaptation of form in trabecular bone", Nature, 405, 704 (2000). Abstract.
[5] Michael Doube, Michał M. Kłosowski, Alexis M. Wiktorowicz-Conroy, John R. Hutchinson, Sandra J. Shefelbine, "Trabecular bone scales allometrically in mammals and birds", Proceedings of the Royal Society B, 278, 3067 (2011). Abstract.
[6] Daniel Rayneau-Kirkhope, Yong Mao, Robert Farr, "Ultralight Fractal Structures from Hollow Tubes", Physical Review Letters, 109, 204301 (2012). Abstract.

Measurement of Photon Statistics with Live Photoreceptor Cells

Leonid Krivitsky

Author: Leonid Krivitsky

Affiliation: Data Storage Institute, Agency for Science Technology and Research (A*STAR), Singapore

Conventional light sources, such as lamps, stars, laser pointers etc. are known to exhibit intrinsic photon fluctuations. This means that the number of photons emitted by the source is not strictly defined but is given by a specific statistical distribution. For example, the photon number distribution of a laser obeys a Poisson distribution, whilst the photon number distribution of a thermal source (lamp, star) obeys an exponential distribution.

The question which we address in this work is how fluctuations of various light sources are perceived by visual systems of living organisms [1]. A simple analogy which illustrates this is our human perception of the stars in the night sky. It is known that faint stars blink because of the atmospheric turbulence, which disturbs the star light on its way to the eye. At the same time, we may notice that bright stars, e.g. Polaris, observed under the same conditions, seem almost stable. This observation suggests that the ability of the eye to perceive blinking (fluctuating) lights is related to the brightness of the source. This scenario can be carefully reproduced in the lab by interfacing photosensitive eye cells, known as photoreceptors, with flashes of light from sources with different photon statistics.

Photoreceptor cells within the eye, known as retinal rods, are responsible for vision under low light conditions [2]. They are capable of detecting light down to the single photon level. When stimulated by light, the cells respond in ways that can be measured. In particular, the electrical activity of the cell, which is driven by the absorption of individual photons by the cells, can be measured by using fine glass microelectrodes. Moreover, since the cell is constrained within the recording microelectrode, moving the microelectrode allows us to position the cell close to the tip of an optical fiber, which is used to perform targeted light delivery into the cell (see Fig. 1) [3].

Fig.1 Microscope image of the retinal rod cell constrained in a glass suction pipette (on the right) and a tapered optical fiber (on the left) used for light delivery to the cell.

In our experiment, we send flashes of light into the cell by feeding flashes of light from the laser and pseudo-thermal light source into an optical fiber. We then measure the average and standard deviation of the cell response to repetitive light flashes at different flash intensities. The relation between the average <A> and the standard deviation ΔA of the amplitude of the cell response is characterized by a signal-to-noise ratio SNR= <A>/√ΔA.

It turns out that the fluctuation of the cell’s response depends crucially on the saturation of the cell response. Firstly, the dependence of the average cell response on the number of impinging photons behaves differently for light sources with different photon statistics (see Fig.2). As we can see, for the case of the pseudo-thermal light source (open symbols) the saturation is considerably smoother than for the laser light (solid symbols). This is explained by the fact that for bright (on average) pseudo-thermal light source there is always a considerable chance of observing flashes with low photon numbers, which prevents sharp saturation of the average response.

Fig.2 Dependence of the average normalized amplitude of the cell response on the normalized number of impinging photons for laser (solid symbols, solid lines) and pseudo-thermal (open symbols, dashed lines) light sources. Lines are results of theoretical modelling. Typical values of saturation amplitudes are in the range of 18-25 pA, and of photon numbers are in the range of 700-2500 photons per pulse. Saturation of the response is different for the two sources due to the difference in their photon statistics.

Secondly, the saturation of the cell at relatively bright flashes leads to a sharp increase of the SNR (see Fig.3). Indeed, if the cell is saturated by bright lights, its response does not fluctuate and this automatically results in a high value of SNR since ΔA becomes vanishingly small. This may be the reason why we are able to see fluctuating dim stars, but the bright stars in the night sky appear almost stable.

