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Intracellular solute movements: a problem-orientated lecture for final year undergraduates
32 l"Linn, M C and Thier, D H (1975) The effect of experimental science on development of logical thinking in children, Journal of Research in Science Teaching 12, 49-62 ~ Charen, G (1970) Do laboratory methods stimulate critical thinking? Science Education 54, 267-271 12Ferguson, G A ( 1981) Statistical analysis in psychology and education. McGraw-Hill, New York 13Okey, J R, Wise, K C and Burns, J C (1982) Integrated Process Skill Test-2 (Available from Dr James R Okey, Department of Science Education, University of Georgia, Athens, Georgia 30602, USA) 14Campbell, D and Stanley, J (1966) Experimental and Quasi-Experimental Design for Research, Rand McNally, New York
week later, was consistent with the majority opinion. The student responses suggest that (a) the format I used, and (b) perhaps the topic chosen, might be useful for other teachers of biochemistry and related disciplines at advanced level. A transcript of parts of the lecture follows, annotated with comments about aims. Points where visual aids were used are indicated as ~stage directions' [square brackets]. Student responses to the questions asked are shown in italics.
Intracellular Solute Movements: A ProblemOrientated Lecture for Final Year Undergraduates
The Lecture
PAUL S A G U T T E R
Department of Biological Sciences Napier University Colinton Road Edinburgh EHIO 5DT, UK
You have often heard of substances entering and leaving cells by 'passive diffusion', and of solutes 'diffusing' from one part of the cell interior to another. What do you understand by these words 'diffusion' and 'diffusing'?
Introduction
Lectures are commonly believed to transmit factual information, imperfectly, to a passive audience whose response is uncritical and whose attention span is limited• As a proponent of problem-based teaching, I have previously subscribed to this view. However, students in a lecture need not be passive, and if the session is appropriately structured the limitations of attention span can be circumvented. Wood 1 has suggested various ways of making lectures more interesting, and Sigiyama et al 2 showed that the lecture format can be recruited to the service of problem-based teaching. I have tried to follow their advice and example. In November 1992 I tape-recorded one problem-directed lecture to final honours students. The general aims of this lecture were: (1) to encourage critical evaluation, not only of current literature, but of long-established ideas; (2) to recognize and acknowledge the quality of good experimental and theoretical science; (3) to re-emphasize the indispensibility of a historical perspective for making informed and balanced judgments; and (4) to draw attention to a subject that I consider scientifically important. The students were told the topic of the lecture two weeks before the session and were advised (a) to review their knowledge of diffusion theory, (b) to read reviews by Peters 3 and by Paine and Horowitz4, before the lecture. It was made clear that issues raised in the lecture would be discussed at subsequent tutorials and that the topic might appear in the final examinations. Out of 43 students who attended the lecture, 15 subsequently (2-3 h after the end of the session) described it as 'unsettling' or 'disconcerting', 20 described it as 'stimulating' or 'interesting', and eight described it as 'of no interest'. The level of discussion in the follow-up tutorials, which took place one BIOCHEMICAL
EDUCATION
The opening part of the lecture was an orientation to the topic and emphasized the need for clear and consistent use of terminology.
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Migration that depends only on random thermal movements of solute and other molecules. So the word 'passive' adds nothing to the meaning in 'passive diffusion', because you have just defined 'diffusion' as a passive process. Why then is the phrase used? As you know, 'passive diffusion' is supposed to contrast with, for example, 'facilitated transport'. 'Facilitated transport' is sometimes called 'facilitated diffusion', which is evidently an oxymoron if we accept your definition of 'diffusion' (and in essence yours is the accepted definition). I advise you against using expressions such as 'facilitated diffusion' . . . • . . Not all movements across membranes are facilitated or 'active', and certainly solute movements inside cells are not generally regarded as carrier-mediated or energydependent. What process do we invoke to explain these apparently uninteresting movements?
Diffusion. We should be cautious about using diffusion as a kind of 'default explanation' for molecular movements when facilitated transport or other specific biological processes are not involved; that is, of using it to imply 'no biologically interesting mechanism is involved, therefore there is no mechanism of any kind and hence nothing to discuss'. Diffusion is a mechanism; a physical process, supposedly inevitable in any fluid medium. I must emphasize this point: when you say that a solute X moves through the cell by diffusion, you are making a substantive assertion about the way X behaves in a biological situation• Am I right? Are you really asserting something definite about the mechanism?
(Some uncertainty) Consider: when you use the word 'diffusion', do you intend merely to describe an observation, ie to state that a substance is moving, apparently at random, and that its concentration gradient is concomitantly diminishing; or
33 do you intend to explain this observation, by implicit reference to the physical theory of diffusion?
