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Diffusion theory, the cell and the synapse
BioSystems 45 (1998) 151 – 163
Diffusion theory, the cell and the synapse D.N. Wheatley * Cell Pathology Unit, Uni6ersity Medical School, Foresterhill, Aberdeen, AB25 2ZD, UK Received 12 May 1997; received in revised form 7 October 1997; accepted 1 November 1997
Abstract The possibility exists that the cell internum is far more highly organised right down to the molecular level than was hitherto appreciated, to the point where ideas of a relatively solid-state chemistry model have been entertained (Coulson, R.A., 1993. The flow theory of enzyme kinetics — a role of solid geometry in the control reaction velocity in live animals. Int. J. Biochem. 25, 1445–1474). This contrasts sharply with the traditional dogma that diffusion is the mechanism by which molecules interact within an aqueous solution of the cell internum, although it should have been clear from an early stage that diffusion could not play other than a very resticted role in metabolic regulation. When physicists began to question certain aspects of the fundamental Law of Heat Conductance formulated over 170 years ago by Fourier, Diffusion Theory was also implicated (Maddox, J., 1989. Heat conductance is a can of worms. Nature 338, 373), and application of Fick’s Laws of Diffusion to living systems criticised (Agutter P.S., Malone, P.C., Wheatley, D.N., 1995. Intracellular transport mechanisms: a critique of diffusion theory. J. Theoret. Biol. 176, 261–272). While we have argued (Wheatley, D.N., Malone, P.C., 1993. Heat conductance, diffusion theory and intracellular metabolic regulation. Biol. Cell 79, 1–5) that diffusion cannot be prevented from occurring, we found that, irrespective of whether it was a valid theory, diffusion was of little relevance in most actively metabolising cell systems. However, diffusion is still perceived as essential for interacting molecules to demonstrate their specificities. Any new model of the internal state of the living cell has to resolve this dilemma. The question also relates to molecular movement and ligand–receptor interactions outside the cell. In looking at this situation, attention was paid to one site in the body in which diffusion has long been assumed to be essential, namely in the passage of the chemical transmitter between one neurone and the next across the synaptic cleft. A detailed examination of this assumption has helped to identify one possible place in which the importance of diffusion over a distance of no more than 20 – 30 nm occurs, although objections to diffusion being involved have been raised. The outcome, however, only re-enforces the conviction that diffusion has little role in metabolic activity and is normally ‘assisted’ in almost all aspects of cell physiology. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Diffusion; Intracellular movement; Synaptic transmission; Metabolic regulation
* Tel: + 44 1224 663123; fax: +44 1224 663002; e-mail: [email protected] 0303-2647/98/$19.00 © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S 0 3 0 3 - 2 6 4 7 ( 9 7 ) 0 0 0 7 3 - 7
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‘‘Science has always suffered from the vice of overstatement. In this way conclusions true within strict limitations have been generalised dogmatically into a fallacious universality’’. Whitehead (1926)
1. Introduction: the problem with diffusion This paper is about a fundamental canon called ‘diffusion’, which through its early inculcation into students of the science of biology inevitably influences their subsequent conceptualisation. Since the fundamental theory of heat conductance proposed by Fourier (1822) (for translation, see Freeman, 1878) is believed to have serious shortcomings (Joseph and Preziosi, 1989), its corollary —Diffusion Theory — also becomes suspect. Should Fourier’s Law be found deficient, then there is every reason to look more closely at diffusion (Maddox, 1989; Malone and Wheatley, 1991). The wag categorises theories into two broad groups, those with unanswered questions, and those with unquestioned answers. Diffusion theory falls squarely into the latter, being an easy way to ‘explain’ molecular behaviour in a living cell or organism, a tacit assumption which normally obviates the need to furnish formal evidence or proof, and rarely (if ever) expecting the proponent to make actual measurements. The opening statement by Whitehead could not be more true of diffusion theory, where its limitations were ignored from the start, resulting in sweeping generalisations that have become unquestioningly accepted, as already discussed at length elsewhere (Wheatley and Malone, 1993; Agutter et al., 1995). In many discussions of biological systems, the term ‘diffusion’ slips imperceptibly from its vernacular to its scientific connotation and vice versa, and herein lies much trouble. Molecules that take ‘random walks’ (Hille, 1984) are ‘diffusing’ in the vernacular sense of the word, but in the absence of a gradient, its scientific connotation is lost. Diffusion, scientifically and statistically, involves directionality, that associated with the random movements occurring within a gradient, thereby allowing one to calculate diffusion coeffi-
cients under the particular circumstances. Without random molecular movement one can impose directionality and harness the energy, information and availability of the molecules to an even greater extent (Fig. 1). When the movements of individual molecules become co-ordinated and vectorially directed by some mechanism such as a contractile pump, then highly efficient metabolism can occur, and Whitehead (1926) was probably not far from the truth when he said that it is most unlikely that ‘the bodily molecules run blindly’. However, the question relevant to life is not just how this can be brought about, but the extent to which such transport occurs in the body (predominantly) and in the cell (received wisdom, unnecessary, but arguably also the predominant form; for a fuller development of this idea, see Wheatley, 1998). Also, if it is indulged in on a major scale, what are the active processes which keep it going? This leaves us with the opposite and quite intrguing question of whether there is an essential role or need for diffusion, for example, in molecular interactions, so that their specificities can be fully exhibited and explored? This is highlighted in the recent hypothesis of Bray (1995), but the reader should consider the caveat concerning diffusion discussed in Agutter and Wheatley (1997) in this context. The purpose of this paper, therefore, is to extend the argument already put forward (Wheatley
Fig. 1. (a) Random movements of different species of molecules depicted as straight line rather than random walks, but showing no coordination, as would occur in a soup; (b) same molecules placed under a common external constraint which makes them move in only one direction. Throughout the body, and the cell, it is argued that much of movement is coordinated and directed in this manner, leaving few molecules running blindly around, as in (a).
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and Malone, 1993) as to why diffusion probably has little to do with the way molecules move around inside cells and throughout the whole body. The discussion will concentrate on a particular area in which a challenge might be considered most unlikely, namely in the passage of acetylcholine (ACh) across the synapse. At the risk of setting up a strawman, it is hoped that this particular example will show why our critical appraisal of the general relevance of diffusion theory in biology has to be pursued down to the finest detail in physiological functioning. The argument that diffusion theory is valid in terms of atomic theory does not allow us to apply it uncritically to biological systems. There are also a couple of further points which need to be re-emphasised. While we may argue that diffusion is not particularly relevant in the metabolism of living organisms, it cannot be denied that it occurs (Wheatley and Malone, 1993). It would be almost impossible to prevent it, unless all gradients in the cell were dissipated and/or the system turned from liquid to a completely solid state. But so often diffusion may prove more disadvantageous than beneficial since the process tends to obliterate expensively created gradients. There is also a plea that Diffusion Theory should stay in place until some alternative is found, but first we have to ask whether it is better to have a poor theory in place than none at all. And second, we have argued extensively elsewhere that there is in fact a perfectly reasonable and acceptable alternative available (Wheatley, 1985).
2. The synapse and the passage of an action potential An electrical signal running down a nerve axon by membrane depolarisation eventually results in a rapid Ca2 + uptake at the synaptic ending, which in turn causes the fusion of synaptic vesicles with the presynaptic membrane. This process is extraordinarily complex in itself (Bennett and Scheller, 1993), and biochemical sorting and docking of vesicles at the presynaptic membrane involves no less than four families of control molecules (So¨llner et al., 1993). Eventually, acetyl-
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choline (ACh) is released by exocytosis into the synaptic cleft, and has, on average, to move about 20–30 nm in order to trigger the postsynaptic membrane (Fig. 2). The important molecular events up to this point have been far from random because all the ionic movements have been carefully arranged and orchestrated by the nerve axon and the synapse itself; indeed the complex regulation in the latter involving four families of proteins is the epitome of careful predetermined arrangement of vSNARES and tSNARES of the synaptic vesicles and the presynaptic membrane, respectively. Although now the situation radically changes, for: ‘‘the acetylcholine molecules emptied into the cleft diffuse across to the postsynaptic membrane, where they bind to specific receptor proteins’’. (Becker, 1986) On depolarisation of the postsynaptic membrane, the message passes on (Fig. 1). Similar descriptions can be found in most general texts (Eckert and Randall, 1983; Darnell et al., 1986), and throughout specialised articles (Adelman, 1987). The speed of transmission of the signal across the synaptic cleft is quoted at about 0.2 mm s − 1, i.e. \ 1000 times slower than when the electrical impulse was travelling down the myelinated nerve axon (\ 25 m s − 1). Minimising the gap will reduce synaptic delay, but the more synapses in a pathway, the slower the overall transmission time, which accounts for the advantage of having as few synapses as possible in reflex arcs. The conversion of the electrical impulse to a chemical signal is responsible for much of the delay, as mentioned above, since it involves the processes of Ca2 + uptake, vesicle fusion and the actual exocytotic release of ACh, i.e. 0.3–0.4 ms of the total synaptic delay of 0.4–0.5 ms. Katz and Miledi (1966, 1967) microinjected ACh adjacent to the presynaptic membrane and confirmed that about 0.1 ms was needed to elicit a postsynaptic response, corresponding (conveniently) with the difference in delay noted above. The assumptions made are that the cleft contains an aqueous medium, and that ACh is free to free diffuses through it unhindered, although our
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Fig. 2. Typical diagram of a (chemical) synpase in which the main features of the synaptic vesicles are depicted, with their release of acetylcholine assumed to result in the diffusion of the neurotransmitter across the cleft.
