Physics / Experiment Review

Vol. 4, NO. 1 / May 2018

Quantum Critical Proteins

Stuart Lindsay

Letters to the Editors

In response to “Quantum Critical Proteins

Hydrogen atoms are explained by quantum mechanics; cats are not. In this article, I argue that proteins may be closer to hydrogen atoms than to cats. Hydrogen atoms are held together by energies that are many hundreds of times larger than thermal energy. The dephasing of pure quantum states through normal thermal interactions is improbable. This is not true of cats. Proteins are poised at an interesting point. While the bare charges on the surface of a protein are strongly screened in electrolyte solutions, there are no free charges in the interior of a protein in its ground state. Simple dielectric screening reduces the bare Coulomb interaction by only a small amount so that interactions between charges on the surface of a protein, mediated via its interior, can exceed thermal energy over distances of more than 10 nm.

Proteins could be more like hydrogen atoms than cats.

The Fenna–Matthews–Olsen protein acts as an energy-coupling agent between bacterial chlorophylls and membrane proteins. A wonderful experiment recording optical fluorescence signals from well-separated chromophores showed the distinct interference patterns of quantum coherence.1 Crude energy scale arguments suggest that this may not be surprising. In a more sophisticated approach to quantum coherence, David Beratan introduced the notion of flickering resonance to explain quantum effects in a noisy environment.2 Seth Lloyd has gone further in showing how a certain amount of environmental noise can actually enhance quantum effects.3 There is evidence that large proteins can behave as quantum objects, though whether this is essential to their function is yet to be established.4

In their ground state, proteins are obviously insulators. Proteins look like transparent dielectric solids in bulk, and their dielectric response is clearly that of an insulator.5 There are good theoretical reasons for this. They are aperiodic systems with strong vibronic coupling, and high barriers to electron or hole injection.6 Yet many experiments suggest that proteins can be excellent conductors. Perhaps the most amazing feat of conduction is that of the bacterial nanowires produced by members of the genus Geobacter. These organisms live in soil and exploit the soil’s natural electrochemical potential gradient by shooting out protrusions, or pillae, that are tiny in diameter, but long in length. Their length allows electrical properties to be measured directly by probing the pillae. The results are startling. Geobacter conduct as well as metals, with a temperature dependence characteristic of a metallic conductor.7

There are other examples. Proteins are being explored for their potential as programmable electronic materials. Many types of proteins have been incorporated into metallic sandwiches that allow for measurements of conductance across a monolayer of proteins connected by two electrodes. Much of this work has been reviewed by David Cahen et al., and the results are really rather surprising.8 In figure 2 of their review, the dependence of current density on molecular length was compared for a series of conjugated molecules, saturated molecules, and proteins.9 The proteins constituted by far the best conductors. There was little evidence of significant decay in conductance as a function of increasing molecular length. Many of the proteins that were examined contained redox centers, which are assumed to be important in transport. Distance and temperature dependence ruled out electrochemical transport.10  Increased transport in devices exposed to moist air has been attributed to proton conductance, a phenomenon that can be readily checked by electrochemical means.11

A Conductor and an Insulator

In the face of this contradictory evidence, it seems reasonable to ask whether something can be both a conductor and an insulator at the same time. The answer, in fact, is yes, at least in a sense. In a 1958 paper, Philip Anderson examined the effect of disorder on quantum transport in a lattice of connected sites in which the energy varies randomly.12 He discovered that at a critical density of disorder, quantum diffusion ceased. The transition is abrupt, but three regimes can be identified: the metallic, the insulating, and the quantum critical. The distribution of energy-level spacings in each regime is quite distinct.13 At the quantum critical point, small fluctuations might move the system between its insulating and metallic states. The difficulty with this proposal lies in its improbability. Only an infinitesimal density of random states exists near the critical point. Nonetheless, the distinctive distributions of energy-level spacings can be used as a simple tool to probe the state of the system. Gábor Vattay et al. recently examined a number of proteins and conducting and insulating polymers.14 The distribution for the insulators and conductors were as expected, but the functional proteins all fell on the quantum-critical distribution. Such a result cannot be a consequence of chance.

It could only have come about as the result of evolutionary pressure.


Recently, Bintian Zhang et al. measured conductance in a single protein molecule.15 Many challenges stand in the way of such measurements. In air, metal surfaces are hydrophobic, and proteins denature readily in contact with bare electrodes. Application of significant potential differences drives electrochemical processes that denature proteins and can generate free ions. The scanning tunneling microscope uses a servo-stabilized gap that relies on the known electrical properties of materials in the gap. In the presence of materials that do not behave in a simple way, the gap remains uncharacterized. For the same reason, it is very hard to change the voltage applied in order to measure electrical characteristics.

We overcame these limitations in our own experiment using a solid-state tunnel device with a small opening such that only a few molecules could enter it. We first carried out conventional scanning tunneling studies. These were useful in validating the surface chemistry we developed to attach our target protein selectively and without denaturation. They were also useful in establishing the magnitude of conductance signals found in a solid-state device. Very high conductances were observed even when the probe was pulled some eight nm from the surface. This finding is subject to all of the uncertainties inherent in scanning tunneling measurements. We also carried out extensive electrochemical measurements on the electrodes and molecules used in this study, in order to establish a regime of electrode potentials in which no electrochemical events, such as proton generation, occurred.