Both• You should always be aware whether you are using 'diffusion' (or any other word) to describe or to explain a phenomenon; but I accept that it is possible to use 'diffusion' for both purposes. I have no quarrel with your descriptive use of the word. However, I do want you to reconsider its explanatory use. This is the main thrust of this lecture: a reexamination of diffusion theory, and particularly its relevance to c e l l s . . . A revision of Fick's law and the Einstein-Smoluchowski model of Brownian motion followed, with emphasis on the limiting conditions under which the Einstein-Smoluchowski model is valid• During this exposition the following opportunity to reiterate the generality of scientific method was exploited. • . . What is Brownian motion, and why is it so called?
It was discovered by a microscopist called Brown, who saw suspended pollen grains making short rapid random movements, and it happens to all small particles suspended in fluids. Yes - - that observation was made in the 1820s, and Brown's first explanation was that the vital force in the pollen grains caused the movements; but being a good scientist, he tested this hypothesis critically. How?
(No offers from the audienceO He made a suspension of pollen grains from plants that had been dead for more than 100 years and found that they still exhibited the same motion. Brown thus falsified his vitalistic hypothesis by experiment and realized that a physical explanation was needed; but neither he, nor anyone else at that time, could offer o n e . . . At the end of this revision exercise the central problem was highlighted. In the ensuing discussion the students were forcibly reminded that they should not take the lecturer's word for granted. • . . Such is the theory of diffusion. Fick's Law is taken to be a summary mathematical description of experimental measurements of diffusion; but it is also deducible, approximately, from the mathematical theory of Brownian motion developed by Einstein and Smoluchowski. This is reassuring: experimental results demonstrate what theory predicts; reassuring, that is, if both Fick's Law and the Einstein-Smoluchowski model are valid at least within the restrictions delineated by Einstein. Suppose for a moment that they were not valid, not even approximately. What physical meaning could we then attach to the diffusivity, D?
(No answer.) Precisely. Now let us turn to biology. Suppose the cell had no internal structure; that it was a bag of homogeneous dilute aqueous solution containing spherical, rigid, non-interacting protein molecules. Some of these proteins have glucose binding sites; hexokinase, for example. A glucose molecule enters the cell. How long will it take that glucose molecule to bind to a protein with an appropriate binding site? BIOCHEMICAL
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That could be calculated from the Einstein-Smoluchowski equations if we knew the temperature and the viscosity of the medium, and how many enzyme molecules there were. Quite so. But so long as there are ten or so enzyme molecules, the average or expected time for complex formation would be very brief in terms of individual Brownian movements. Would you agree?
(Hesitation. Then:) No, surely the time would be very long unless the number of binding sites was large? Good. Quite right• However, let us consider a m e , realistic view, the one illustrated in this diagram. [OI-iP of 'typical' eukaryotic cell structure.] The cell is highly structured and heterogeneous and the protein concentration in the cytoplasm is high. Most of the cytoplasmic water, probably two thirds of it, is immobile. How do we know that?... The next part of the lecture reviewed the implications of our modern understanding of intracellular organization for the applicability of the Einstein-Smoluchowski model. It included a discussion about the 'microtrabecular lattice' of Wolosevicz and Porter5 (reality or artefact?), concluding in the acceptance of at least transient long-range proteinprotein associations in the cytoplasm, and continued with questions that the students could not initially answer. A series of viewpoints on these questions was therefore taken until some clarification was achieved: • . . Now, remembering that we expect two thirds of the water enclosed in this transient fibrillar meshwork to be immobilized, will this have a significant obstructive or filtering effect on the small solute molecule?
Probably. (Some hesitation.) Let us approach the question from this point of view. Would you expect the number of individual Brownian movements experienced by the solute molecule in passing from one side to the other of a ten or twenty nanometer wide compartment to be very large or not very large?
Not very large• The Einstein-Smoluchowski model assumes a large (ideally infinite) number of such movements in the medium under study. Let me ask a different question now. Contrast our two models of the cell again: the first, unrealistic model, assuming an unstructured interior; and the second, more realistic one, illustrated in our diagram here, that seems to be presenting a problem for diffusion theory. Consider our travelling glucose molecule• Do you think that its average, expected time between entry to the cell and binding to a protein will be greater or less in the second model than in the first?
(Two-thirds of the audience opted for "less" and one-third opted for "greater".) Please will someone who said "less" explain their answer?
If the total space available for random walk is much smaller and the binding proteins are immobile, or fairly immobile, then the probability of a binding collision at any instant has to be much greater• Fine. Now would someone who gave the opposite answer, "greater", please explain their reasoning?
