Is there a biology of quantum information?
Koichiro Matsuno
a, Raymond C. Paton
b,*
aDepartment of BioEngineering,Nagaoka Uni6ersity of Technology,Nagaoka940-2188,Japan bDepartment of Computer Science,The Uni6ersity of Li6erpool,Li6erpool L69 3BX,UK
Abstract
This paper briefly considers the notion of a biology of quantum information from a number of complementary points of view. We begin with a very brief look at some of the biomolecular systems that are thought to exploit quantum mechanical effects and then turn to the issue of measurement in these systems and the concomitant generation of information. This leads us to look at the internalist stance and the exchange interaction of quantum particles. We suggest that exchange interaction can also be viewed using ecological ideas related to apparatus-object. This can also help develop the important notion of complementarity in biosystems in relation to the nature and generation of information at the microphysical scale. © 2000 Elsevier Science Ireland Ltd. All rights reserved.
Keywords:Quantum mechanics; Energy-time uncertainty relation; Microphysics; Internal measurement; Actin
www.elsevier.com/locate/biosystems
1. Introduction
The purpose of this paper is to reflect on some questions concerned with the quantum level in biological systems and to address the issue as to whether or not information is or could be pro-cessed at this level. We contend that at the scale of interacting molecules in the cell we must deal with the influence of quantum effects in relation to materials, energy and information. Many peo-ple may view quantum effects as mere noise. However, we would wish to qualify such a posi-tion and will argue that quantum level informa-tion is being processed in biological systems.
Fundamentally, it is the case that when molecules interact, especially in proteins and polynucleotides, quantum processes are taking place. It can be related to shape-based interac-tions and molecular recognition as well as to more long-range phenomena. Cellular microenviron-ments are very far removed from in vitro homoge-neous high dilution experimental systems. They are highly structured, with (relatively) low local water content and complex microarchitectures. Another albeit more teleological argument may also be summoned to support our contention. Many man-made devices are currently being con-sidered that could exploit the quantum (nanoscale) level. Not least is the outworking of Feynman’s oft-quoted talk ‘There is Plenty of Room at the Bottom’ and the rise of nanotechnol-ogy and quantum computing. We turn the ques-tion around and ask: who got ‘there’ first — biosystems or Richard Feynman?
* Corresponding author. Tel.:+44-151-7943781; fax:+ 44-151-7943715.
E-mail address:[email protected] (R.C. Paton)
2. The quantum level and biological information
Following an established tradition that cer-tainly in recent times can be traced back to Rosen (1960), we will argue that information is gener-ated at the quantum (microscopic) level and is manifested at mesoscopic and macroscopic levels within molecular and cellular systems. Quantum effects can be related to many biological pro-cesses. Clearly, interactions between photons and matter are quantum mechanical in nature and so we may think about UV-induced mutation, ‘bio-photons’, bioluminescence, photosynthesis and photodetection. In addition there are electromag-netic field effects involving for example ‘ordered’ water, biomolecules, cells, and living organisms (see e.g. Hong, 1995). A number of molecules and molecular systems that could form part of cellular quantum information processing systems may be described. The following short list (based on Tusynski et al., 1998) summarises a selection of examples (of which quite a lot more could be added):
Wiring — polyene antibiotics, conductive
biopolymers,
Storage — photosystem II reaction centres,
cytochromes, blue proteins, ferritin, collagen, DNA,
Gates and switches — bacteriorhodopsin,
pho-tosynthetic systems, cell receptors, ATPase. Soliton-like mechanisms may result in the conduc-tion of electrons and bond vibraconduc-tions along sec-tions of alpha-helices, and Ciblis and Cosic (1997) discuss the potential for vibrational signalling in proteins. As a specific experimental example, Al-brecht-Buehler (1991, 1995) described a set-up in which 3T3 mouse fibroblasts approached distant infrared light spots and suggested that the most likely explanation for this phenomenon involved the long-range processing of electromagnetic sig-nals by these cells. This involved the quantum level processing of information. Conrad (1990) has described the quantum level by elaborating the notion of vertical information processing in biological systems. In his self-assembly model macroscopic signals are transduced to mesoscopic and then microphysical representations, processed largely at the microphysical level, and then am-plified for macroscopic action.
