Upsala J Med Sci 81: 201-212, 1976 The Migrating Thermodynamic Quantum Hypothesis for Cytoplasmic Streaming, Sodium Pumping and Other Cell Biological Phenomena, Deduced from Biofunctional Considerations of the Ultrastructure of Brush Border Microvilli ERIK CERVEN From the Institute of Medical and Physiological Chemistry, Biomedical Center, University of Uppsala, Uppsala, Sweden. ABSTRACT An attempt is made to reconcile experimental data dealing with, inter alia, cytoplasmic streaming in Characean algae, contraction in actomyosin systems, Na+- and -K+ - stimulated ATPase activity and the ultrastructure of brush border microvilli. I t is postu- lated that myosin molecules transfer energy from ATP to a n actin-containing filament and that a high energy conformation is subsequently propagated along the filament. A t regularly spaced intervals corresponding to the length of an actin-tropomyosin subunit, the propagation of high energy involves re- jection of a pressure pulse in the direction of cyto- plasmic streaming. Proteins in solution capable of storing the thermodynamic energy represented by the pressure pulse will either migrate in the opposite direc- tion or conserve the quantized cytoplasmic flow generated by the actin-containing filaments. At sites where actin filaments are attached to the plasma membrane the high energy is propagated in another direction leading to expulsion of sodium ions and neutralization of the vectorial pressure pulse. INTRODUCTION In 1956-57 (9, 12) it was discovered by darkfield microscopy that protoplasma droplets from Characeae contain fibrils, rapidly moving for- ward or in circle, longitudinally dissociating and associating. The multiply associated state was also observed to display undulating movement. Cytoplasmic particles that came close to these fibrils were captured and without Brownian motion translocated in the opposite direction and it was therefore concluded that the observed fibrils are responsible for cytoplasmic streaming in this and other species (9, 10, 12.) The moving fibrils generating cytoplasmic streaming have recently been shown by decoration (22) with myosin to contain F-actin oriented as if able to pull myosin filaments in the direction of the cyto- plasmic flow (14). During recent years, actin and actin-like pro- teins have been found in a number of nonmuscle cells (4, 15, 17, 19, 24,28, 32), including bacteria (21), and their interaction with myosin from distant unrelated species suggests that actin has maintained its original molecular properties during the course of evolution pointing to a general function not restricted to cytoplasmic streaming or muscular contraction (15). In cases where a transmembraneous gradient of sodium is suggested to play a main role in a physiological function, such as propagation of action potentials in nerve cells and sodium-dependent transport of certain metabolites in intestinal epithelial cells (25), actin-containing filaments are found in close association with the plasma membrane (1 9, 24). Electron microscopic investigations of nerve cell axones (19) and brush border microvilli (24) in- dicate that the actin-containing filaments may be involved in excitation (19) and in functional co- operation with proteins in the plasma membrane of brush border microvilli. In the latter case this is because the attachment sites are regularly spaced at a distance that corresponds to the length of an actin-tropomyosin subunit (16, 22, 24). In- volvement of actin-containing filaments in plasma membrane phenomena is also suggested by the findings that release from “contact inhibition” of cultured cells may be accompanied both by a decreased transmembraneous potential (8) and a diminished association of actin-containing fila- Upsala J Med Sci 81 202 Erik Cervkn ments to the plasma membrane (17). Furhter, a mutant strain of E. coli lacking the ability to accumulate potassium from a potassium-depleted medium is characterized by a mutant actin that fails to polymerize at that particular potassium concentration (2 1). When taken together, these and other findings suggest that sub-plasma- membraneous actin-containing filaments may be part of phenomena involved in generating a transmembraneous electrochemical gradient of sodium and potassium without reference to the mechanism of this involvement. The polarity of the actin-containing filaments in brush border microvilli (see Fig. 1) has recently been determined by decoration (22) with myosin subfragment 1, by means of immunologic loca- lization of a-actinin predominantly in the distal tips of the microvilli and by ultrastructural evid- ence for myosin filaments in the proximal terminal web (24). The diverging observations on micro- villar contraction, which has been described as either shortening or undulating (cf 29) move- ment, could be unified by assuming that actin- containing filaments behave in brush border microvilli as they do in protoplasma droplets from Churuceue (c$ 9, 10, 12) carrying with them a cytoplasmic flow. The