The cytoplasmic viscosity is higher in the second model so the diffusion constant must be lower, which makes the
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expected time longer• Also, not every channel will contain a binding enzyme, so there is always a good chance of entering the 'wrong' channel and this will increase the binding time. Also, if proteins are sticky and covered in bound water, will the moving solute molecule not have a chance of associating non-specifically, for a more or less long time, with a protein or its hydration shell? Again, fine. You have given good arguments for each possibility, and I shall take some of these up again in a few moments. Meanwhile, I want you to consider yet another question• In the first model, the imaginary unstructured cell, would you agree that the glucose movements constituted 'diffusion' in the Fick sense, and that they were explicable by Brownian motion as formulated by Einstein and Smoluchowski? Could an observer outside the cell measure these movements and calculate the diffusivity of glucose in the cell? Yes. What about the second model? Are the m o v e m e n t s 'diffusion'? (The audience was uncertain and opinion was divided.) Very well, let us pursue this question further. If for the m o m e n t we overlook the possibility of association with the immobile phase that one of you mentioned a few m o m e n t s ago, does glucose exhibit Brownian motion in this model? Yes. Is this motion properly described by the EinsteinSmoluchowski model? (After hesitation and debate) No, because movement is restricted except in certain directions, so the statistical assumptions break down. That's what you said, isn't it? Could an observer calculate the diffusivity of glucose in the cell from her or his experimental measurements? Yes, they could make the observations and calculate a value of D from them, but it would not mean the same thing as in the first model. What would it mean? (No answer.) It seems that there are genuine difficulties in applying the fundamentals of diffusion theory to the internum of the cell. A n d yet, you have never hesitated before today to dismiss solute m o v e m e n t s across intracellular spaces as ' m e r e diffusion' . . . The lecture then went on to consider what the terms 'viscosity' and 'temperature' signify in the cell internum. Reference was made to the doubts about these concepts expressed by Wiener. 6 A further difficulty with the 'diffusion' concept was then introduced. • . . T h e r e is another problem as well, quite separate from the ones we have discovered so far. D o you expect the unbound intracellular water, the solvent water, to be stationary? No. What makes it move? Reactions that use or produce water occurring at specific sites; movements into and out of the cel# dynamic changes in the cytoskeleton. Those are at least some of the reasons. But you r e m e m b e r B I O C H E M I C A L
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Einstein's restrictions on the applicability of the model? [OHP listing conditions of applicability of Einstein Smoluchowski model indicated.] The fluid must be unstirred, stationary. If there is net directional solvent m o v e m e n t then the motion of solute or suspended particles is not, or not entirely, diffusion. That is a matter of principle. Given that the solvent moves, what are the implications for our interpretations of experimentally measured intracellular diffusion coefficients?
They are uninterpretable. That may be putting it too strongly, but certainly their interpretation becomes even more difficult than we have already shown. Of course, good biophysicists recognize that experimentally calculated diffusivities are not simple to interpret. As Reiner Peters says in the review you have read, "the quoted diffusion coefficients are . . . apparent entities."... After a summary of the lecture so far, the students readily (and actively) dismissed the idea that intracellular proteins 'diffuse' in the accepted physical sense of the term. I reiterated their conclusion for emphasis and continued by switching from theoretical argument to experiment design and interpretation. . . . T h e r e f o r e you are saying that, as a matter of principle, intracellular proteins cannot and do not diffuse. They cannot exhibit Brownian motion, in the strict sense of r a n d o m thermal movements, for more than a brief interval in a restricted space. This adds to the complications, already established in the cases of glucose and sodium ions, of microheterogeneity, variable channels, compartmentalization and obstruction, surface adsorption, and net solvent flow. A beautiful experimental demonstration of the nondiffusibility of intracellular proteins was obtained by Philip Paine ~ and his colleagues. Some of you may have read the relevant papers, cited in Peters' review . . . [OHP illustrating Paine's experiment followed by a brief summary of the steps in the procedure on the blackboard.] . . . Out of 90 polypeptides examined, only 12 equilibrated completely between cytoplasm and reference phase; 23 did not enter the reference phase at all. O f the 12 that equilibrated, what were the kinetics of m o v e m e n t between the phases like?