So far we have listed examples of where quan-tum processes are attributable to biological mate-rials. In order to begin our examination of the issue of information processing at the quantum level we now consider the fundamental informa-tion generating process of measurement. The de-velopment of ideas of measurement in relation to biological information has an important history related to the work of for example Rosen, Pattee and Comorosan (for short review see Witten, 1982). More recent developments extended this through the work of for example, Conrad, Ro¨ssler, Kampis and Matsuno to general ideas in endophysics. In order to clarify the notion of measurement at the microphysical level, we shall begin with a fairly intuitive proposal that may be applied to a physical system:
interaction between components
before and after and,
energy exchange.
In order to explain this we shall look at the uncertainty relation between energy and time, that is:
DE.Dt'
The energy quantum to be exchanged is subject to an uncertainty in the timing of its actual ex-change between the material bodies involved in the interaction. This uncertainty provides the ex-change interaction with the most primitive at-tribute of information in the sense that there is an explicit distinction between a priori indefiniteness and a posteriori definiteness in the timing. In this case, when quantum particles interact (via ex-change interaction) measurements are made. It is legitimate to say that this interaction involves measurement, because there is no means by which it would be possible to identify what quantum particles could be transmitted to the receiving end before they have actually been transmitted. We summarise this situation in Fig. 1.
The standard understanding of quantum me-chanics tells us that time is not an operator, and that the time-energy uncertainty is an enigma. We however do not want to directly confront this uncertainty. Rather, we want to focus on how we could measure energy in the first place. The en-ergy in the time-enen-ergy uncertainty relationship is not clear about how the process of measuring the energy would proceed. Exactly at this point, the interplay between the local and global times en-ters. The original formulation of quantum me-chanics is fuzzy on the distinction between the
two classes of time. Matsuno (1995) notes how biological computation that is founded on inter-nal measurement provides an irreversible en-hancement of organisation and quantum coherency through the algorithmic and non-programmable procedures of generating varia-tions in accordance with the operation of the uncertainty principle. The notion of quantum smart matter has been introduced by Hogg et al. to take account of the possibility of exploiting quantum information processing in the regulation of nanoscale devices (e.g. Hogg and Chase, 1996). A number of macromolecular protein assem-blies have been considered in the literature for generating quantum information that becomes measurable by external observers in mesoscopic systems. Note the emphasis placed on external. As noted previously we have discussed the microscale events from the viewpoint of internal and local interactions between quantum information. Much recent discussion has focussed on a number of possible quantum effects in microtubules as in the case of the Hameroff-Penrose scheme of Orches-trated Reduction (e.g. Hameroff, 1998). Beck and Eccles (1992) proposed a quantum mechanical model underlying neuronal synaptic transmitter release based on a tunnelling process within the proteinaceous quasi-crystalline presynaptic vesicu-lar grid.
Welch (1992) suggested an analogue field model of the metabolic state of a cell based on ideas from Quantum Field Theory. He proposed that the structure of intracellular membranes and filaments, which are fractal in form, might gener-ate or sustain local fields. Virtually all biomem-branous structures in vivo can generate local electric fields and proton gradients. Enzymes can act as the energy transducing measuring devices of such local fields. In some ways we may say that the field provides a ‘glue’ which was not available at the individual, localised level of discrete com-ponents (see also, Paton, 1997). Popp et al. (1984) discussed the possibility of DNA acting as a source of lased ‘biophotons’. This was based on experiments in which DNA conformational changes induced with ethidium bromide in vivo were reflected by changes of the photon emission of cells. In another study Popp et al. (1988)
Fig. 2. Reaction co-ordinates and switch-like behaviour for (a) classical enzyme and (b) showing tunnelling.
compared theoretically expected results of photon emission from a chaotic (thermal) field with those of an ordered (fully coherent) field with experi-mental data and concluded that there are ample indications for the hypothesis that ‘biophotons’ originate from a coherent field occurring within living tissues.