knowledge of the content and organisation of the synaptic cleft is still poor: ‘‘the synaptic cleft may contain a network of fibrous proteins, such as collagen, that binds the two cells together. In some cases enzymes attached to this network destroy the chemical signal after it has functioned. In other cases the chemical signal diffuses away or is reincorporated into the presynaptic cell’’. (Darnell et al., 1986). However, synaptic vesicle discharge could not only be directionally assisted, but explosively so into the bargain, in which case diffusion would be a poor description of the movement of neurotransmitter towards its target. The findings of Katz and Miledi (1966, 1967) can be criticised as at best only an approximation to the maximal time of delay, since the evidence is only circumstantial that the 100 ms taken for molecules to cross the synapse is the least time they obtained for ACh (presumably to diffuse) across. Microin-
jection also involves force, and might mimic a more explosive local release from the presynaptic membrane, especially if the latter involves some element of propulsion of ACh across the gap when vesicles are released. So diffusion probably offers the simplest explanation, but it need not be the correct one (see below). Also, Schmidt and Samson (1969) have proposed that the fibrous lamina actively transports ACh towards the postsynaptic membrane along some form of molecular channels. However, most authors seem content to adopt a much simpler view of the synapse and diffusion, and Gray (1987) gives a typical position statement on synaptic design in which inferences abound: ‘‘The synaptic cleft is 20–30 nm across and contains vague proteinaceous bonding material. The width of the cleft is sufficient to ensure adequate ion fluxes in the synaptic membranes yet is narrow enough to permit diffusion of the transmitter across in microseconds, a time too insignificant to affect synaptic delay’’.
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While it is difficult to justify the statement that the width of the cleft can be (conveniently) ‘sufficient to ensure adequate ion fluxes’, the remark that it is (also conveniently) ‘narrow enough to permit diffusion…’ is typical, unquestioningly accepting (rightly or wrongly) that diffusion is the mechanism by which the transmitter substance reaches the postsynaptic membrane without a shred of evidence. However, Gray goes further still by stating that diffusion time is seemingly ‘too insignificant to affect synaptic delay’, as if any small delay here is of little or no consequence. Since Katz and Miledi (1966, 1967) have shown this delay to be about 100 ms, it could easily make the difference between life and death to some prey in a moment of attempted escape through a reflex action. In terms of the Theory of Natural Selection, this can scarcely be considered ‘insignificant’ with regard to that animal. Biologists have long been wary of small differences, the excuse often being that the inherent variability of living material makes it pointless to indulge in excessively high degrees of precision. Thus, if total synaptic delay could be reduced from, say, 400 to 350 ms by some means which accelerates (the more commonly used word is ‘facilitates’) diffusion of ACh across the synaptic cleft (i.e. by reducing the quoted delay due to the diffusion of the chemical transmitter across the cleft from 100 to 50 ms), few would be inclined to measure this reduction accurately, even given the necessary instrumentation, and fewer still would see whether it conferred a survival advantage. Yet we have just discussed two ways in which ACh might cross the gap faster than by ‘diffusion alone’. Such compounding of assumptions and inferences is the reason why the persistence of Diffusion Theory as a basic tenet of biology has to be constantly questioned and critically evaluated; the status quo is not an acceptable option. Why, then, do we mostly continue to believe that transmission of ACh across the synapse has to be by diffusion ‘alone’?
3. Diffusion is not a ‘simple’ thing Diffusion is nearly always referred to, or qualified, in a number of different ways. Darnell
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et al. (1986) use the phrase ‘diffusion alone’, and later ‘simple diffusion’. Simple diffusion is used on many occasions (Darnell et al., 1990; Alberts et al., 1996), while Pasternak (1979) prefers the expression ‘passive diffusion’, which might be more accurate a description. Occasionally the expression ‘exchange diffusion’ is introduced (Giese, 1979), which is refreshing because it recognises that molecular movements occur between cells and their environment as part of a continuum and not in the kind of vacuum or under highly abstract or contrived conditions indicated in many diagrammatic representations of the phenomenon. ‘‘What is usually measured in experiments is the net flux, that is, the net gain by, or net loss from, cells. However, outflow (efflux)…’’ (in this process of diffusion) …‘‘occurs at the expense of kinetic energy, not metabolic energy’’. (Giese, 1979). In many cases, biologists are aware that diffusion alone is too restrictive and inadequate to explain some phenomena, and that various means exist to ‘facilitate’ it. The use of the word ‘facilitate’ is indeed widespread in many instances where diffusion has been invoked in cell biology. It acknowledges that diffusion is not ‘simple’, and ‘facilitation’ implies a contrivance which conveniently allows one to make special cases for certain types of diffusion-based molecular movements. The word ‘pathway’ is actually used in this context, e.g. in the way in which a membrane can have a special channel with a permease/carrier molecule behaving as if it were an enzyme (Karp, 1979; Pasternak, 1979). We also need to look within the cell itself, where we come across other qualifications of diffusion, notable expressions such as diffusion-controlled or diffusion-restricted reactions. Stryer (1981) notes that ‘the rate (of a biochemical reaction) cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate’. Also, in this sphere, we are suffering the legacy of traditional biochemistry, reactions taking place in bulk phase (i.e. in a test-tube), dependent upon diffusion and obeying the law of mass action. There are instances in which reactions proceed
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faster than the expected collision or encounter rates on Stokes–Einstein calculations relating to radius of the molecules and viscosity of the milieu. Later Stryer (1986) accepts this by stating that where this happens, other mechanisms than diffusion must be involved, but enters into no discussion at to what these might be. Despite the reservations which clearly emerge from modern ideas on enzyme flux and substrate handling within recognised pathways (see below), the notion is still prevalent that diffusion largely accounts for, or can account for, the metabolic processes that proceed within a cell. Darnell et al. (1986) in their first edition made the quite outrageous statement, corrected in the second edition (Darnell et al., 1990), that: ‘‘Because a cell co-ordinates its metabolic acti6ities by diffusion alone, the rate at which molecules diffuse through the cell limits the typical cell size to between 30 and 50 microns in diameter’’. (My emphasis)
4. Diffusion theory and the detection of motion within cells A fundamental assumption in Fourier’s law is that the medium in which heat conductance is occurring should be still. This raises the question of whether Fick’s equation for diffusion, analogised from Fourier, can ever be truly applicable in a biological context, as discussed in detail in Wheatley and Malone (1993), Agutter et al. (1995). Intrinsically, a bar of metal (as originally used by Fourier for his measurements of heat conductance) can be considered non-moving, but no fluid medium is ever still. No living body or cell contains any completely still aqeuous phase, and even more importantly, the internum of the cell is incessantly moving because of cortical flow (Bray and White, 1988), cyclosis, cytoplasmic streaming, microcirculation and the syneretic effects of frequent actomyosin contractions and relaxation (Wheatley, 1985; Wheatley and Malone, 1987; Malone and Wheatley, 1991). Gerard (1940)
drew attention to ‘the apparent stillness’ of cells when examined by light microscopy microscopy, but quickly pointed out that at the molecular level the internum of the living cell was unresting, hence the title of his book. If diffusion is equated with molecular movement and the internum of the cell is a membranous bag containing a relatively non-viscous fluid, a soup of enzymes, and their substrates, intermediates and products, Brownian motion should be as easily seen as in a bleb produced by an injured cell. However, this is only at the level of resolution where oscillation, vibrations and translocations of particles rather than individual molecules, which can be detected in the light microscope. At the level of the water molecules themselves, much ‘self-diffusion’ (random movements?) is occurring within the cytoplasm, at least in rotational terms, but not so much in translational terms, as in completely free water in a beaker (Mastro et al., 1984; Wheatley et al., 1991). Diffusion is almost always occurring in the context of convective movements (Fig. 1), i.e. along with an element of bulk flow. We seem to have erred most notably in assuming the latter to be negligible within the domain of the cell internum, when in reality it probably dominates. However, it remains a major task at the end of the 20th century to provide further convincing evidence and argument that flow within cells is not just a universal phenomenon, but one that is vital for physiological functioning. Movement is always occurring within the living cells, no matter how still they may appear. If one, however, observes a cell which has been heated to 44–45°C for 5–10 min, this stillness is paradoxically even more remarkable (Wheatley et al., 1989). While the normal cell shows superficially only small agitations of organelles and resolvable particles by optical microscopy which can be attributable to Brownian motion, classical description of enzyme activity demands that massive Brownian motion occurs for substrates to move from one enzyme to the next, as they diffuse (in the vernacular) around and make interactions with frequencies of encounters based on the law of mass action. Why, then is there less evidence of this in the heated cell. Borelli et al. (1986) main-