We don't know because the point of the work was to study the equilibrium situation, but in terms of Brownian movements, a very long time was allowed for equilibration. I am sure that Paine and his colleagues would agree entirely with y o u . . . Yet diffusion theory is deeply entrenched in our systems of explanation in biology. Paine and others tacitly assume it. I now tried to lead the students to consider the historical reasons for this entrenchment. • . . Why, given the difficulities that you have identified yourselves during this lecture, is this faith in diffusion theory and its application so apparently unshakeable? Earlier, I suggested one reason: Fick's Law is intuitively 'obvious'. Can you suggest other reasons? Diffusion theory makes no assumptions; the mechanism given for Brownian motion could hardly be simpler. Also, as that quotation you just gave says, it's physico-chemical;
35 rock solid. Anyway, you only have to watch smoke dispersing in a still room to know that diffusion happens in real life. There is lots o f experimental evidence to support Fick's Law. Finally, what alternative theory is there? The richness of this response took me by surprise. I wanted to concentrate on the fourth and final answers. I think those are the reasons that most people would give; but I wonder whether they are valid. I remind you again that you have already found excellent arguments against the applicability of the theory in the cell. Let us take your reasons for faith one at a time and examine them closely... I used material from the earlier discussions to refute the first three of the students' lines of defence and then proceeded as follows. . . . Fourth, you suggest that there is a large body of supporting evidence. Unfortunately, this is not the case. Fick's 8 paper describes attempts to study the rate of migration of sodium chloride along a concentration gradient. His results were irreproducible (his diffusivity values varied from 9 to 12 mm 2 day -1 in the same experiment) and were therefore difficult to interpret. Also he assumed, rather than demonstrated, the linearity of his concentration gradients at steady s t a t e . . . His measuring system was clumsy (inevitably so since the work was done long before micromethods became a v a i l a b l e ) . . . Not surprisingly, therefore, his results did not permit him to establish a mathematical formulation by inductive reasoning. H e was therefore obliged to borrow a suitable equation from another branch of physics, and he chose one of Fourier's equations for heat conduction. The equation was 'suitable' in that it gave a reasonable fit to his data, and his adapted version of the Fourier equation 9 became 'Fick's Law'. Now all this seems reasonable enough, and if you read Fick's paper you have the impression of a highly able scientist coping sensibly with serious experimental d i f f i c u l t i e s . . . The difficulties with Fick's theoretical argument were then exposed. In short: both theoretically and experimentally, Fick's paper is unsound; it provides no justification for the law of diffusion that you said, at the beginning of this lecture, is the best-known law in the entire theory. In view of these facts of history, just what is the rock-solid, assumptionfree, experimentally-validated, physical theory of diffusion in which we have all expressed so much faith? In less than an hour, we have shown (1) that even if it were valid it could have no intelligible applicability to the cell internum, and (2) its validity is fundamentally dubious in any case. Nevertheless, Fick's formulation seemed to reflect a common 'pattern of nature' revealed in quite different physical contexts by, for example, Fourier and Ohm. Also, its historical roots and early acceptance were intimately entangled with the origins of kinetic theory. Almost all its critics were opponents of kinetic theory; so once kinetic theory was established beyond reasonable doubt, Fick's law became accepted as a firm part of the knowledge base of physical chemistry• Over the very same BIOCHEMICAL
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historical period, faith in the reductionist programme of biology - - the ultimate explanation of all biology in terms of experimentally-based chemistry and physics - - became firmer and more widespread. The key developments took place between 1847, the time of the H e l m h o l t z - B r i i c k e Ludwig publication, and 1912, when Loeb's book was published, and Fick himself made major contributions to t h e m . . . This is why diffusion theory, and Fick's law in particular, have come to be accepted uncritically as irrefutable components of the explanatory framework of modern biology . . . My final intention was to convince the students that biochemistry and cell biology still contain fundamental problems that they might choose to address in their postgraduate careers. At least they were encouraged to reflect on the problem of intracellular movement for tutorial and examination purposes. • . . And that brings me to your fifth and final point about the general acceptance of diffusion theory: where is the alternative? I acknowledge the need for a sound alternative theory, but I can offer you little help in finding it. This is a matter that we must discuss further. Before we meet in tutorials, I should like you to think about possibilities for an alternative theory; possibilities that take into account the nature of the cell internum structured, heterogeneous, and moving. I shall be glad to discuss any ideas you have, however rudimentary. In the end, however, the problem is not mine. The explanation for intracellular solute movements is an unresolved scientific issue that my generation will bequeath to yours.
References t Wood, E J (1989) Making lectures more exciting,Biochem Educ 17, 912 2Sigiyama, T, Isohashi, F, Higashi, T, Kagamiyama, H, Tagawa, K and Taniguchi, N (1991) Introduction and implementation of problemsolving lectures for instruction in medical biochemistry,Biochem Educ 19, 58-63 3peters, R (1986) Fluorescencemicrophotolysisto measure nucleocytoplasmic transport and intracellularmobility,Biochim Biophys Acta 864, 305-359 4Paine, P L and Horowitz, S B (1980) The movement of material between nucleus and cytoplasm, in Goldstein, L and Prescott, D M (eds) Cell Biology: a Comprehensive Treatise, Academic Press, New York 5Wolosewick, J J and Porter, K R (1976) Microtrabecularlattice of the cytoplasmic ground substance, J Cell Biol 82, 8531-8534 6Weiner, N (1948) Cybernetics, Wiley, New York 7paine, P L (1984) Diffusive and non-diffusiveproteins in vivo, J Cell Biol 99, 188s-195s SFick, A (1855) ldber Diffusion, Annal Phys Lepizig 94, 59-86 9Fourier, J-B (1822) Theorie Analytique de la Chaleur, Oevres, Paris (trans Freeman, A (1878) The Analytical Theory of Heat, Cambridge University Press, London)
Corrigendum In the article by Sayyab et al entitled 'Immunological Exercise for Beginners' (Biochemical Education 21(3), 155-157, 1993) it is regretted that there were a number of errors. In three places (on p 156) rabbit anti-human BSA should read rabbit anti-BSA. Also on this page under Double immunodiffusion, left hand column, line 23, 1% (v/v) acetic acid should read 7% (v/v) acetic acid.