One criticism of how the microscopic process-ing of quantum information could impact on meso- and macro- scopic levels is related to the lack of experimental systems that can deal with quantum events. Hopefully, we have presented a number of examples already where this is the case. In order to clarify the argument some more let us briefly two examples in some more detail.
Klinman (1989) discusses in vitro experiments of hydrogen tunnelling at room temperature in yeast alcohol dehydrogenate and bovine serum amine oxidase. She shows that the reaction co-or-dinate for these enzymes, rather than being a sharp transition (giving a step function) is ‘smoothed’ to give a sigmoidal/logistic shaped curve (see Fig. 2). This is very interesting from a measurement point-of-view. These molecules are measuring quantum effects which are magnified to the meso-/macro- scale to produce fuzzy/ fluctuat-ing effects. Given that enzyme-substrate com-plexes and many other protein-based interactions provide switching functions we here have an
ex-ample of a quantum mechanical switch albeit within a test-tube rather than intracellular experi-ment. Enzymes are fuzzy not just because of thermal/thermodynamical effects but because of interactions and measurements taking place at the microscale. This capacity for interaction implies local measurement and information generation.
We now examine a more detailed case devel-oped by Matsuno (1999). Actin-activated myosin ATPase activity that underlies muscle contraction can be characterised by the time interval tATP in
which one ATP molecule is hydrolysed per myosin molecule. During this time the stored energy eATP is released with typical values of
tATP$10−2 s and eATP$5×10−13 erg (or 7
kcal/mol) (Harada et al., 1990; Uyeda et al., 1991). A unique feature of actomyosin ATPase activity is the extreme slowness in releasing the energy stored in an ATP molecule. It is proposed that the energy release is punctuated by measure-ments internal to the actomyosin system as ex-pressed in the energy-time uncertainty principle (Matsuno, 1989). If the energy release by the amount ofeATP$5×10
−13erg happens to occur
in the form of emitting a single quantum, the uncertainty principle would give an uncertainty in the timing of the emission only as much as '/
eATP$2×10−15 s. This value is far less than the
actual time interval required for releasing energy
Matsuno (1993) has argued that the actual en-ergy release from an ATP molecule with the aid of an actomyosin complex proceeds by emitting a sequence of quanta, each of which carries energy
em, at every time interval of Dtmwhile satisfying
the constraints
In this case m denotes a quantum being responsi-ble for internalmeasurement. We may think of the energy flow associated with measuring each quan-tum as carrying energy em over the time interval Dtm. This is eventually imputed to the energy
release from a single ATP molecule (Matsuno, 1993). The corresponding values em$2.2×
10−19 erg and Dt
m$4.5×10−9 s would then
come to imply that the number of energy quanta, each of which carries energy em, emitted
coher-ently during one cycle of energy release from an ATP molecule at an actomyosin complex would roughly betATP/Dtm$2.2×106. Actomyosin
AT-Pase activity is thus associated with emission of quanta, whose typical energy is 2.2×10−19
erg or 1.6×10−3
K in temperature. The effective tem-perature of an actomyosin complex in the pres-ence of ATP molecules comes to decrease down to as low as 1.6×10−3 K (Matsuno, 1993, 1999).
The realisation of such an extremely loweffec
-ti6etemperature serves as a means of precipitating
a quantum coherence. The sliding movement of an actin filament on myosin molecules just mani-fests that the linear velocity of each actin monomer along the filament attains as much as 10
mm/s in a mutually coherent manner. Since this velocity gives each actin monomer linear momen-tum as much as 2.2×10−21
erg s/cm, the corre-sponding de Broglie length turns out be 4.5 nm. In this case we can begin to envisage how local coherence could generate semi-local, i.e. meso-copic coherence. The entangled system is related to the coherence of the interacting (co-measuring) protein molecules. Information gain from this en-tangled system is represented in the coherence persisting beyond individual actin monomers. So the 4.5 nm unit is achieved through the
semi-lo-calised (i.e. long range) ‘glue’ effects due to local exchange and measurement. Moreover, the de Broglie wavelength of 4.5 nm can make it possible to form more mesoscopic or macroscopic quan-tum coherence over adjacent actin monomers along the actin filament through the quantum entanglement, since the diameter of an actin monomer is only 2.5 nm that is less than the de Broglie length.