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tained that the heated cell blebbed, with increased Brownian occurring quite violently within such extrusions. However, this is rarely the case in cells which have been recently ‘overheated’, although it may describe their activity much later. If a short heat treatment (5 min) is followed by ‘rescue’ at 37°C, extensive blebbing rapidly occurs. Within their blebs, violent Brownian motion can be clearly seen, which sharply contrasts with the low level of such activity in normal cytoplasmic extrusions from a cell (Albrecht-Buehler, 1982). From this, one can quite categorically state that the internum of the normal cell does not allow a great deal of Brownian movement of (resolvable) particles to occur, but when the fabric of the cytoplasm has been disrupted, a massive amount suddenly becomes apparent. However, within the unperturbed cell, convective flow is also observed, although it takes the highest resolution light microscopy available, preferably with video-enhanced image processing, cells in their healthiest condition, a lot of patience and the right skills to document its nature, especially in small cells such as mammalian cells (Wheatley, 1985; Wheatley et al., 1991). Particles are often being whisked along transient channels at the rate of up to 2 – 3 m s − 1 in these cells, and up to 3 – 4 times faster than this in many larger cells or syncytia in which cytoplasmic streaming is an obvious feature (e.g. Physarum; see Nations et al., 1981). The movements are orders of magnitude facter than particles driven by dynein or kinesin on cytoskeletal elements. The point which needs to be emphasised is that bulk flow of this type within cells is not a feature of size, i.e. it is not first and foremost a strategy purely indulged in by large cells to surmount an intracellular transport or distribution problem, but a necessary phenomenon of all cells. Before developing this argument further, there are recognised strategies by which diffusion might be assisted in its ability to cope with size and metabolic intensity within cells. Alberts et al. (1996) graphically describe some of these. One is compartmentalisation, in which molecules to be specifically reacted together are concentrated into designated places to increase the frequency of their encounters in bulk phase. Another mechanism is to prevent molecules from drifting away
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from a site of metabolic activity by restricting their freedom to diffuse out of the cell, as expressed by Davis (1958) in his exceptionally perceptive essay on the ionisation of molecules by living cells. A third is to bring diffusing molecules down from three dimensions on to surfaces, such as a membrane, and allow them to move in just two dimensions towards their targets. And the fourth is to raise the temperature, which has meant that life can operate more rapidly when a temperature of 37°C is maintained rather than an ambient of, say, 7°C. However, the strategy to which we will now pay particular attention is the deliberate bringing together of molecules by passing them over the surfaces on which interactions take place, the perfusion principle. Oddly, this most feasible of strategies fails to be mentioned in a single textbook of (cell) biology and cell physiology, and yet it is the pervading mechanism in all living creatures right down to within their smallest cells. What has been proposed is that intracellular movements of a convective nature (through to overt bulk flow, as in cyclosis) is an extension of the Harveian principle, the requirement for a circulation, to the subcellular and molecular level (Malone and Wheatley, 1991; Wheatley and Malone, 1993). It is no longer enough to state and assume that diffusion suffices for transport within all cells but the exceptionally large ones. Biologists need to grasp the significance and implications of this situation, because it calls for a radical reappraisal of the way in which we believe how molecules move and are moved around in living cells and organisms, and in particular how these movements can be rigorously and sensitively controlled to adjust the rate of metabolic functioning (Wheatley and Clegg, 1994). These are by no means trivial issues. We need to turn to the thorny issue of the possibility that there is, however, an essential requirement for diffusion at the molecular level in order for interacting molecules to sort themselves out according to their individual specificities. If this is a general phenomenon, then we have every right to expect there to be extensive Brownian movement throughout the cytoplasm. The larger the molecules involved the slower will their movement be throughout the cell,
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Fig. 3. Illustration of the three main types of synapses in neural tissue: (a) represents an electrical synapse with a very narrow cleft of 2–3 nm, i.e. ten times narrower than the chemical synapse. This type is found predominantly in brain tissue where local signalling of a weak nature between neurones is required; (b) represents a mixed synapse, with elements of an electrical synapse and a chemical synapse (to the right) is involved; (c) is a typical chemical synapse found throughout the rest of the nervous system, and important in the propagation of strong signals which are not quickly attenuated over relatively long distances. In this case an inhibitory synapse is also shown on the presynaptic bulb, an arrangement which allows some modulation of the transmission of the action potential from the presynaptic neurone to the postsynaptic neurone.
given that it is a simple aqueous solution despite all the barriers of its compartments, membranes, granules, droplets, etc. It might take an ATP molecule less than a second to diffuse across the average 10 micron diameter cell, but a calculation based on the passage through a primarily aqueous solution suggests that it would take a moderate sized protein of 100 Kda with a generally spherical quaternary structure about 10 – 12 min (Wheatley, 1985; Wojcieszyn et al., 1981). As cellular activity increases with workload, diffusion would become limiting because the only way in which it can now increase is through a significant rise in temperature. Taking the principle of Coulson (1986) that the cell would have been designed along the lines laid down by the finest chemical engineer, the important thing is to force reacting molecules together over a catalytic surface within
narrow confined spaces to maximise encounter rate per unit time. The rate at which this is done will sensitively adjust the reaction rate, making it fully controllable, thereby allowing product manufacturing to be commensurate with their ‘market’ use. In the absence of molecular freedom to make random walks (self-diffusion within the cell in this context), interactions between molecules will rise in proportion to the rate at which convection of the cytosolic compartment occurs over the surfaces within the cell (see Fig. 3 in Wheatley and Clegg, 1994). The problem of molecular sorting on the basis of specificities is a function of total encounters per unit time whether the movement is occurring by diffusion or by any other assisted/coordinated movement. The model emerging of the functioning cell differs from the classical one on the organisation of the internum
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as a huge catalytic surface on which reactions can take place in a sequential manner, with the cytosol equally being organised as a compartment in which convection results in the perfusion of reactants over these surfaces at rates commensurate with metabolic activity. The message is to keep the big catalytic molecules anchored and suffuse them with their substrates. There need be no absolute requirement for ‘undirected’ activity (diffusion in the vernacular), but it would still occur where intracellular convection has been abolished. However, the question is whether this could sustain an active metabolism, and this seemingly simple but critical experiment (discussed in Wheatley and Malone, 1993) has yet to be successfully designed and executed.
5. Perfusion and life: convective diffusion and living processes Estimates of diffusion of small molecules in cells are usually based on the assumption that the internum can be approximated to a simple aqueous phase or solution, but the fact that it can be two-three times slower does not make this credible (Clegg, 1984; Mastro and Keith, 1984; Luby-Phelps, 1994). Dispersion within the cell, however, can be seen to be greatly assisted by the incessant movement of the bulk aqueous phase through the labyrinthine honeycomb of the microtrabecular lattice and other membranes (see Paine, 1984; Kohen et al., 1989). It has been argued and evidence presented that all cells, not just large cells, possess a microcirculation (or sometimes a rhythmical ebbing and flowing along ‘a system of transient channels’, as in Physarum; see Nations et al., 1981) which allows both very large and small molecules to be moved around with almost equal speed and freedom, and at rates which for all including the smallest molecules will be far greater than by diffusion. [A perceived weakness in this argument is that transient channels can be seen when intracellular microcirculation is filmed, and yet in ultrastructural or microanatomical terms, we are at the same point as Harvey was when he realised there was a blood circulation but could not see the capillaries that
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completed the circle. Malpighi used the newly invented microscope to resolve this problem. We can see intracellular channels while they are functioning, but our critics call for anatomical verification, a tangible structure, when the cell is fixed, which has been like chasing a ‘will o’ the wisp’.] This process of circulation requires considerable energy (which has yet to feature in audits of cell energy expenditure), but it naturally assists all metabolic reactions because it becomes effectively a self-stoking operation, which is an important aspect of efficient metabolic regulation (Clegg and Wheatley, 1991). The distance over which ‘simple diffusion’ occurs in the movement of oxygen from the air to the muscles of the foot, relative to the total distance travelled is truly miniscule; and even in some of the situations of a few tenths of a micron where it can be conceded that diffusion is involved, some additional element of convection cannot be ruled out. Schmidt-Nielsen (1979) has calculated that it would take an oxygen molecule arriving in the lungs and travelling at an estimated 10 microns per ms approximately 3 years to reach the foot if convection was not the main means of directed delivery. Now the question remains as to how molecular specificities are sorted out without diffusion. Molecular specificity in interactions are dependent upon molecules encountering one another. In a random walk situation, beautifully described in Hille (1984), molecules will encounter one another with calculable frequencies. If however all the molecules were entrained to pass over a surface on which molecules of species A lay in readiness for molecules of species, then the faster they are streamed passed within narrow confines (see Clegg and Wheatley, 1991; their Fig. 3), the more precisely one can predict the much greater frequency of encounter. Physiological control is clearly based on encounter frequency and Coulson (1986) has more than adequately dealt with the basis of this fundamental problem in living organisms. Even at its lowest metabolic ebb, a living organism needs a small draught of oxygen. As its circulatory rate increases with more active metabolism, oxygen gets delivered at a faster rate to the cells, and they in turn can work more
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vigorously. It has been argued that this is the basis of regulation of metabolic activity in animals as different in size as a mouse and an elephant or whale; their cells metabolise at rates which are over two orders of magnitude different (Coulson, 1986). The same argument can be rehearsed with respect to all other essential nutrients or substrates required to sustain life over a wide metabolic range (such as glucose, amino acids, fatty acids, etc.; see Wheatley, 1985). We should now return to consider the way in which the synapse is constructed and operates, the question of speed of synaptic transmission having recently been described as ‘one of the fastest things animal cells do’ (Almers, 1994).