week later, was consistent with the majority opinion. The student responses suggest that (a) the format I used, and (b) perhaps the topic chosen, might be useful for other teachers of biochemistry and related disciplines at advanced level. A transcript of parts of the lecture follows, annotated with comments about aims. Points where visual aids were used are indicated as ~stage directions' [square brackets]. Student responses to the questions asked are shown in italics.
Intracellular Solute Movements: A ProblemOrientated Lecture for Final Year Undergraduates
The Lecture
PAUL S A G U T T E R
Department of Biological Sciences Napier University Colinton Road Edinburgh EHIO 5DT, UK
You have often heard of substances entering and leaving cells by 'passive diffusion', and of solutes 'diffusing' from one part of the cell interior to another. What do you understand by these words 'diffusion' and 'diffusing'?
Introduction
Lectures are commonly believed to transmit factual information, imperfectly, to a passive audience whose response is uncritical and whose attention span is limited• As a proponent of problem-based teaching, I have previously subscribed to this view. However, students in a lecture need not be passive, and if the session is appropriately structured the limitations of attention span can be circumvented. Wood 1 has suggested various ways of making lectures more interesting, and Sigiyama et al 2 showed that the lecture format can be recruited to the service of problem-based teaching. I have tried to follow their advice and example. In November 1992 I tape-recorded one problem-directed lecture to final honours students. The general aims of this lecture were: (1) to encourage critical evaluation, not only of current literature, but of long-established ideas; (2) to recognize and acknowledge the quality of good experimental and theoretical science; (3) to re-emphasize the indispensibility of a historical perspective for making informed and balanced judgments; and (4) to draw attention to a subject that I consider scientifically important. The students were told the topic of the lecture two weeks before the session and were advised (a) to review their knowledge of diffusion theory, (b) to read reviews by Peters 3 and by Paine and Horowitz4, before the lecture. It was made clear that issues raised in the lecture would be discussed at subsequent tutorials and that the topic might appear in the final examinations. Out of 43 students who attended the lecture, 15 subsequently (2-3 h after the end of the session) described it as 'unsettling' or 'disconcerting', 20 described it as 'stimulating' or 'interesting', and eight described it as 'of no interest'. The level of discussion in the follow-up tutorials, which took place one BIOCHEMICAL
EDUCATION
The opening part of the lecture was an orientation to the topic and emphasized the need for clear and consistent use of terminology.
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Migration that depends only on random thermal movements of solute and other molecules. So the word 'passive' adds nothing to the meaning in 'passive diffusion', because you have just defined 'diffusion' as a passive process. Why then is the phrase used? As you know, 'passive diffusion' is supposed to contrast with, for example, 'facilitated transport'. 'Facilitated transport' is sometimes called 'facilitated diffusion', which is evidently an oxymoron if we accept your definition of 'diffusion' (and in essence yours is the accepted definition). I advise you against using expressions such as 'facilitated diffusion' . . . • . . Not all movements across membranes are facilitated or 'active', and certainly solute movements inside cells are not generally regarded as carrier-mediated or energydependent. What process do we invoke to explain these apparently uninteresting movements?
Diffusion. We should be cautious about using diffusion as a kind of 'default explanation' for molecular movements when facilitated transport or other specific biological processes are not involved; that is, of using it to imply 'no biologically interesting mechanism is involved, therefore there is no mechanism of any kind and hence nothing to discuss'. Diffusion is a mechanism; a physical process, supposedly inevitable in any fluid medium. I must emphasize this point: when you say that a solute X moves through the cell by diffusion, you are making a substantive assertion about the way X behaves in a biological situation• Am I right? Are you really asserting something definite about the mechanism?
(Some uncertainty) Consider: when you use the word 'diffusion', do you intend merely to describe an observation, ie to state that a substance is moving, apparently at random, and that its concentration gradient is concomitantly diminishing; or
33 do you intend to explain this observation, by implicit reference to the physical theory of diffusion?
Both• You should always be aware whether you are using 'diffusion' (or any other word) to describe or to explain a phenomenon; but I accept that it is possible to use 'diffusion' for both purposes. I have no quarrel with your descriptive use of the word. However, I do want you to reconsider its explanatory use. This is the main thrust of this lecture: a reexamination of diffusion theory, and particularly its relevance to c e l l s . . . A revision of Fick's law and the Einstein-Smoluchowski model of Brownian motion followed, with emphasis on the limiting conditions under which the Einstein-Smoluchowski model is valid• During this exposition the following opportunity to reiterate the generality of scientific method was exploited. • . . What is Brownian motion, and why is it so called?