Fig.3 Dependence of the Signal to Noise Ratio (SNR) on the normalized number of impinging photons for laser (solid symbols, solid lines) and pseudo-thermal (open symbols, dashed lines) light sources. Lines are results of theoretical modelling. Sharp increase of SNR is a signature of the bleaching of the cell.

In conclusion, this work contributes to a better understanding of the sensitivity of retinal rod cells to photo-stimulation. It shows that under certain conditions, the cell can, like other man-made photodetectors, be used to measure the photon statistics of various light sources. It is of further interest to us to investigate how the cell interacts with sources of non-classical light and this study is currently in progress. More practical applications of the above work could include building a detector with retinal rods that can mimic the natural detection of light by our eyes.

References:
[1] "Measurement of Photon Statistics with Live Photoreceptor Cells", Nigel Sim, Mei Fun Cheng, Dmitri Bessarab, C. Michael Jones, Leonid A. Krivitsky, Physical Review Letters, 109, 113601 (2012). Abstract.
[2] "Single-photon detection by rod cells of the retina", F. Rieke and D. A. Baylor, Review of Modern Physics, 70, 1027 (1998). Abstract.
[3] "Method of targeted delivery of laser beam to isolated retinal rods by fiber optics", Nigel Sim, Dmitri Bessarab, C. Michael Jones, Leonid Krivitsky, Biomedical Optics Express, 2, 2926 (2011). Abstract.

Avian Compass Reloaded

Dagomir Kaszlikowski

Author: Dagomir Kaszlikowski

Affiliation: Centre for Quantum Technologies, Department of Physics, National University of Singapore, Singapore

Recently there has been a fundamental change in our understanding of how biological systems operate; new research revealed that quantum phenomena could play an essential part in biological processes. Understanding the fundamental mechanisms contributing to biological processes is an essential step in developing our understanding of life, its origins and evolution. However, one has to be cautious how to approach this problem to avoid triviality.

Molecules are purely quantum mechanical objects which must behave according to quantum mechanical laws. Therefore life is governed by the laws of quantum mechanics; it is the result of a series of chemical reactions between molecules happening inside of any living organism. There is nothing insightful in this observation. However, if one could demonstrate that biological systems utilize certain peculiar aspects of quantum mechanics such as coherence, entanglement or tunneling to their advantage, it would be a highly non-trivial statement.

Scientists have recently discovered strong evidence for complex quantum mechanical mechanisms in two interesting biological processes: photosynthesis [1] and the avian compass [2,3]. In this article I would like to focus on the latter.

It has been observed that some species of migratory birds can sense the direction of the Earth’s magnetic field. They use this sensitivity to the geomagnetic field to navigate during seasonal migration. This is extremely surprising because the magnetic field of our planet is very weak and it is difficult to imagine how it can affect a bird’s nervous system or trigger a behavioral response. In 2008 scientists realized that birds may directly observe the magnetic field by utilizing a magnetically sensitive photochemical reaction called the radical pair mechanism.

In a nutshell: it is assumed that the bird’s retina contains a photoreceptor pigment with molecular axis direction dependent on its position in the retina. Absorption of incident light by a part of the pigment results in electron transfer to a suitable nearby part and in this way a radical pair is formed, i.e. a pair of charged molecules each having an electron with unpaired spin. In the external magnetic field the state of the electron spins undergoes singlet-triplet transitions and at random times the radical pairs recombine forming singlet (triplet) chemical reaction products. In a bird’s brain, the amount of these chemical products varies along the retina as the direction of molecular axis changes, and the shape of this profile is believed to be correlated with the orientation of the geomagnetic field. I would like to mention at this point that singlet and triplet states of two electrons, which are examples of entangled states, are purely quantum mechanical phenomena that cannot be modeled using classical physics.

We need to put this hypothesis in the context of behavioral experiments carried on European Robins. During these experiments researchers determined that (i) the avian compass is only sensitive to inclination of the magnetic field, not its polarity; (ii) investigated birds were disoriented after being subjected to a weak radio frequency magnetic field whose frequency is adjusted to the characteristic frequency of the radical pair mechanism; (iii) the compass stopped working if the local geomagnetic field was weakened or strengthened by around 30%.