6. The synapse revisited Chemical synapses (Fig. 3c) are by far the most common type in the mammalian CNS and peripheral nervous system, there being a very small percent of electrical (Fig. 3a) and mixed (Fig. 3b) synaptic endings, with different physiologies (Bennett, 1972). It was suggested earlier that ACh could be shot across the gap in chemical synapses to reduce transmission time, but this argument begins to lose its force in some respects because it can now be seen that there is barely any such delay in an electrical synapse. Why, then, did chemical synapses with their 20 – 30 nm gaps evolve and become predominant, and for what reason do they seem to be set to ‘waste’ precious time in sending signals along nerve pathways when other arrangements already exist that would obviate this delay? One answer seems to be that specialised signalling of a co-ordinating nexus relies upon the use of low-resistance electrical synapses in situations where the next neurone in the pathway needs to be quickly and repeatedly stimulated, e.g. along with the many other simultaneously incoming and outgoing signals found in complex brain circuitry. The gap in the electrical synapse of only 2 nm is ‘sufficient’ to allow ‘instant’ but relatively weak depolarisation of the low-resistance postsynaptic membrane characteristic of this type of synapse, otherwise too much current would flow out into the surrounding
medium causing undesirable triggering of local neurones. Furthermore, signal attenuation will be very fast. Under these circumstances, there is little opportunity for modulation of the signal and only weak efferent nerve depolarisation occurs because these is no amplification mechanism assisting its passage from the presynaptic cell. Such an impulse would be inadequate to depolarise, for example, a large muscle fibre at a neuromuscular junction. In contrast, the cleft in the chemical synapse is actually considerably wider than the average intercellular gap between cells, and depolarisation of the presynaptic membrane by as much as 100 mV would scarcely affect the postsynaptic membrane by less than 0.01 mV, if only electrical transmission was operating. The depolarisation caused per quantum (vesicle) of a chemical transmitter can be calculated, however, and at any time as many as ten such events may be taking place. But a threshold of 100–300 quantal events are needed as a pulse before the postsynaptic membrane is abruptly depolarised and the signal passed on. Each quantum is equivalent to about 5 ×104 molecules of ACh being released, and each ACh molecule is potentially capable of eliciting a permeability change in the postsynaptic membrane equivalent to a flux of 1–5× 104 Na + ions, thus effectively amplifying the signal. Furthermore, the responsiveness of the membranes and other parts of the complex within the 100 ms synaptic delay can be modified and modulated by various means, such as alteration in receptor sensitivity on the postsynaptic nerve or slightly earlier firing of an inhibitory nerve axon on the presynaptic region (Fig. 3c), which can retard vesicle release. Thus, it is ironic that if diffusion is truly involved in ACh movement across the synapse, it appears to be a rate-limiting factor in transmission, and we can postulate that this retardation evolved through natural selection because time for signal augmentation and modulation introduced some further selective advantage. Through amplification, signal strength is maintained and this is needed to depolarise postsynaptic membranes or a large muscle fibre bundle at a motor-end plate. It is noteworthy that the distance over which diffusion rules in the case of the
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chemical synapse is limited to 20 – 30 nm, and in a situation where a steep gradient is created by the localised release of the neurotransmitter at the presynaptic membrane in a cleft which is normally kept clear of ACh by the presence of choline esterase. This rather exceptional case of diffusion might then prove the rule that the random dispersion of molecules is not normally resorted to in most physiological circumstances.
7. Implications of perfusion in the organisation of cells Life is based on surface chemistry to a far greater extent than conventional biochemistry has, at least until recently, led us to believe. Indeed, the gentlest homogenisation is a cataclysmic event to the cell (McConkey, 1982), but biochemists had spent decades studying enzyme kinetics on solubilised preparations made in this way (Coulson, 1993). This is far removed from the delicate and intricate organised complexes of catalytic units on topographically well-ordered surfaces and membranes actually found in vivo (Welch, 1977; Srivastava and Bernhard, 1986; Berry et al., 1987; Srere, 1987). As Sherrington (1940) and others have pointed out over half a century ago, the cell internum amounts to a gigantic superbly organised collection of surfaces (Tracey, 1968; Clegg, 1984), on and in which directed transfer effectively eliminates the involvement and supposed randomness of diffusive processes in metabolic pathways by which one reaction product would otherwise have to wander aimlessly about in order to encounter by chance the next enzyme in the sequence. Indeed, the almost universal acceptance and frequency of use of the word ‘pathway’ strongly connotes that intermediates are prohibited from taking random walks. Surfaces allow reactants a greater chance of intimate contact. A precisely sculpted surface may not only allow two reactants to adopt close proximity, but actually assist them to rearrange their bonds; the surface can achieve catalytic status. In life, the surfaces (arrayed enzymes) are perfused or suffused with
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medium (the cytosol) which delivers reactants and takes away the products to deliver them quickly elsewhere (Clegg and Wheatley, 1991). Intermediates are not usually found in abundance, for one may now speculate that most will be held within the multicatalytic units or complexes which undertake the pathway until the final product itself and waste products are ‘released’. The speed of reaction no longer has to be governed by the concentrations of the reactants, but can be increased as much as 10fold simply by perfusing the system and delivering the precursors ten times faster (Coulson, 1986). Like a fire (Kleiber, 1961), it be delicately tuned to the appropriate level of activity within its individual cells under the prevailing circumstances. It also links activity directly to the ‘demand’ for work (Clegg and Wheatley, 1991). If life is commonly judged in man by whether his heart is pumping and his blood circulating, then it may be argued at the cellular level that when his cells can no longer circulate the soluble phase (Wheatley and Malone, 1993, see hypothesis on p. 3 therein), they will be in an extremely low state of metabolic activity, as in suspended animation, or dead. What is happening at the molecular level inside the cell ceases, perhaps, to be adequately described by words such as ‘diffusion’ or ‘flow’ because they cannot be so easily divorced or distinguished in reality, only in the abstraction of the mathematician’s or theoretical biologist’s equations. It is therefore ironic that our long-held belief that diffusion suffices in the synapse really needs to be reviewed. There is no question that the gap is wider than between most cells and therefore it probably has a design which relates to some functional control such as modulation. Would it help to speed up the process by a factor of two or more, or would this jeopardise the ability to modulate the postsynaptic response? Is diffusion over this short distance a selected strategy for slowing things down, since it seriously weakend the claim that the transmission of neural impulses is one of the ‘fastest things we do’ (Almers, 1994)?
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Acknowledgements I wish to thank Professor Brian Goodwin, Drs Paul Agutter and Attila Miseta for many helpful discussion on different aspects of this study. The work was supported by a Wellcome History of Medicine grant, for which I am most grateful.
References Adelman, G., 1987. Encyclopedia of Neurosciences. Birkhauser, Boston. Agutter, P.S., Wheatley, D.N., 1997. Information processing and intracellular ‘neural’ (protein) networks: considerations regarding the diffusion-based hypothesis of Bray. Biol. Cell 89, 13 – 18. Agutter, P.S., Malone, P.C., Wheatley, D.N., 1995. Intracellular transport mechanisms: a critique of Diffusion Theory. J. Theoret. Biol. 176, 261–272. Alberts, B., Bray, D., Lewis, J., Raff, M., Roberts, K., Watson, J.D., 1996. Molecular Biology of the Cell, 3rd ed. Garland, New York. Albrecht-Buehler, G., 1982. Does blebbing reveal the convulsive flow of liquid and solutes through the cytoplasmic network? Cold Spring Harbor Symp. 44, 45–59. Almers, W., 1994. How fast can you get? Nature 367, 682– 683. Becker, W.M., 1986. The World of the Cell. Benjamin/Cummings, Menlo Park. Bennett, M.V.L., 1972. A comparison of electrically and chemically mediated transmission. In: Pappas, G.D., Purpura, D.P. (Eds.), Structure and Function of Synapses. Raven Press, New York. Bennett, M.K., Scheller, R.H., 1993. The molecular machinery for secretion is conserved from yeast to neurons. Proc. Natl. Acad. Sci. USA. 90, 2559–2563. Berry, M.N., Gregory, R.B., Grivell, A.R., Henly, D.C., Phillips, J.W., Wallace, P.G., Welch, G.R., 1987. Linear relationships between mitochondrial forces and cytoplasmic flows argue for the organized energy-coupled nature of cellular metabolism. FEBS Lett. 224, 201–207. Borelli, M.J., Wong, R.S.L., Dewey, W.C., 1986. A direct correlation between hyperthermia-induced membrane blebbing and survival in synchronous G1 CHO cells. J. Cell. Physiol. 126, 181 – 190. Bray, D., 1995. Protein molecules as computational elements in living cells. Nature 376, 307–312. Bray, D., White, J., 1988. Cortical flow in animal cells. Science 289, 883 – 888. Clegg, J.S., 1984. Properties and metabolism of the aqueous cytoplasm and its boundaries. Am. J. Physiol. 246, R133– R151. Clegg, J.S., Wheatley, D.N., 1991. Intracellular organization: evolutionary origins and possible consequences to
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D.N. Wheatley / BioSystems 45 (1998) 151–163 Nations, C., Guevara, A., Cameron, I.L., 1981. Protoplasmic streaming during the cell cycle in Physarum polycephalum. Exp. Cell Res. 132, 493–495. Paine, P.L., 1984. Diffusive and non-diffusive proteins in vivo. J. Cell Biol. 99, 188S–194S. Pasternak, C.A., 1979. An Introduction to Human Biochemistry. Oxford Medical Publications, Oxford, pp. 134–135. Schmidt-Nielsen, K., 1979. Scaling: Why is Animal Size so Important? Cambridge University Press, Cambridge. Schmidt, F.O., Samson, F.E., 1969. Brain cell microenvironment: a report based on an NRP work session. Neurosci. Res. Prog. Bull. 7, 335–339. Sherrington, C., 1940. Man on His Nature: The Gifford Lectures, 1937. Penguin Books, Harmondsworth. So¨llner, T., Bennett, M.K., Whiteheart, S.W., Scheller, R.H., Rothman, J.E., 1993. A protein assembly-disassembly pathway in vitro that may correspond to sequential steps of synaptic vesivle docking, activation, and fusion. Cell 75, 409 – 418. Srere, P.A., 1987. Complexes of sequential metabolic enzymes. Annu. Rev. Biochem. 56, 21–62. Srivastava, D.K., Bernhard, S., 1986. Metabolite transfer via enzyme – enzyme complexes. Science 234, 1081–1086. Stryer, L., 1981. Biochemistry, 2nd ed. WH Freeman and Co., San Francisco. Stryer, L., 1986. Biochemistry, 3rd ed. WH Freeman and Co., San Francisco. Tracey, M.V., 1968. Fitting the environment by modifying water structure. Proc. Roy. Soc. (Lond.) B 171, 59–66. Welch, G.R., 1977. On the role of organized multienzyme systems in cellular metabolism: a general synthesis. Prog. Biophys. Mol. Biol. 32, 103–112.