Once it is accepted that biological information processing has a quantum-mechanical underpin-ning, two major players turn to come to the fore. One is the occurrence of a quantum coherence by means of exchange interaction. The other is the enlargement of the coherence through the process of quantum entanglement. An actomyosin com-plex underlying muscle contraction certainly serves as a concrete example demonstrating both the occurrence of the quantum coherence and the quantum entanglement.
It is worth recapping on actin monomers in an actin filament are in contact with each other. If they are in a quantum coherence, a necessary condition must be that the de Broglie wavelength of each actin monomer should be greater than the diameter of the monomer, otherwise there could be no such quantum coherence over the length of a unit monomer. Although we have emphasised a necessary condition indirectly, this property of the de Broglie wavelength being greater than the di-ameter of an actin monomer must be verified directly. X-ray diffraction investigations would be a case in point. What is technically crucial is how to make F-actin crystallise. Some action has been going on in this direction. Uno Lindberg in Stock-holm and Clarence Schutt in Princeton are now heavily involved in an X-ray diffraction study of an F-actin.
3. The ecology of quantum information
methods for determining such interactions have yet to be elaborated. The interaction can be con-sidered in terms of an ecology in the same way that the macroscopic counterparts involve multi-ple interacting ‘agents’.
An internalist interactional view can be taken down in scale to the quantum level, as for exam-ple the object-apparatus interaction of DNA and energetic photons (Home and Chattopadhyaya, 1996). In this case the action of an energetic photon places the DNA in a quantum superposi-tion of states which we view at the mesoscopic level in terms of whether a mutation in a base(s) has taken place. However, in scaling up from the measuring event (i.e. photon-nucleotide interac-tion), other molecules including water and repair enzymes are also involved. Igamberdiev (1993) shows how quantum non-demolition measure-ments can be made internally. Energy dissipation is low and is provided by the slow conformational relaxation of biomolecules which could facilitate long-distance non-local transfer of electrons and protons. For example, during enzyme catalysis and electron transfer in proteins an electron’s energy can be tranformed into coherent vibra-tional movements without heat production. Igam-bandiev hypothesises that enzyme are large so that they can make quantum non-demolition measurements.
In a biological system object-apparatus interac-tion goes on all the time. Indeed, sometimes the object is a measuring apparatus. As noted earlier interaction implies measurement and the genera-tion of informagenera-tion. A crucial lesson from quan-tum mechanics is that the interaction between object and apparatus cannot be made insignificant or compensated for. Phenomena and apparatus are inextricably linked. Harre´ (1988) applied the Gibsonian idea of an affordance to help clarify the relationship between measuring apparatus and quantum events. Affordances are distinctly eco-logical in nature and interaction and context are dispositions of physical things relativised to that with which they interact. The energy flux detected by a piece of apparatus is shaped or formed by that apparatus. Put into the context of the present discussion, the molecular detector shapes what it detects. In the wave-particle duality sense, the
detection of a particulate phenomenon is a conse-quence of the energy flux interacting with appara-tus of that kind. Thus, particles can exist nowhere else but in relation to particle-forming apparatus. Apparatus and energy flux exist as a reciprocal pair. The former affords particulate phenomena for one species of apparatus and field phenomena for another. In addition pieces of apparatus are themselves afforded by the interaction with hu-man scientists with the energy flux. In the tradi-tional sense of a preparation in a quantum physical experiment, the humanity of the per-ceiver is always incorporated in the results of the experimentation.1
Harre´ presents an interesting analogy concern-ing the role of apparatus in chemistry, usconcern-ing the example of the preparation of liquid bromine in a retort. In this case, both the retort and the liquid bromine are products of preparations and proce-dures, they are both artefacts. In Harre´’s terms not only is the retort shaped by exigencies of condensing vapours, the liquid bromine is only made possible, as a stuff, by that apparatus. This disposition of the retort is only made available to the bromine. In a similar sense and from this ecological viewpoint one could say that the dispo-sition of one biomolecule within a measuring event is only made available to its interacting partner.