There are two essential physical parameters, in the radical pair mechanism model, which determine a bird’s ability to navigate: the average lifetime of the radical pair and its robustness to disturbances from the environment. The lifetime of the radical pair must be long enough to produce the chemical product profile necessary to stimulate the bird’s nervous system. Disturbances from the environment is called decoherence in quantum theory. Decoherence directly effects electronic singlet and triplet states making them lose their entanglement. This results in the bird’s compass being insensitive to the inclination of the magnetic field. The coherence time of the radical pair must be sufficient to prevent this from happening.

My colleagues from the National University of Singapore and Oxford University (UK) showed, in their recent paper [2], that both the average lifetime and the coherence time of the radical pair in the European Robin’s eye can be of the order of 100 microseconds. This is a surprising result, given that the longest coherence times of molecular electron spin states achieved in the laboratory (where the influence of the environment is minimized as much as possible) are 80 microseconds! It would imply that evolution created protection for fragile quantum processes beyond what humans can engineer.

In my recent paper [3] -- together with my collaborators Tomek Paterek and Jayendra Bandyopadhyay -- we arrived at different lifetime and coherence time estimations based on the same radical pair mechanism model. We estimated that lifetime and coherence of radical pair in the European Robin’s eye is of the order of 10 microseconds. The difference between our results and those in [2] stems from the fact that we considered all the results (i) to (iii) of the behavioral experiments whereas the result (iii) was not accounted for in the paper by my colleagues. Let me explain this.

The graphs above represent the angular dependence of the yield of radical pair chemicals produced in the theoretical model of the avian compass. The black curve corresponds to the local geomagnetic field near Frankfurt, Germany, where the behavioral experiments were carried out. The blue curve represents a static magnetic field that is 30% weaker than the one in Frankfurt. The green curve is the yield in the presence of a weak radio frequency oscillating magnetic field. The inverse of the parameter k is the lifetime of radical pair and a parameter in the theoretical model that must be adjusted in order to reproduce the experimental data.

According to behavioral experiments (ii) and (iii) a European Robin becomes disoriented if either it is subjected to a weak radio frequency magnetic field oscillating at a specific frequency or if the magnitude of the local geomagnetic field is changed by 30%. Therefore, for those values of the parameter k for which the green curve enters the region (called the “functional window” of the compass) one gets contradiction with the experiment because birds were disoriented in the presence of the RF magnetic field. As you can see from the right-most graphs this happens for radical pair lifetimes of the order of 10 microseconds. This is our estimation of the average lifetime of the radical pair in the European Robin’s retina. It also agrees with in vitro experiments on cryptochrome molecules [4]. These molecules are believed to constitute the photo-receptor pigment responsible for the radical pair based avian compass of European Robins.

Based on this value of the parameter k we were able to investigate the sensitivity of the avian compass as a function of the environmental noise as shown in graphs below:

The upper graph corresponds to the situation where the coupling strength of one of the electrons from the radical pair is slightly stronger than the strength of the geomagnetic field in Frankfurt (Larmor precession period of 0.78 microseconds). The lower graph corresponds to where the coupling is slightly weaker. I would like to mention that the compass only works for a small range of the coupling strength centered on 0.78 microseconds.

If the coupling strength is larger than the strength of the geomagnetic field then the sensitivity of the compass in the presence of the environmental noise (corresponding to coherence time of the order of one microsecond) is better than if there is no noise! This is not the case if the coupling strength is weaker but we still observe a local increase in the sensitivity for a coherence time of around one microsecond. A similar phenomenon is also found in studies of energy transfer during photosynthesis [5].

A plausible conclusion one can draw from these results is that nature may be optimizing performance of some biological processes by utilizing inevitable noise present in the environment, which is definitely a non-trivial statement about the role quantum mechanics can play in biology. More insight into this conjecture can be obtained from further studies of the resonance that magnetic sensitivity displays as a function of environmental noise -- as identified in this work.