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Wheatley, D.N., 1985. On the possible importance of an intracellular circulation. Life Sci. 36, 299 – 307. Wheatley, D.N., 1998. On the vital role of fluid movement in organisms and cells: a brief historical account from Harvey to Coulson, extending the hypothesis of circulation. Medical Hypotheses (in press). Wheatley, D.N., Clegg, J.S., 1994. What determines the basal metabolic rate of vertebrate cells in vivo? BioSystems 32, 83 – 92. Wheatley, D.N. and Malone, P.C., 1987. Diffusion or perfusion in the living cell: implications for metabolic regulation and organization. In: Welch, G.R. and Clegg, J.S. (Eds.), The organization of cell metabolism. NATO ARI series A 127, 171-173. Plenum Press, New York. Wheatley, D.N., Malone, P.C., 1993. Heat conductance, diffusion theory and intracellular metabolic regulation. Biol. Cell 79, 1 – 5. Wheatley, D.N., Kerr, C., Gregory, D.W., 1989. Heat-induced damage to HeLa S-3 cells: correlation of viability, permeability, osmosensitivity, phase-contrast light-, scanning electron- and transmission electron-microscopical findings. Int. J. Hypertherm. 5, 145 – 162. Wheatley, D.N., Redfern, A., Johnson, R.P.C., 1991. Heat-induced disturbances of intracellular movement and the consistency of the aqueous cytoplasm in HeLa S-3 cells: a laser-Doppler and proton NMR study. Physiol. Chem. Phys. Med. NMR 23, 199 – 216. Whitehead, A.N., 1926. Science and the Modern World. Cambridge University Press, Cambridge. Wojcieszyn, J.W., Schlegel, R.A., Wu, E.S., Jacobson, K.A., 1981. Diffusion of injected macromolecules within the cytoplasm of living cells. Proc. Natl. Acad. Sci. USA. 78, 4407 – 4410.
Diffusion theory, the cell and the synapse D.N. Wheatley * Cell Pathology Unit, Uni6ersity Medical School, Foresterhill, Aberdeen, AB25 2ZD, UK Received 12 May 1997; received in revised form 7 October 1997; accepted 1 November 1997
Abstract The possibility exists that the cell internum is far more highly organised right down to the molecular level than was hitherto appreciated, to the point where ideas of a relatively solid-state chemistry model have been entertained (Coulson, R.A., 1993. The flow theory of enzyme kinetics — a role of solid geometry in the control reaction velocity in live animals. Int. J. Biochem. 25, 1445–1474). This contrasts sharply with the traditional dogma that diffusion is the mechanism by which molecules interact within an aqueous solution of the cell internum, although it should have been clear from an early stage that diffusion could not play other than a very resticted role in metabolic regulation. When physicists began to question certain aspects of the fundamental Law of Heat Conductance formulated over 170 years ago by Fourier, Diffusion Theory was also implicated (Maddox, J., 1989. Heat conductance is a can of worms. Nature 338, 373), and application of Fick’s Laws of Diffusion to living systems criticised (Agutter P.S., Malone, P.C., Wheatley, D.N., 1995. Intracellular transport mechanisms: a critique of diffusion theory. J. Theoret. Biol. 176, 261–272). While we have argued (Wheatley, D.N., Malone, P.C., 1993. Heat conductance, diffusion theory and intracellular metabolic regulation. Biol. Cell 79, 1–5) that diffusion cannot be prevented from occurring, we found that, irrespective of whether it was a valid theory, diffusion was of little relevance in most actively metabolising cell systems. However, diffusion is still perceived as essential for interacting molecules to demonstrate their specificities. Any new model of the internal state of the living cell has to resolve this dilemma. The question also relates to molecular movement and ligand–receptor interactions outside the cell. In looking at this situation, attention was paid to one site in the body in which diffusion has long been assumed to be essential, namely in the passage of the chemical transmitter between one neurone and the next across the synaptic cleft. A detailed examination of this assumption has helped to identify one possible place in which the importance of diffusion over a distance of no more than 20 – 30 nm occurs, although objections to diffusion being involved have been raised. The outcome, however, only re-enforces the conviction that diffusion has little role in metabolic activity and is normally ‘assisted’ in almost all aspects of cell physiology. © 1998 Elsevier Science Ireland Ltd. All rights reserved. Keywords: Diffusion; Intracellular movement; Synaptic transmission; Metabolic regulation
* Tel: + 44 1224 663123; fax: +44 1224 663002; e-mail: [email protected] 0303-2647/98/$19.00 © 1998 Elsevier Science Ireland Ltd. All rights reserved. PII S 0 3 0 3 - 2 6 4 7 ( 9 7 ) 0 0 0 7 3 - 7
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‘‘Science has always suffered from the vice of overstatement. In this way conclusions true within strict limitations have been generalised dogmatically into a fallacious universality’’. Whitehead (1926)
1. Introduction: the problem with diffusion This paper is about a fundamental canon called ‘diffusion’, which through its early inculcation into students of the science of biology inevitably influences their subsequent conceptualisation. Since the fundamental theory of heat conductance proposed by Fourier (1822) (for translation, see Freeman, 1878) is believed to have serious shortcomings (Joseph and Preziosi, 1989), its corollary —Diffusion Theory — also becomes suspect. Should Fourier’s Law be found deficient, then there is every reason to look more closely at diffusion (Maddox, 1989; Malone and Wheatley, 1991). The wag categorises theories into two broad groups, those with unanswered questions, and those with unquestioned answers. Diffusion theory falls squarely into the latter, being an easy way to ‘explain’ molecular behaviour in a living cell or organism, a tacit assumption which normally obviates the need to furnish formal evidence or proof, and rarely (if ever) expecting the proponent to make actual measurements. The opening statement by Whitehead could not be more true of diffusion theory, where its limitations were ignored from the start, resulting in sweeping generalisations that have become unquestioningly accepted, as already discussed at length elsewhere (Wheatley and Malone, 1993; Agutter et al., 1995). In many discussions of biological systems, the term ‘diffusion’ slips imperceptibly from its vernacular to its scientific connotation and vice versa, and herein lies much trouble. Molecules that take ‘random walks’ (Hille, 1984) are ‘diffusing’ in the vernacular sense of the word, but in the absence of a gradient, its scientific connotation is lost. Diffusion, scientifically and statistically, involves directionality, that associated with the random movements occurring within a gradient, thereby allowing one to calculate diffusion coeffi-
cients under the particular circumstances. Without random molecular movement one can impose directionality and harness the energy, information and availability of the molecules to an even greater extent (Fig. 1). When the movements of individual molecules become co-ordinated and vectorially directed by some mechanism such as a contractile pump, then highly efficient metabolism can occur, and Whitehead (1926) was probably not far from the truth when he said that it is most unlikely that ‘the bodily molecules run blindly’. However, the question relevant to life is not just how this can be brought about, but the extent to which such transport occurs in the body (predominantly) and in the cell (received wisdom, unnecessary, but arguably also the predominant form; for a fuller development of this idea, see Wheatley, 1998). Also, if it is indulged in on a major scale, what are the active processes which keep it going? This leaves us with the opposite and quite intrguing question of whether there is an essential role or need for diffusion, for example, in molecular interactions, so that their specificities can be fully exhibited and explored? This is highlighted in the recent hypothesis of Bray (1995), but the reader should consider the caveat concerning diffusion discussed in Agutter and Wheatley (1997) in this context. The purpose of this paper, therefore, is to extend the argument already put forward (Wheatley
Fig. 1. (a) Random movements of different species of molecules depicted as straight line rather than random walks, but showing no coordination, as would occur in a soup; (b) same molecules placed under a common external constraint which makes them move in only one direction. Throughout the body, and the cell, it is argued that much of movement is coordinated and directed in this manner, leaving few molecules running blindly around, as in (a).