It was discovered by a microscopist called Brown, who saw suspended pollen grains making short rapid random movements, and it happens to all small particles suspended in fluids. Yes - - that observation was made in the 1820s, and Brown's first explanation was that the vital force in the pollen grains caused the movements; but being a good scientist, he tested this hypothesis critically. How?
(No offers from the audienceO He made a suspension of pollen grains from plants that had been dead for more than 100 years and found that they still exhibited the same motion. Brown thus falsified his vitalistic hypothesis by experiment and realized that a physical explanation was needed; but neither he, nor anyone else at that time, could offer o n e . . . At the end of this revision exercise the central problem was highlighted. In the ensuing discussion the students were forcibly reminded that they should not take the lecturer's word for granted. • . . Such is the theory of diffusion. Fick's Law is taken to be a summary mathematical description of experimental measurements of diffusion; but it is also deducible, approximately, from the mathematical theory of Brownian motion developed by Einstein and Smoluchowski. This is reassuring: experimental results demonstrate what theory predicts; reassuring, that is, if both Fick's Law and the Einstein-Smoluchowski model are valid at least within the restrictions delineated by Einstein. Suppose for a moment that they were not valid, not even approximately. What physical meaning could we then attach to the diffusivity, D?
(No answer.) Precisely. Now let us turn to biology. Suppose the cell had no internal structure; that it was a bag of homogeneous dilute aqueous solution containing spherical, rigid, non-interacting protein molecules. Some of these proteins have glucose binding sites; hexokinase, for example. A glucose molecule enters the cell. How long will it take that glucose molecule to bind to a protein with an appropriate binding site? BIOCHEMICAL
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That could be calculated from the Einstein-Smoluchowski equations if we knew the temperature and the viscosity of the medium, and how many enzyme molecules there were. Quite so. But so long as there are ten or so enzyme molecules, the average or expected time for complex formation would be very brief in terms of individual Brownian movements. Would you agree?
(Hesitation. Then:) No, surely the time would be very long unless the number of binding sites was large? Good. Quite right• However, let us consider a m e , realistic view, the one illustrated in this diagram. [OI-iP of 'typical' eukaryotic cell structure.] The cell is highly structured and heterogeneous and the protein concentration in the cytoplasm is high. Most of the cytoplasmic water, probably two thirds of it, is immobile. How do we know that?... The next part of the lecture reviewed the implications of our modern understanding of intracellular organization for the applicability of the Einstein-Smoluchowski model. It included a discussion about the 'microtrabecular lattice' of Wolosevicz and Porter5 (reality or artefact?), concluding in the acceptance of at least transient long-range proteinprotein associations in the cytoplasm, and continued with questions that the students could not initially answer. A series of viewpoints on these questions was therefore taken until some clarification was achieved: • . . Now, remembering that we expect two thirds of the water enclosed in this transient fibrillar meshwork to be immobilized, will this have a significant obstructive or filtering effect on the small solute molecule?
Probably. (Some hesitation.) Let us approach the question from this point of view. Would you expect the number of individual Brownian movements experienced by the solute molecule in passing from one side to the other of a ten or twenty nanometer wide compartment to be very large or not very large?
Not very large• The Einstein-Smoluchowski model assumes a large (ideally infinite) number of such movements in the medium under study. Let me ask a different question now. Contrast our two models of the cell again: the first, unrealistic model, assuming an unstructured interior; and the second, more realistic one, illustrated in our diagram here, that seems to be presenting a problem for diffusion theory. Consider our travelling glucose molecule• Do you think that its average, expected time between entry to the cell and binding to a protein will be greater or less in the second model than in the first?
(Two-thirds of the audience opted for "less" and one-third opted for "greater".) Please will someone who said "less" explain their answer?
If the total space available for random walk is much smaller and the binding proteins are immobile, or fairly immobile, then the probability of a binding collision at any instant has to be much greater• Fine. Now would someone who gave the opposite answer, "greater", please explain their reasoning?