Any local quantum event can be seen as a message if it is taken to be under the wider context of quantum entanglement. Exchange in-teraction consists of three basic processes, namely, experiencing the presented, transforming the expe-rienced and representing the transformed to the others. This sequence of experiencing, transform-ing and representtransform-ing propagates indefinitely in the medium mediated by exchange interaction. A con-sequence is that each representation of the trans-formed, that is necessarily local, is constantly updated in the process. Updating the molecular representation from the internalist perspective (Matsuno, 1996) is no more than an indication of the procession of quantum mechanical computa-tion of a local character.
1Ray Paton thanks Rom Harre´ for clarifying this point to
Focusing on exchange interaction helps to shed new light on the issue of quantum information in biology. In view of the fact that exchange interac-tion consists of three basic processes of experienc-ing the presented, transformexperienc-ing the experienced and representing the transformed to the others, it becomes natural to see that those quantum me-chanical processes uphold by exchange interaction is informational. Biology is no exception. That is, exchange interaction consists of local processes and the procession of local processes is necessarily informational because there is a definite contrast between the a priori and the a posteriori. More-over, each procession from the a priori to the a posteriori corresponds to updating the representa-tion of the underlying quantum mechanical molecules. The quantum mechanical computation underlying the updating is extremely versatile in accommodating a huge array of parallel process-ing. This competency rests upon the molecular capacity of experiencing the presented exclusively from the internalist perspective. Although it is rather common from the externalist perspective to see that quantum computation is prepro-grammable under a fixed global boundary condi-tion (e.g. Deutsch, 1985), the nonprogrammability of exchange interaction of a local character can now rely upon the nonprogrammable molecular capacity of experiencing something new presented every time.
Once we pay legitimate attention to the molecu-lar capacity of experiencing something that has been presented but that has not yet been specified by whatever means, the potential capability of quantum computation that has not been appreci-ated in the externalist perspective would come to surface. Exchange interaction of a local character is by no means to denigrate its significance in the global extent. If one assumes the existence of exchange interaction on the global scale as prac-tised in field theory, a physicist practising such a global theoretical scheme would also have to as-sume to have the capacity of completing the com-putation that guaranteed the global consistency in theory, even if it is no feasible in practice. In contrast, exchange interaction of a local character
tends to approach the global consistency through each quantum computation of a local character. Quantum information in biology just focuses upon the informational capacity of molecules for approaching the global co-ordination from within.
4. Concluding comment
The role of quantum information in biology is intriguing. Rather, biology is quite unique in tai-loring quantum mechanics for its own sake. A mere phenomenology of biological phenomena tells us that biology is full of energy consumers as active agents, that is to say, biological organisms. What is imperative to these energy consumers is to find out whatever energy resources available. Quantum mechanics is intrinsically capable for gluing smaller components into a coherent body while realising a quantum coherence and further for extending the coherence to a greater extent through the quantum entanglement. Biological in-formation manifested in the biological realm is just an instance of tailoring intrinsic quantum information for the sake of energy consumers on their own.
We hope that this paper has highlighted at least two fundamental aspects of how to apply quan-tum mechanics to biology. One is the nature of time, whether local or global, or equivalently whether synchronous or asynchronous. The other is how to maintain a quantum coherence on a mesoscopic or even a macroscopic scale. What we wanted to explore in this paper is to focus on some aspects of these two problems in an explicit manner. Biology is not about applying quantum mechanics as it is already known through the experiences of traditional physics, but rather about an attempt to extend quantum mechanics in the manner that the physicists have not tried.
Acknowledgements
References
Albrecht-Buehler, G., 1991. Surface extensions of 3T3 cells towards distant infrared light sources. J. Cell. Biol. 114 (3), 493 – 502.