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and Malone, 1993) as to why diffusion probably has little to do with the way molecules move around inside cells and throughout the whole body. The discussion will concentrate on a particular area in which a challenge might be considered most unlikely, namely in the passage of acetylcholine (ACh) across the synapse. At the risk of setting up a strawman, it is hoped that this particular example will show why our critical appraisal of the general relevance of diffusion theory in biology has to be pursued down to the finest detail in physiological functioning. The argument that diffusion theory is valid in terms of atomic theory does not allow us to apply it uncritically to biological systems. There are also a couple of further points which need to be re-emphasised. While we may argue that diffusion is not particularly relevant in the metabolism of living organisms, it cannot be denied that it occurs (Wheatley and Malone, 1993). It would be almost impossible to prevent it, unless all gradients in the cell were dissipated and/or the system turned from liquid to a completely solid state. But so often diffusion may prove more disadvantageous than beneficial since the process tends to obliterate expensively created gradients. There is also a plea that Diffusion Theory should stay in place until some alternative is found, but first we have to ask whether it is better to have a poor theory in place than none at all. And second, we have argued extensively elsewhere that there is in fact a perfectly reasonable and acceptable alternative available (Wheatley, 1985).
2. The synapse and the passage of an action potential An electrical signal running down a nerve axon by membrane depolarisation eventually results in a rapid Ca2 + uptake at the synaptic ending, which in turn causes the fusion of synaptic vesicles with the presynaptic membrane. This process is extraordinarily complex in itself (Bennett and Scheller, 1993), and biochemical sorting and docking of vesicles at the presynaptic membrane involves no less than four families of control molecules (So¨llner et al., 1993). Eventually, acetyl-
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choline (ACh) is released by exocytosis into the synaptic cleft, and has, on average, to move about 20–30 nm in order to trigger the postsynaptic membrane (Fig. 2). The important molecular events up to this point have been far from random because all the ionic movements have been carefully arranged and orchestrated by the nerve axon and the synapse itself; indeed the complex regulation in the latter involving four families of proteins is the epitome of careful predetermined arrangement of vSNARES and tSNARES of the synaptic vesicles and the presynaptic membrane, respectively. Although now the situation radically changes, for: ‘‘the acetylcholine molecules emptied into the cleft diffuse across to the postsynaptic membrane, where they bind to specific receptor proteins’’. (Becker, 1986) On depolarisation of the postsynaptic membrane, the message passes on (Fig. 1). Similar descriptions can be found in most general texts (Eckert and Randall, 1983; Darnell et al., 1986), and throughout specialised articles (Adelman, 1987). The speed of transmission of the signal across the synaptic cleft is quoted at about 0.2 mm s − 1, i.e. \ 1000 times slower than when the electrical impulse was travelling down the myelinated nerve axon (\ 25 m s − 1). Minimising the gap will reduce synaptic delay, but the more synapses in a pathway, the slower the overall transmission time, which accounts for the advantage of having as few synapses as possible in reflex arcs. The conversion of the electrical impulse to a chemical signal is responsible for much of the delay, as mentioned above, since it involves the processes of Ca2 + uptake, vesicle fusion and the actual exocytotic release of ACh, i.e. 0.3–0.4 ms of the total synaptic delay of 0.4–0.5 ms. Katz and Miledi (1966, 1967) microinjected ACh adjacent to the presynaptic membrane and confirmed that about 0.1 ms was needed to elicit a postsynaptic response, corresponding (conveniently) with the difference in delay noted above. The assumptions made are that the cleft contains an aqueous medium, and that ACh is free to free diffuses through it unhindered, although our
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Fig. 2. Typical diagram of a (chemical) synpase in which the main features of the synaptic vesicles are depicted, with their release of acetylcholine assumed to result in the diffusion of the neurotransmitter across the cleft.
knowledge of the content and organisation of the synaptic cleft is still poor: ‘‘the synaptic cleft may contain a network of fibrous proteins, such as collagen, that binds the two cells together. In some cases enzymes attached to this network destroy the chemical signal after it has functioned. In other cases the chemical signal diffuses away or is reincorporated into the presynaptic cell’’. (Darnell et al., 1986). However, synaptic vesicle discharge could not only be directionally assisted, but explosively so into the bargain, in which case diffusion would be a poor description of the movement of neurotransmitter towards its target. The findings of Katz and Miledi (1966, 1967) can be criticised as at best only an approximation to the maximal time of delay, since the evidence is only circumstantial that the 100 ms taken for molecules to cross the synapse is the least time they obtained for ACh (presumably to diffuse) across. Microin-
jection also involves force, and might mimic a more explosive local release from the presynaptic membrane, especially if the latter involves some element of propulsion of ACh across the gap when vesicles are released. So diffusion probably offers the simplest explanation, but it need not be the correct one (see below). Also, Schmidt and Samson (1969) have proposed that the fibrous lamina actively transports ACh towards the postsynaptic membrane along some form of molecular channels. However, most authors seem content to adopt a much simpler view of the synapse and diffusion, and Gray (1987) gives a typical position statement on synaptic design in which inferences abound: ‘‘The synaptic cleft is 20–30 nm across and contains vague proteinaceous bonding material. The width of the cleft is sufficient to ensure adequate ion fluxes in the synaptic membranes yet is narrow enough to permit diffusion of the transmitter across in microseconds, a time too insignificant to affect synaptic delay’’.
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While it is difficult to justify the statement that the width of the cleft can be (conveniently) ‘sufficient to ensure adequate ion fluxes’, the remark that it is (also conveniently) ‘narrow enough to permit diffusion…’ is typical, unquestioningly accepting (rightly or wrongly) that diffusion is the mechanism by which the transmitter substance reaches the postsynaptic membrane without a shred of evidence. However, Gray goes further still by stating that diffusion time is seemingly ‘too insignificant to affect synaptic delay’, as if any small delay here is of little or no consequence. Since Katz and Miledi (1966, 1967) have shown this delay to be about 100 ms, it could easily make the difference between life and death to some prey in a moment of attempted escape through a reflex action. In terms of the Theory of Natural Selection, this can scarcely be considered ‘insignificant’ with regard to that animal. Biologists have long been wary of small differences, the excuse often being that the inherent variability of living material makes it pointless to indulge in excessively high degrees of precision. Thus, if total synaptic delay could be reduced from, say, 400 to 350 ms by some means which accelerates (the more commonly used word is ‘facilitates’) diffusion of ACh across the synaptic cleft (i.e. by reducing the quoted delay due to the diffusion of the chemical transmitter across the cleft from 100 to 50 ms), few would be inclined to measure this reduction accurately, even given the necessary instrumentation, and fewer still would see whether it conferred a survival advantage. Yet we have just discussed two ways in which ACh might cross the gap faster than by ‘diffusion alone’. Such compounding of assumptions and inferences is the reason why the persistence of Diffusion Theory as a basic tenet of biology has to be constantly questioned and critically evaluated; the status quo is not an acceptable option. Why, then, do we mostly continue to believe that transmission of ACh across the synapse has to be by diffusion ‘alone’?
3. Diffusion is not a ‘simple’ thing Diffusion is nearly always referred to, or qualified, in a number of different ways. Darnell
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et al. (1986) use the phrase ‘diffusion alone’, and later ‘simple diffusion’. Simple diffusion is used on many occasions (Darnell et al., 1990; Alberts et al., 1996), while Pasternak (1979) prefers the expression ‘passive diffusion’, which might be more accurate a description. Occasionally the expression ‘exchange diffusion’ is introduced (Giese, 1979), which is refreshing because it recognises that molecular movements occur between cells and their environment as part of a continuum and not in the kind of vacuum or under highly abstract or contrived conditions indicated in many diagrammatic representations of the phenomenon. ‘‘What is usually measured in experiments is the net flux, that is, the net gain by, or net loss from, cells. However, outflow (efflux)…’’ (in this process of diffusion) …‘‘occurs at the expense of kinetic energy, not metabolic energy’’. (Giese, 1979). In many cases, biologists are aware that diffusion alone is too restrictive and inadequate to explain some phenomena, and that various means exist to ‘facilitate’ it. The use of the word ‘facilitate’ is indeed widespread in many instances where diffusion has been invoked in cell biology. It acknowledges that diffusion is not ‘simple’, and ‘facilitation’ implies a contrivance which conveniently allows one to make special cases for certain types of diffusion-based molecular movements. The word ‘pathway’ is actually used in this context, e.g. in the way in which a membrane can have a special channel with a permease/carrier molecule behaving as if it were an enzyme (Karp, 1979; Pasternak, 1979). We also need to look within the cell itself, where we come across other qualifications of diffusion, notable expressions such as diffusion-controlled or diffusion-restricted reactions. Stryer (1981) notes that ‘the rate (of a biochemical reaction) cannot be faster than the diffusion-controlled encounter of an enzyme and its substrate’. Also, in this sphere, we are suffering the legacy of traditional biochemistry, reactions taking place in bulk phase (i.e. in a test-tube), dependent upon diffusion and obeying the law of mass action. There are instances in which reactions proceed
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faster than the expected collision or encounter rates on Stokes–Einstein calculations relating to radius of the molecules and viscosity of the milieu. Later Stryer (1986) accepts this by stating that where this happens, other mechanisms than diffusion must be involved, but enters into no discussion at to what these might be. Despite the reservations which clearly emerge from modern ideas on enzyme flux and substrate handling within recognised pathways (see below), the notion is still prevalent that diffusion largely accounts for, or can account for, the metabolic processes that proceed within a cell. Darnell et al. (1986) in their first edition made the quite outrageous statement, corrected in the second edition (Darnell et al., 1990), that: ‘‘Because a cell co-ordinates its metabolic acti6ities by diffusion alone, the rate at which molecules diffuse through the cell limits the typical cell size to between 30 and 50 microns in diameter’’. (My emphasis)