The cytoplasmic viscosity is higher in the second model so the diffusion constant must be lower, which makes the
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expected time longer• Also, not every channel will contain a binding enzyme, so there is always a good chance of entering the 'wrong' channel and this will increase the binding time. Also, if proteins are sticky and covered in bound water, will the moving solute molecule not have a chance of associating non-specifically, for a more or less long time, with a protein or its hydration shell? Again, fine. You have given good arguments for each possibility, and I shall take some of these up again in a few moments. Meanwhile, I want you to consider yet another question• In the first model, the imaginary unstructured cell, would you agree that the glucose movements constituted 'diffusion' in the Fick sense, and that they were explicable by Brownian motion as formulated by Einstein and Smoluchowski? Could an observer outside the cell measure these movements and calculate the diffusivity of glucose in the cell? Yes. What about the second model? Are the m o v e m e n t s 'diffusion'? (The audience was uncertain and opinion was divided.) Very well, let us pursue this question further. If for the m o m e n t we overlook the possibility of association with the immobile phase that one of you mentioned a few m o m e n t s ago, does glucose exhibit Brownian motion in this model? Yes. Is this motion properly described by the EinsteinSmoluchowski model? (After hesitation and debate) No, because movement is restricted except in certain directions, so the statistical assumptions break down. That's what you said, isn't it? Could an observer calculate the diffusivity of glucose in the cell from her or his experimental measurements? Yes, they could make the observations and calculate a value of D from them, but it would not mean the same thing as in the first model. What would it mean? (No answer.) It seems that there are genuine difficulties in applying the fundamentals of diffusion theory to the internum of the cell. A n d yet, you have never hesitated before today to dismiss solute m o v e m e n t s across intracellular spaces as ' m e r e diffusion' . . . The lecture then went on to consider what the terms 'viscosity' and 'temperature' signify in the cell internum. Reference was made to the doubts about these concepts expressed by Wiener. 6 A further difficulty with the 'diffusion' concept was then introduced. • . . T h e r e is another problem as well, quite separate from the ones we have discovered so far. D o you expect the unbound intracellular water, the solvent water, to be stationary? No. What makes it move? Reactions that use or produce water occurring at specific sites; movements into and out of the cel# dynamic changes in the cytoskeleton. Those are at least some of the reasons. But you r e m e m b e r B I O C H E M I C A L
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Einstein's restrictions on the applicability of the model? [OHP listing conditions of applicability of Einstein Smoluchowski model indicated.] The fluid must be unstirred, stationary. If there is net directional solvent m o v e m e n t then the motion of solute or suspended particles is not, or not entirely, diffusion. That is a matter of principle. Given that the solvent moves, what are the implications for our interpretations of experimentally measured intracellular diffusion coefficients?
They are uninterpretable. That may be putting it too strongly, but certainly their interpretation becomes even more difficult than we have already shown. Of course, good biophysicists recognize that experimentally calculated diffusivities are not simple to interpret. As Reiner Peters says in the review you have read, "the quoted diffusion coefficients are . . . apparent entities."... After a summary of the lecture so far, the students readily (and actively) dismissed the idea that intracellular proteins 'diffuse' in the accepted physical sense of the term. I reiterated their conclusion for emphasis and continued by switching from theoretical argument to experiment design and interpretation. . . . T h e r e f o r e you are saying that, as a matter of principle, intracellular proteins cannot and do not diffuse. They cannot exhibit Brownian motion, in the strict sense of r a n d o m thermal movements, for more than a brief interval in a restricted space. This adds to the complications, already established in the cases of glucose and sodium ions, of microheterogeneity, variable channels, compartmentalization and obstruction, surface adsorption, and net solvent flow. A beautiful experimental demonstration of the nondiffusibility of intracellular proteins was obtained by Philip Paine ~ and his colleagues. Some of you may have read the relevant papers, cited in Peters' review . . . [OHP illustrating Paine's experiment followed by a brief summary of the steps in the procedure on the blackboard.] . . . Out of 90 polypeptides examined, only 12 equilibrated completely between cytoplasm and reference phase; 23 did not enter the reference phase at all. O f the 12 that equilibrated, what were the kinetics of m o v e m e n t between the phases like?