References:
[1] Gregory S. Engel, Tessa R. Calhoun, Elizabeth L. Read, Tae-Kyu Ahn, Tomá Manal, Yuan-Chung Cheng, Robert E. Blankenship, Graham R. Fleming, "Evidence for wavelike energy transfer through quantum coherence in photosynthetic systems", Nature 446, 782 (2007). Abstract.
[2] Erik M. Gauger, Elisabeth Rieper, John J. L. Morton, Simon C. Benjamin, and Vlatko Vedral, "Sustained Quantum Coherence and Entanglement in the Avian Compass", Physical Review Letters, 106, 040503 (2011). Abstract.
[3] Jayendra N. Bandyopadhyay, Tomasz Paterek, and Dagomir Kaszlikowski, "Quantum Coherence and Sensitivity of Avian Magnetoreception", Physical Review Letters, 109, 110502 (2012). Abstract.
[4] Till Biskup, Erik Schleicher, Asako Okafuji, Gerhard Link, Kenichi Hitomi, Elizabeth D. Getzoff, Stefan Weber, "Direct Observation of a Photoinduced Radical Pair in a Cryptochrome Blue-Light Photoreceptor", Angewandte Chemie International Edition, 48, 404 (2009). Abstract.
[5] Masoud Mohseni, Patrick Rebentrost, Seth Lloyd, and Alán Aspuru-Guzik, "Environment-assisted quantum walks in photosynthetic energy transfer", Journal of Chemical Physics, 129, 174106 (2008). Abstract.

Making Use of the Audible Hiss Around the Second Law of Thermodynamics

Felix Ritort

Author: Felix Ritort 

Affiliation:
Small Biosystems Lab, Departament de Fisica Fonamental, Facultat de Fisica, Universitat de Barcelona, Spain.
Ciber BBN de Bioingenieria, Biomateriales y nanomedicina, Instituto de Sanidad Carlos III, Madrid, Spain.

The second law of thermodynamics pervades the natural world. Using a non-specialized jargon we may say that systems (and the universe as a whole) tend to become unstructured and disordered by the sole action of the naturally occurring physical forces.

From Clausius to Boltzmann the second law of thermodynamics has emerged around the concept of entropy. Entropy is a quantity that characterizes the thermodynamic state of a system and quantifies the degree of usefulness of its energy content. The combination of energy and entropy gives the free energy, a thermodynamic state function that determines, in concert with the second law, the natural fate of thermodynamic transformations.

A useful formulation of the second law states that for any irreversible transformation of a system kept in contact with a thermal bath, the amount of work performed on the system by an external agent is greater or equal to the free energy difference between the initial and final states. In other words, any thermodynamic transformation requires the expenditure of a minimum amount of work typical of reversible or quasi-static (i.e. slow enough) transformations. Faster transformations always require larger amounts of work incurring in finite amounts of energy that are dissipated to the environment. Such transformations are generally called irreversible: the larger the amount of work, the more the process is irreversible. The second law stands amongst the most fundamental laws of nature, yet some hiss around it has started to emerge over the past years. That hiss -- already known to Boltzmann, Smoluchowski, Schroedinger and others -- is now experimentally accessible.

Indeed, the second law inequality has to be understood in terms of averages. For very small systems (often called mesoscopic) or enough short times some realizations of the irreversible transformation transiently violate the second law, whereas others (the vast majority) preserve it. Such variability stems for the thermal or Brownian forces in the environment that produce noise and fluctuations in the dynamical evolution of the system. Every time the same experiment is repeated a different outcome for the actual performed work is observed. Only by averaging over many (actually infinite) repetitions of the same transformation, the second law inequality is preserved.

Over the past years a series of remarkable results that go under the generic name of fluctuation theorems have shown that such hiss around the second law can be used to recover free energy differences during irreversible transformations (for a review see [1]). This is unexpected: the second law -- being mathematically expressed as an inequality -- does not provide a clue about how to extract free energy differences in irreversible transformations. In 1997 Chris Jarzynski derived a beautiful equality that shows how free energy differences can be recovered from repeated work measurements along irreversible processes [2]. A few years later Gavin Crooks extended Jarzynski’s results and proved a fluctuation relation by considering a thermodynamic process and its time reversal [3].