The Device

Our solid-state device consisted of two palladium electrodes supported on a thin silicon nitride membrane and separated by a few nanometers of alumina dielectric. An opening is made to expose the edges of two metal electrodes and a small peptide used to capture the target protein selectively. The exact size of the insulating gap is measured by cutting a section from the electrode system, and imaging it in a transmission electron microscope. We chose a gap of about five nm. This is much larger than any distance over which electron tunneling through an insulator could occur. Other than a background leakage current, no signals were observed for a modified protein that did not bind the peptide specifically. When the target molecule was added, large stepwise increases in current were observed. They corresponded to the conductances observed in the scanning tunneling experiments. No signals were observed at any bias below about one hundred millivolts. There appears to be a threshold for the onset of molecular conductance fluctuations.

This result is consistent with the other experimental data that I have reviewed. In the absence of a small applied bias, our protein was clearly an insulator. But above a small threshold, the molecules appeared to turn on. We examined other sources of conduction, which are described in our paper. Our results are new because

  • just one, or, at most, a very few molecules were trapped;
  • because of specific attachments to the selective peptides, the target molecules were known not to be denatured;
  • electrochemical sources of current were eliminated; and
  • a threshold for the initiation of conductance fluctuations was observed.

If it applies to other proteins, this threshold can account for the disparities in the literature.


What of quantum criticality? Vattay et al. carried out electronic structure calculations for the very large protein used in our work. They found that the distribution of energy-level spacings fell on exactly the quantum-critical distribution, implying that this protein is also quantum critical. There is no obvious evolutionary reason why a protein should evolve toward a quantum-critical state, and there is no chance at all that the state could occur randomly.

Many open questions remain. What turns the protein on? How are free-electron states accessed? Or is the conduction a consequence of some completely new type of electronic state? The known states near the HOMO–LUMO (highest occupied molecular orbital to lowest unoccupied molecular orbital) gap of proteins are widely spaced and unlikely to contribute to a conduction band. Nonetheless, we should not ignore the experimental evidence that something unexpected is to be found in the electrical properties of proteins.

The role of electric potential distributions in the development of living organisms, although not widely appreciated, is clearly crucial. This has been demonstrated by the brilliant work of Michael Levin at Tufts University.16 The one hundred millivolts threshold that we measured lies at the upper end of the range of transmembrane potentials generated by ion gradients across cell membranes. A useful control or signaling mechanism may involve a potential-dependent switch. Potential differences in the very soil might turn on the pillae of Geobacter.


  1. Gregory Engel et al., “Evidence for Wavelike Energy Transfer Through Quantum Coherence in Photosynthetic Systems,” Nature 446 (2007): 782–86. 
  2. Yuqi Zhang et al., “Biological Charge Transfer via Flickering Resonance,” Proceedings of the National Academy of Sciences of the United States of America 111, no. 28 (2014): 10,049–54. 
  3. Seth Lloyd, “Quantum Coherence in Biological Systems,” Journal of Physics: Conference Series 302 no. 1 (2011). 
  4. David Wilkins and Nikesh Dattani, “Why Quantum Coherence is Not Important in the Fenna–Matthews–Olsen Complex,” Journal of Chemical Theory and Computation 11, no. 7 (2015): 3,411–19. 
  5. Daniel Martin and Dmitry Matyushov, “Terahertz Absorption of Lysozyme in Solution,” Journal of Chemical Physics 147, no. 8 (2017). 
  6. Abraham Nitzan, Chemical Dynamics in Condensed Phases: Relaxation, Transfer and Reactions in Condensed Molecular Systems (Oxford: Oxford University Press, 2006). 
  7. Nikhil Malvankar et al., “Tunable Metallic-Like Conductivity in Microbial Nanowire Networks,” Nature Nanotechnology 6 (2011): 573–79. 
  8. Nadav Amdursky et al., “Electronic Transport via Proteins,” Advanced Materials 26, no. 42 (2014): 7,142–61. 
  9. Nadav Amdursky et al., “Electronic Transport via Proteins,” Advanced Materials 26, no. 42 (2014): 7,142–61. 
  10. Bintian Zhang et al., “Observation of Giant Conductance Fluctuations in a Protein,” Nano Futures 1, no. 3 (2017); Nikhil Malvankar et al., “Tunable Metallic-Like Conductivity in Microbial Nanowire Networks,” Nature Nanotechnology 6 (2011): 573–79; Lior Sepunaru et al., “Temperature-Dependent Solid-State Electron Transport through Bacteriorhodopsin: Experimental Evidence for Multiple Transport Paths through Proteins,” Journal of the American Chemical Society 134, no. 9 (2012): 4,169–76. 
  11. Jenny Lerner Yardeni et al., “Sequence Dependent Proton Conduction in Self-assembled Peptide Nanostructures,” Nanoscale 8, no. 4 (2016): 2,358–66. 
  12. Philip Anderson, “Absence of Diffusion in Certain Random Lattices,” Physical Review 109, no. 5 (1958): 1,492–503. 
  13. Boris Shklovskii et al., “Statistics of Spectra of Disordered Systems near the Metal-Insulator Transition,” Physical Review B 47, no. 17 (1993): 11,487. 
  14. Gábor Vattay et al., “Quantum Criticality at the Origin of Life,” Journal of Physics: Conference Series 626 (2015); Gábor Vattay, Stuart Kauffman, and Samuli Niiranen, “Quantum Biology on the Edge of Quantum Chaos,” PLOS One 9, no. 3 (2014). 
  15. Bintian Zhang et al., “Observation of Giant Conductance Fluctuations in a Protein,” Nano Futures 1, no. 3 (2017). 
  16. The Levin Lab,” Tufts University. 

Stuart Lindsay is University Professor of Physics and Chemistry at Arizona State University.

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