We don't know because the point of the work was to study the equilibrium situation, but in terms of Brownian movements, a very long time was allowed for equilibration. I am sure that Paine and his colleagues would agree entirely with y o u . . . Yet diffusion theory is deeply entrenched in our systems of explanation in biology. Paine and others tacitly assume it. I now tried to lead the students to consider the historical reasons for this entrenchment. • . . Why, given the difficulities that you have identified yourselves during this lecture, is this faith in diffusion theory and its application so apparently unshakeable? Earlier, I suggested one reason: Fick's Law is intuitively 'obvious'. Can you suggest other reasons? Diffusion theory makes no assumptions; the mechanism given for Brownian motion could hardly be simpler. Also, as that quotation you just gave says, it's physico-chemical;
35 rock solid. Anyway, you only have to watch smoke dispersing in a still room to know that diffusion happens in real life. There is lots o f experimental evidence to support Fick's Law. Finally, what alternative theory is there? The richness of this response took me by surprise. I wanted to concentrate on the fourth and final answers. I think those are the reasons that most people would give; but I wonder whether they are valid. I remind you again that you have already found excellent arguments against the applicability of the theory in the cell. Let us take your reasons for faith one at a time and examine them closely... I used material from the earlier discussions to refute the first three of the students' lines of defence and then proceeded as follows. . . . Fourth, you suggest that there is a large body of supporting evidence. Unfortunately, this is not the case. Fick's 8 paper describes attempts to study the rate of migration of sodium chloride along a concentration gradient. His results were irreproducible (his diffusivity values varied from 9 to 12 mm 2 day -1 in the same experiment) and were therefore difficult to interpret. Also he assumed, rather than demonstrated, the linearity of his concentration gradients at steady s t a t e . . . His measuring system was clumsy (inevitably so since the work was done long before micromethods became a v a i l a b l e ) . . . Not surprisingly, therefore, his results did not permit him to establish a mathematical formulation by inductive reasoning. H e was therefore obliged to borrow a suitable equation from another branch of physics, and he chose one of Fourier's equations for heat conduction. The equation was 'suitable' in that it gave a reasonable fit to his data, and his adapted version of the Fourier equation 9 became 'Fick's Law'. Now all this seems reasonable enough, and if you read Fick's paper you have the impression of a highly able scientist coping sensibly with serious experimental d i f f i c u l t i e s . . . The difficulties with Fick's theoretical argument were then exposed. In short: both theoretically and experimentally, Fick's paper is unsound; it provides no justification for the law of diffusion that you said, at the beginning of this lecture, is the best-known law in the entire theory. In view of these facts of history, just what is the rock-solid, assumptionfree, experimentally-validated, physical theory of diffusion in which we have all expressed so much faith? In less than an hour, we have shown (1) that even if it were valid it could have no intelligible applicability to the cell internum, and (2) its validity is fundamentally dubious in any case. Nevertheless, Fick's formulation seemed to reflect a common 'pattern of nature' revealed in quite different physical contexts by, for example, Fourier and Ohm. Also, its historical roots and early acceptance were intimately entangled with the origins of kinetic theory. Almost all its critics were opponents of kinetic theory; so once kinetic theory was established beyond reasonable doubt, Fick's law became accepted as a firm part of the knowledge base of physical chemistry• Over the very same BIOCHEMICAL
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historical period, faith in the reductionist programme of biology - - the ultimate explanation of all biology in terms of experimentally-based chemistry and physics - - became firmer and more widespread. The key developments took place between 1847, the time of the H e l m h o l t z - B r i i c k e Ludwig publication, and 1912, when Loeb's book was published, and Fick himself made major contributions to t h e m . . . This is why diffusion theory, and Fick's law in particular, have come to be accepted uncritically as irrefutable components of the explanatory framework of modern biology . . . My final intention was to convince the students that biochemistry and cell biology still contain fundamental problems that they might choose to address in their postgraduate careers. At least they were encouraged to reflect on the problem of intracellular movement for tutorial and examination purposes. • . . And that brings me to your fifth and final point about the general acceptance of diffusion theory: where is the alternative? I acknowledge the need for a sound alternative theory, but I can offer you little help in finding it. This is a matter that we must discuss further. Before we meet in tutorials, I should like you to think about possibilities for an alternative theory; possibilities that take into account the nature of the cell internum structured, heterogeneous, and moving. I shall be glad to discuss any ideas you have, however rudimentary. In the end, however, the problem is not mine. The explanation for intracellular solute movements is an unresolved scientific issue that my generation will bequeath to yours.
References t Wood, E J (1989) Making lectures more exciting,Biochem Educ 17, 912 2Sigiyama, T, Isohashi, F, Higashi, T, Kagamiyama, H, Tagawa, K and Taniguchi, N (1991) Introduction and implementation of problemsolving lectures for instruction in medical biochemistry,Biochem Educ 19, 58-63 3peters, R (1986) Fluorescencemicrophotolysisto measure nucleocytoplasmic transport and intracellularmobility,Biochim Biophys Acta 864, 305-359 4Paine, P L and Horowitz, S B (1980) The movement of material between nucleus and cytoplasm, in Goldstein, L and Prescott, D M (eds) Cell Biology: a Comprehensive Treatise, Academic Press, New York 5Wolosewick, J J and Porter, K R (1976) Microtrabecularlattice of the cytoplasmic ground substance, J Cell Biol 82, 8531-8534 6Weiner, N (1948) Cybernetics, Wiley, New York 7paine, P L (1984) Diffusive and non-diffusiveproteins in vivo, J Cell Biol 99, 188s-195s SFick, A (1855) ldber Diffusion, Annal Phys Lepizig 94, 59-86 9Fourier, J-B (1822) Theorie Analytique de la Chaleur, Oevres, Paris (trans Freeman, A (1878) The Analytical Theory of Heat, Cambridge University Press, London)
Corrigendum In the article by Sayyab et al entitled 'Immunological Exercise for Beginners' (Biochemical Education 21(3), 155-157, 1993) it is regretted that there were a number of errors. In three places (on p 156) rabbit anti-human BSA should read rabbit anti-BSA. Also on this page under Double immunodiffusion, left hand column, line 23, 1% (v/v) acetic acid should read 7% (v/v) acetic acid.