Fluctuation theorems provide an elegant way to extract free energy differences by repeating the same experiment many times back and forth. Single molecule manipulation offers excellent opportunities for exploring such theoretical predictions. One can use AFM (Atomic Force Microscope), magnetic tweezers or optical tweezers to repeatedly pull back and forth a folded biomolecule (e.g. a nucleic acid hairpin or a protein) to unfold the native structure and refold the unfolded structure many times. In 2005 the first experimental test of the fluctuation theorem by Crooks and the measurement of free energy of folded RNA native structures from irreversible mechanical experiments were carried out [4].

Since then and until recently all applications of fluctuation theorems to recover free energy differences only considered native states. However, much less known but equally relevant in biophysics are kinetic states, i.e. states that are metastable in the thermodynamics sense (i.e. they have free energies that are higher than the lowest free energy of the native state). The paper recently published in Nature Physics by Anna Alemany et al. [5] addresses the recovery of free energy of kinetic states in DNA molecular structures from irreversible pulling experiments with optical tweezers.

Figure 1. Illustration of the transformation between two sets containing partially equilibrated states. Configurations inside each colored phase-space region are sampled according to the Boltzmann factor. In contrast, the statistical weight of the regions is not determined by its equilibrium free energy. λ(t) denotes the pulling protocol in the experiments, whereas A,B,C stand for any native or kinetic (intermediate or misfolded) state.

We apply an extended version of the fluctuation relation originally introduced by our group in 2010 to recover free energy branches [6]. In a nutshell such extended version requires that the initial state during the thermodynamic transformation be partially (rather than globally) equilibrated (Figure 1). Physically this means that the system is locally equilibrated in one or more metastable states for a finite time. The application of the extended relation then follows the same route as the standard Crooks relation. The new feature is that the different unfolding and folding trajectories must be classified into different sets -- based upon which state they start and end with; and the fraction of trajectories belonging to each set together with the partial work distributions for each set must be measured accordingly. We applied the extended relation to DNA structures exhibiting kinetic intermediates and misfolded structures (Figure 2). In all cases we showed that the extended fluctuation relation provides free energy estimates of the different kinetic states even in cases where equilibrium methods are not applicable (i.e. when full equilibrium cannot be reached in the experimentally accessible timescales).

Figure 2. Pulling experiment. (Left panel) Schematics of the pulling experiment with optical tweezers. The bead captured in the optical trap (red colored region) is used to measure the force acting on the molecular construct (hairpin plus handles). The position of the trap relative to the bead in the pipette defines the control parameter λ in the experiment. (Right panels) Force-distance curves.

The extended fluctuation relation paves the way to future free energy measurements of short-lived or inaccessible states that are not affordable with other bulk techniques. Applications are abound in RNA, proteins, DNA-protein, DNA-peptide, protein-protein systems. It is remarkable that that hiss around the second law finally turned out to be so useful for the measurements of pure thermodynamic quantities.

References
[1] Felix Ritort, "Nonequilibrium fluctuations in small systems: from physics to biology", Advances in Chemical Physics, 137, 31-123 (2008). Abstract.
[2] C. Jarzynski, "Nonequilibrium equality for free energy differences", Physical Review Letters, 78, 2690–2693 (1997). Abstract.
[3] G. E. Crooks, "Path-ensemble averages in systems driven far from equilibrium", Physical Review E 61, 2361–2366 (2000). Abstract.
[4] D. Collin, F. Ritort, C. Jarzynski, S. B. Smith, I. Tinoco, Jr and C. Bustamante, "Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies", Nature, 437, 231–234 (2005). Abstract.
[5] Anna Alemany, Alessandro Mossa, Ivan Junier, Felix Ritort, "Experimental free-energy measurements of kinetic molecular states using fluctuation theorems", Nature Physics, 8, 688–694 (2012). Abstract.
[6] Ivan Junier, Alessandro Mossa, Maria Manosas, Felix Ritort, "Recovery of free energy branches in single molecule experiments", Physical Review Letters, 102, 070602 (2009). Abstract.