4. Diffusion theory and the detection of motion within cells A fundamental assumption in Fourier’s law is that the medium in which heat conductance is occurring should be still. This raises the question of whether Fick’s equation for diffusion, analogised from Fourier, can ever be truly applicable in a biological context, as discussed in detail in Wheatley and Malone (1993), Agutter et al. (1995). Intrinsically, a bar of metal (as originally used by Fourier for his measurements of heat conductance) can be considered non-moving, but no fluid medium is ever still. No living body or cell contains any completely still aqeuous phase, and even more importantly, the internum of the cell is incessantly moving because of cortical flow (Bray and White, 1988), cyclosis, cytoplasmic streaming, microcirculation and the syneretic effects of frequent actomyosin contractions and relaxation (Wheatley, 1985; Wheatley and Malone, 1987; Malone and Wheatley, 1991). Gerard (1940)
drew attention to ‘the apparent stillness’ of cells when examined by light microscopy microscopy, but quickly pointed out that at the molecular level the internum of the living cell was unresting, hence the title of his book. If diffusion is equated with molecular movement and the internum of the cell is a membranous bag containing a relatively non-viscous fluid, a soup of enzymes, and their substrates, intermediates and products, Brownian motion should be as easily seen as in a bleb produced by an injured cell. However, this is only at the level of resolution where oscillation, vibrations and translocations of particles rather than individual molecules, which can be detected in the light microscope. At the level of the water molecules themselves, much ‘self-diffusion’ (random movements?) is occurring within the cytoplasm, at least in rotational terms, but not so much in translational terms, as in completely free water in a beaker (Mastro et al., 1984; Wheatley et al., 1991). Diffusion is almost always occurring in the context of convective movements (Fig. 1), i.e. along with an element of bulk flow. We seem to have erred most notably in assuming the latter to be negligible within the domain of the cell internum, when in reality it probably dominates. However, it remains a major task at the end of the 20th century to provide further convincing evidence and argument that flow within cells is not just a universal phenomenon, but one that is vital for physiological functioning. Movement is always occurring within the living cells, no matter how still they may appear. If one, however, observes a cell which has been heated to 44–45°C for 5–10 min, this stillness is paradoxically even more remarkable (Wheatley et al., 1989). While the normal cell shows superficially only small agitations of organelles and resolvable particles by optical microscopy which can be attributable to Brownian motion, classical description of enzyme activity demands that massive Brownian motion occurs for substrates to move from one enzyme to the next, as they diffuse (in the vernacular) around and make interactions with frequencies of encounters based on the law of mass action. Why, then is there less evidence of this in the heated cell. Borelli et al. (1986) main-
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tained that the heated cell blebbed, with increased Brownian occurring quite violently within such extrusions. However, this is rarely the case in cells which have been recently ‘overheated’, although it may describe their activity much later. If a short heat treatment (5 min) is followed by ‘rescue’ at 37°C, extensive blebbing rapidly occurs. Within their blebs, violent Brownian motion can be clearly seen, which sharply contrasts with the low level of such activity in normal cytoplasmic extrusions from a cell (Albrecht-Buehler, 1982). From this, one can quite categorically state that the internum of the normal cell does not allow a great deal of Brownian movement of (resolvable) particles to occur, but when the fabric of the cytoplasm has been disrupted, a massive amount suddenly becomes apparent. However, within the unperturbed cell, convective flow is also observed, although it takes the highest resolution light microscopy available, preferably with video-enhanced image processing, cells in their healthiest condition, a lot of patience and the right skills to document its nature, especially in small cells such as mammalian cells (Wheatley, 1985; Wheatley et al., 1991). Particles are often being whisked along transient channels at the rate of up to 2 – 3 m s − 1 in these cells, and up to 3 – 4 times faster than this in many larger cells or syncytia in which cytoplasmic streaming is an obvious feature (e.g. Physarum; see Nations et al., 1981). The movements are orders of magnitude facter than particles driven by dynein or kinesin on cytoskeletal elements. The point which needs to be emphasised is that bulk flow of this type within cells is not a feature of size, i.e. it is not first and foremost a strategy purely indulged in by large cells to surmount an intracellular transport or distribution problem, but a necessary phenomenon of all cells. Before developing this argument further, there are recognised strategies by which diffusion might be assisted in its ability to cope with size and metabolic intensity within cells. Alberts et al. (1996) graphically describe some of these. One is compartmentalisation, in which molecules to be specifically reacted together are concentrated into designated places to increase the frequency of their encounters in bulk phase. Another mechanism is to prevent molecules from drifting away
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from a site of metabolic activity by restricting their freedom to diffuse out of the cell, as expressed by Davis (1958) in his exceptionally perceptive essay on the ionisation of molecules by living cells. A third is to bring diffusing molecules down from three dimensions on to surfaces, such as a membrane, and allow them to move in just two dimensions towards their targets. And the fourth is to raise the temperature, which has meant that life can operate more rapidly when a temperature of 37°C is maintained rather than an ambient of, say, 7°C. However, the strategy to which we will now pay particular attention is the deliberate bringing together of molecules by passing them over the surfaces on which interactions take place, the perfusion principle. Oddly, this most feasible of strategies fails to be mentioned in a single textbook of (cell) biology and cell physiology, and yet it is the pervading mechanism in all living creatures right down to within their smallest cells. What has been proposed is that intracellular movements of a convective nature (through to overt bulk flow, as in cyclosis) is an extension of the Harveian principle, the requirement for a circulation, to the subcellular and molecular level (Malone and Wheatley, 1991; Wheatley and Malone, 1993). It is no longer enough to state and assume that diffusion suffices for transport within all cells but the exceptionally large ones. Biologists need to grasp the significance and implications of this situation, because it calls for a radical reappraisal of the way in which we believe how molecules move and are moved around in living cells and organisms, and in particular how these movements can be rigorously and sensitively controlled to adjust the rate of metabolic functioning (Wheatley and Clegg, 1994). These are by no means trivial issues. We need to turn to the thorny issue of the possibility that there is, however, an essential requirement for diffusion at the molecular level in order for interacting molecules to sort themselves out according to their individual specificities. If this is a general phenomenon, then we have every right to expect there to be extensive Brownian movement throughout the cytoplasm. The larger the molecules involved the slower will their movement be throughout the cell,
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Fig. 3. Illustration of the three main types of synapses in neural tissue: (a) represents an electrical synapse with a very narrow cleft of 2–3 nm, i.e. ten times narrower than the chemical synapse. This type is found predominantly in brain tissue where local signalling of a weak nature between neurones is required; (b) represents a mixed synapse, with elements of an electrical synapse and a chemical synapse (to the right) is involved; (c) is a typical chemical synapse found throughout the rest of the nervous system, and important in the propagation of strong signals which are not quickly attenuated over relatively long distances. In this case an inhibitory synapse is also shown on the presynaptic bulb, an arrangement which allows some modulation of the transmission of the action potential from the presynaptic neurone to the postsynaptic neurone.
given that it is a simple aqueous solution despite all the barriers of its compartments, membranes, granules, droplets, etc. It might take an ATP molecule less than a second to diffuse across the average 10 micron diameter cell, but a calculation based on the passage through a primarily aqueous solution suggests that it would take a moderate sized protein of 100 Kda with a generally spherical quaternary structure about 10 – 12 min (Wheatley, 1985; Wojcieszyn et al., 1981). As cellular activity increases with workload, diffusion would become limiting because the only way in which it can now increase is through a significant rise in temperature. Taking the principle of Coulson (1986) that the cell would have been designed along the lines laid down by the finest chemical engineer, the important thing is to force reacting molecules together over a catalytic surface within
narrow confined spaces to maximise encounter rate per unit time. The rate at which this is done will sensitively adjust the reaction rate, making it fully controllable, thereby allowing product manufacturing to be commensurate with their ‘market’ use. In the absence of molecular freedom to make random walks (self-diffusion within the cell in this context), interactions between molecules will rise in proportion to the rate at which convection of the cytosolic compartment occurs over the surfaces within the cell (see Fig. 3 in Wheatley and Clegg, 1994). The problem of molecular sorting on the basis of specificities is a function of total encounters per unit time whether the movement is occurring by diffusion or by any other assisted/coordinated movement. The model emerging of the functioning cell differs from the classical one on the organisation of the internum
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as a huge catalytic surface on which reactions can take place in a sequential manner, with the cytosol equally being organised as a compartment in which convection results in the perfusion of reactants over these surfaces at rates commensurate with metabolic activity. The message is to keep the big catalytic molecules anchored and suffuse them with their substrates. There need be no absolute requirement for ‘undirected’ activity (diffusion in the vernacular), but it would still occur where intracellular convection has been abolished. However, the question is whether this could sustain an active metabolism, and this seemingly simple but critical experiment (discussed in Wheatley and Malone, 1993) has yet to be successfully designed and executed.