Albrecht-Buehler, G., 1995. Changes of cell behavior by near-infrared signals. Cell. Motil. Cytoskeleton 32 (4), 299 – 304. Beck, F., Eccles, J.C., 1992. Quantum aspects of brain activity and the role of consciousness. Proc. Natl. Acad. Sci. 89 (23), 11357 – 11361.
Ciblis, P., Cosic, I., 1997. The possibility of soliton/exciton transfer in proteins. J. Theor. Biol. 184 (3), 331 – 338. Conrad, M., 1990. Quantum mechanics and cellular
informa-tion processing: the self-assembly paradigm. Biomed. Biochim. Acta 49 (8 – 9), 743 – 755.
Deutsch, D., 1985. Quantum theory, the Church – Turing prin-ciple and the universal quantum computer. Proc. R. Soc. A. 400, 97 – 117.
Hameroff, S., 1998. Quantum computation in brain micro-tubules? The Penrose-Hameroff Orch OR model of con-sciousness. Philos. Trans. R. Soc. Lond. A 356, 1869 – 1896.
Harada, Y., Sakurada, K., Aoki, T., Thomas, D.D., Yanagida, T., 1990. Mechanochemical coupling in acto-myosin energy transduction studied by in vitro movement assay. J. Mol. Biol. 216, 49 – 68.
Harre´, R., 1988. Parsing the amplitudes. In: Brown, H.R., Harre´, R. (Eds.), Philosophical Foundations of Quantum Field Theory. Clarendon Press, Oxford, pp. 59 – 71. Hogg, T., Chase, J.G., 1996. Quantum smart matter. In:
Toffoli, T., et al. (Eds.), Proceedings of the Workshop on Physics and Computation. New England Complex Systems Institute, Cambridge, MA, pp. 147 – 152.
Hong, F.T., 1995. Magnetic field effects on biomolecules, cells, and living organisms. Biosystems 36 (3), 187 – 229. Igamberdiev, A.U., 1993. Quantum mechanical properties of
biosystems: a framework for complexity, structural stabil-ity, and transformations. Biosystems 31 (1), 65 – 73. Klinman, J.P., 1989. Quantum mechanical effects in
enzyme-catalysed hydrogen transfer reactions. Trends Biochem. Sci. 14 (9), 368 – 373.
Matsuno, K., 1993. Being free from Ceteris Paribus: a vehicle for founding physics on biology rather than the other way around. Appl. Math. Comput. 56, 261 – 279.
Matsuno, K., 1995. Quantum and biological computation. Biosystems 35 (2 – 3), 209 – 212.
Matsuno, K., 1996. Internalist stance and the physics of information. BioSystems 38, 111 – 118.
Matsuno, K., 1999. Cell motility as an entangled quantum coherence. BioSystems (in press).
Popp, F.A., Nagl, W., Li, K.H., Scholz, W., Weingartner, O., Wolf, R., 1984. Biophoton emission. New evidence for coherence and DNA as source. Cell. Biophys. 6 (1), 33 – 52. Popp, F.A., Li, K.H., Mei, W.P., Galle, M., Neurohr, R., 1988. Physical aspects of biophotons. Experientia 44 (7), 576 – 585.
Rosen, R., 1960. A quantum-theoretic approach to genetic problems. Bull. Math. Biophys. 22, 227 – 255.
Tusynski, J.A., Brown, J.A., Hawrylak, P., 1998. Dielectric polarization, electrical conduction, information processing and quantum computation is microtubules. Are they plau-sible? Philos. Trans. R. Soc. Lond. A 356, 1897 – 1926. Uyeda, T.Q.P., Warrick, H.M., Kron, S.J., Spudich, J.A.,
1991. Quantized velocities at low myosin densities in an in vitro motility assay. Nature 352, 307 – 311.
Witten, M., 1982. Some thoughts on quantum non-demolition measurements in biological systems. Bull. Math. Biol. 44 (5), 689 – 696.
