Introduction The quantum level and biological information

BioSystems 55 2000 39 – 46 Is there a biology of quantum information? Koichiro Matsuno a , Raymond C. Paton b, a Department of BioEngineering, Nagaoka Uni6ersity of Technology, Nagaoka 940 - 2188 , Japan b Department of Computer Science, The Uni6ersity of Li6erpool, Li6erpool L 69 3 BX, 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.comlocatebiosystems

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 : rcpcsc.liv.ac.uk R.C. Paton 0303-264700 - see front matter © 2000 Elsevier Science Ireland Ltd. All rights reserved. PII: S 0 3 0 3 - 2 6 4 7 9 9 0 0 0 8 1 - 7

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 vibrations 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. The result of the process of measuring is the generation of information. Information presumes at least two different operations. One is experienc- ing the reception of what seems to be a message coded in the form of a material aggregate, and the other is the interpretation of the received message so as to induce further messages to be transmit- ted. A sequence of measurements proceeding in- ternally is associated with information processing. The notion of internal being used here is related to all ‘observers’ being inside the system i.e. displaying an endosystem or internalist perspec- tive. Measurement by a material body in the form of receiving a message can turn out to be an internal object measured by other bodies. Infor- mation is thus viewed as a sequence of experienc- ing and interpreting messages. Consider the case for the local production of information that hap- pens when quantum particles interact. For a mea- surement to be registered there is an interaction within the quantum system that involves before and after and an energy exchange. Note that the before and after relates to two processes, namely interaction and measurement. The exchange inter- action makes an exchanged quantum particle to be a message to be transmitted. A sequence of exchange interactions is an indication of ongoing information processing. In order to explain this we shall look at the uncertainty relation between energy and time, that is: D E . 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-energy 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 non-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. 1. An internal view from uncertainty to information. 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 sigmoidallogistic 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 fuzzyfluctuat- 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 thermalthermodynamical 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 t ATP in which one ATP molecule is hydrolysed per myosin molecule. During this time the stored energy e ATP is released with typical values of t ATP 10 − 2 s and e ATP 5 × 10 − 13 erg or 7 kcalmol 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 of e ATP 5 × 10 − 13 erg 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 e ATP 2 × 10 − 15 s. This value is far less than the actual time interval required for releasing energy e ATP from an ATP molecule. 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 e m , at every time interval of Dt m while satisfying the constraints e m D t m e m D t m = e ATP t ATP In this case m denotes a quantum being responsi- ble for internal measurement. We may think of the energy flow associated with measuring each quan- tum as carrying energy e m over the time interval D t m . 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 e m , emitted coher- ently during one cycle of energy release from an ATP molecule at an actomyosin complex would roughly be t ATP D t m 2.2 × 10 6 . 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 low effec- ti6e temperature 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 m ms in a mutually coherent manner. Since this velocity gives each actin monomer linear momen- tum as much as 2.2 × 10 − 21 erg scm, 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