5. Perfusion and life: convective diffusion and living processes Estimates of diffusion of small molecules in cells are usually based on the assumption that the internum can be approximated to a simple aqueous phase or solution, but the fact that it can be two-three times slower does not make this credible (Clegg, 1984; Mastro and Keith, 1984; Luby-Phelps, 1994). Dispersion within the cell, however, can be seen to be greatly assisted by the incessant movement of the bulk aqueous phase through the labyrinthine honeycomb of the microtrabecular lattice and other membranes (see Paine, 1984; Kohen et al., 1989). It has been argued and evidence presented that all cells, not just large cells, possess a microcirculation (or sometimes a rhythmical ebbing and flowing along ‘a system of transient channels’, as in Physarum; see Nations et al., 1981) which allows both very large and small molecules to be moved around with almost equal speed and freedom, and at rates which for all including the smallest molecules will be far greater than by diffusion. [A perceived weakness in this argument is that transient channels can be seen when intracellular microcirculation is filmed, and yet in ultrastructural or microanatomical terms, we are at the same point as Harvey was when he realised there was a blood circulation but could not see the capillaries that
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completed the circle. Malpighi used the newly invented microscope to resolve this problem. We can see intracellular channels while they are functioning, but our critics call for anatomical verification, a tangible structure, when the cell is fixed, which has been like chasing a ‘will o’ the wisp’.] This process of circulation requires considerable energy (which has yet to feature in audits of cell energy expenditure), but it naturally assists all metabolic reactions because it becomes effectively a self-stoking operation, which is an important aspect of efficient metabolic regulation (Clegg and Wheatley, 1991). The distance over which ‘simple diffusion’ occurs in the movement of oxygen from the air to the muscles of the foot, relative to the total distance travelled is truly miniscule; and even in some of the situations of a few tenths of a micron where it can be conceded that diffusion is involved, some additional element of convection cannot be ruled out. Schmidt-Nielsen (1979) has calculated that it would take an oxygen molecule arriving in the lungs and travelling at an estimated 10 microns per ms approximately 3 years to reach the foot if convection was not the main means of directed delivery. Now the question remains as to how molecular specificities are sorted out without diffusion. Molecular specificity in interactions are dependent upon molecules encountering one another. In a random walk situation, beautifully described in Hille (1984), molecules will encounter one another with calculable frequencies. If however all the molecules were entrained to pass over a surface on which molecules of species A lay in readiness for molecules of species, then the faster they are streamed passed within narrow confines (see Clegg and Wheatley, 1991; their Fig. 3), the more precisely one can predict the much greater frequency of encounter. Physiological control is clearly based on encounter frequency and Coulson (1986) has more than adequately dealt with the basis of this fundamental problem in living organisms. Even at its lowest metabolic ebb, a living organism needs a small draught of oxygen. As its circulatory rate increases with more active metabolism, oxygen gets delivered at a faster rate to the cells, and they in turn can work more
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vigorously. It has been argued that this is the basis of regulation of metabolic activity in animals as different in size as a mouse and an elephant or whale; their cells metabolise at rates which are over two orders of magnitude different (Coulson, 1986). The same argument can be rehearsed with respect to all other essential nutrients or substrates required to sustain life over a wide metabolic range (such as glucose, amino acids, fatty acids, etc.; see Wheatley, 1985). We should now return to consider the way in which the synapse is constructed and operates, the question of speed of synaptic transmission having recently been described as ‘one of the fastest things animal cells do’ (Almers, 1994).
6. The synapse revisited Chemical synapses (Fig. 3c) are by far the most common type in the mammalian CNS and peripheral nervous system, there being a very small percent of electrical (Fig. 3a) and mixed (Fig. 3b) synaptic endings, with different physiologies (Bennett, 1972). It was suggested earlier that ACh could be shot across the gap in chemical synapses to reduce transmission time, but this argument begins to lose its force in some respects because it can now be seen that there is barely any such delay in an electrical synapse. Why, then, did chemical synapses with their 20 – 30 nm gaps evolve and become predominant, and for what reason do they seem to be set to ‘waste’ precious time in sending signals along nerve pathways when other arrangements already exist that would obviate this delay? One answer seems to be that specialised signalling of a co-ordinating nexus relies upon the use of low-resistance electrical synapses in situations where the next neurone in the pathway needs to be quickly and repeatedly stimulated, e.g. along with the many other simultaneously incoming and outgoing signals found in complex brain circuitry. The gap in the electrical synapse of only 2 nm is ‘sufficient’ to allow ‘instant’ but relatively weak depolarisation of the low-resistance postsynaptic membrane characteristic of this type of synapse, otherwise too much current would flow out into the surrounding
medium causing undesirable triggering of local neurones. Furthermore, signal attenuation will be very fast. Under these circumstances, there is little opportunity for modulation of the signal and only weak efferent nerve depolarisation occurs because these is no amplification mechanism assisting its passage from the presynaptic cell. Such an impulse would be inadequate to depolarise, for example, a large muscle fibre at a neuromuscular junction. In contrast, the cleft in the chemical synapse is actually considerably wider than the average intercellular gap between cells, and depolarisation of the presynaptic membrane by as much as 100 mV would scarcely affect the postsynaptic membrane by less than 0.01 mV, if only electrical transmission was operating. The depolarisation caused per quantum (vesicle) of a chemical transmitter can be calculated, however, and at any time as many as ten such events may be taking place. But a threshold of 100–300 quantal events are needed as a pulse before the postsynaptic membrane is abruptly depolarised and the signal passed on. Each quantum is equivalent to about 5 ×104 molecules of ACh being released, and each ACh molecule is potentially capable of eliciting a permeability change in the postsynaptic membrane equivalent to a flux of 1–5× 104 Na + ions, thus effectively amplifying the signal. Furthermore, the responsiveness of the membranes and other parts of the complex within the 100 ms synaptic delay can be modified and modulated by various means, such as alteration in receptor sensitivity on the postsynaptic nerve or slightly earlier firing of an inhibitory nerve axon on the presynaptic region (Fig. 3c), which can retard vesicle release. Thus, it is ironic that if diffusion is truly involved in ACh movement across the synapse, it appears to be a rate-limiting factor in transmission, and we can postulate that this retardation evolved through natural selection because time for signal augmentation and modulation introduced some further selective advantage. Through amplification, signal strength is maintained and this is needed to depolarise postsynaptic membranes or a large muscle fibre bundle at a motor-end plate. It is noteworthy that the distance over which diffusion rules in the case of the
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chemical synapse is limited to 20 – 30 nm, and in a situation where a steep gradient is created by the localised release of the neurotransmitter at the presynaptic membrane in a cleft which is normally kept clear of ACh by the presence of choline esterase. This rather exceptional case of diffusion might then prove the rule that the random dispersion of molecules is not normally resorted to in most physiological circumstances.
7. Implications of perfusion in the organisation of cells Life is based on surface chemistry to a far greater extent than conventional biochemistry has, at least until recently, led us to believe. Indeed, the gentlest homogenisation is a cataclysmic event to the cell (McConkey, 1982), but biochemists had spent decades studying enzyme kinetics on solubilised preparations made in this way (Coulson, 1993). This is far removed from the delicate and intricate organised complexes of catalytic units on topographically well-ordered surfaces and membranes actually found in vivo (Welch, 1977; Srivastava and Bernhard, 1986; Berry et al., 1987; Srere, 1987). As Sherrington (1940) and others have pointed out over half a century ago, the cell internum amounts to a gigantic superbly organised collection of surfaces (Tracey, 1968; Clegg, 1984), on and in which directed transfer effectively eliminates the involvement and supposed randomness of diffusive processes in metabolic pathways by which one reaction product would otherwise have to wander aimlessly about in order to encounter by chance the next enzyme in the sequence. Indeed, the almost universal acceptance and frequency of use of the word ‘pathway’ strongly connotes that intermediates are prohibited from taking random walks. Surfaces allow reactants a greater chance of intimate contact. A precisely sculpted surface may not only allow two reactants to adopt close proximity, but actually assist them to rearrange their bonds; the surface can achieve catalytic status. In life, the surfaces (arrayed enzymes) are perfused or suffused with
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medium (the cytosol) which delivers reactants and takes away the products to deliver them quickly elsewhere (Clegg and Wheatley, 1991). Intermediates are not usually found in abundance, for one may now speculate that most will be held within the multicatalytic units or complexes which undertake the pathway until the final product itself and waste products are ‘released’. The speed of reaction no longer has to be governed by the concentrations of the reactants, but can be increased as much as 10fold simply by perfusing the system and delivering the precursors ten times faster (Coulson, 1986). Like a fire (Kleiber, 1961), it be delicately tuned to the appropriate level of activity within its individual cells under the prevailing circumstances. It also links activity directly to the ‘demand’ for work (Clegg and Wheatley, 1991). If life is commonly judged in man by whether his heart is pumping and his blood circulating, then it may be argued at the cellular level that when his cells can no longer circulate the soluble phase (Wheatley and Malone, 1993, see hypothesis on p. 3 therein), they will be in an extremely low state of metabolic activity, as in suspended animation, or dead. What is happening at the molecular level inside the cell ceases, perhaps, to be adequately described by words such as ‘diffusion’ or ‘flow’ because they cannot be so easily divorced or distinguished in reality, only in the abstraction of the mathematician’s or theoretical biologist’s equations. It is therefore ironic that our long-held belief that diffusion suffices in the synapse really needs to be reviewed. There is no question that the gap is wider than between most cells and therefore it probably has a design which relates to some functional control such as modulation. Would it help to speed up the process by a factor of two or more, or would this jeopardise the ability to modulate the postsynaptic response? Is diffusion over this short distance a selected strategy for slowing things down, since it seriously weakend the claim that the transmission of neural impulses is one of the ‘fastest things we do’ (Almers, 1994)?
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Acknowledgements I wish to thank Professor Brian Goodwin, Drs Paul Agutter and Attila Miseta for many helpful discussion on different aspects of this study. The work was supported by a Wellcome History of Medicine grant, for which I am most grateful.
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