direction of this cyto- plasmic flow can be deduced from the polarity of the actin-containing filaments in brush border microvilli by analogy with the corresponding filaments in Churuceue (14). This deduction is complicated by the fact that the mechanism generating cytoplasmic streaming must be inhi- bited, or directed towards other functions, along the entire length of at least some actin-containing filaments, in order to ascertain restreaming into the cell. Evidence has been obtained that transport of certain amino acids and sugars against a gradient into brush border microvilli is dependent on co- migration of sodium (25), a phenomenon that is a fundamental principle for the transport of many metabolites into different types of cells (3). In order to ascertain restreaming in brush border microvilli it will therefore be postulated in the present hypothesis that the mechanism generating cytoplasmic streaming is used in the plasma Upsala J Med Sci 81 I 1 ,minal web actin core Fig. I. Schematic illustration of the anatomic structure of a cut microvillus (A, cJ: 24) and the direction of cytoplasmic streaming deduced by analogy with Characean algae (B, c j : 14). membrane for generating a transmembraneous gradient of sodium. The direction of the cyto- plasmic flow that will result from this assumption, is illustrated in Fig. 1 B. Actin-containing fila- ments are attached to the plasma membrane in regularly spaced intervals at a distance that cor- responds to the length of one actin-tropomyosin subunit (24) indicating functional cooperation between the filaments and membraneous proteins. Since no other binding sites have been observed it will be assumed in this hypothesis that both cyto- plasmic streaming and sodium expulsion are governed from these regularly spaced intervals. An additional function of the observed attache- ment-sites (24) is probably that their presence counteract the propulsion of the actin core into the cell interior that would occur in their absence as a result of cytoplasmic streaming in the distal direction. When brush border microvilli are demembra- nated by treatment with Triton-X 100 (23) the subsequent addition of C a + + and ATP results in propulsion of the actin core into the cell interior (23). This finding does not support that the slid- ing filament model for muscular contraction (7, The Migrating Thermodynamic Quantum Hypothesis for Celt Biological Phenomena 203 RELAXED STATE CONTRACTION Fig. 2. Schematic illustration of the sliding filament model according to which contraction of skeletal muscle is mediated by active translocation of myosin filaments along the actin-containing filaments by a mechanism that implies ATPase activity for every translocation step past an actin dimer. (cJ: 7). see Fig. 2)is applicable to contraction of brush border microvilli, since no myosin was reported to be located along the axis of propulsion (23) or is even found in the vicinity of the villous part of the actin core in contracted intact brush border microvilli preparations (29), necessitating the postulation of invisible myosin (29). Filaments reminiscent of striated muscle myosin are instead located perpendicular to the actin core in the underlying terminal web (24) initiating the shortening and undulating movement of microvilli at distance. They apparently do not migrate distally towards the a-actinin-containing tips of microvilli (corresponding to the Z-line of muscle (24)) as they should do according to the sliding filament model for muscular contraction. An alternative interpretation of myosin action is also required in view of failures of the sliding filament model to explain contraction in actomyosin pre- parations lacking myosin filaments (6) and in re- generated actomyosin containing conversely oriented actin filaments (6). Further, the excess of actin in comparison with myosin in many non- muscle cells (15) and the mechanochemical coup- ling in actomyosin systems catalyzed by globular myosin subfragments (27), evoke the suspicion that the sliding filament model is not generally applicable to contractile phemomena ( 1 5 ) . This model has also been criticized on the basis of ul- trastructural observations on contracted striated muscle (30). It is very difficult to devise a mechanism by which the sliding filament model for muscular contraction can explain the cytoplasmic stream- ing in brush border microvilli that is deduced from their shortening or undulating (cf.: 29) movement by analogy with the movement of the corresponding fibrils in protoplasma droplets from Characeae (qf: 9, 12). Since this model implies that myosin filaments sometimes return to a relaxed position it also implies that cyto- plasmic streaming should be reversed at times contrary to what is known about this pheno- menon in other systems (9, 10, 12, 14). If the sliding filament model is modified by assuming that myosin molecules of the myosin filaments upon reaching the a-actinin-containing distal tips of microvilli are detached and subsequently pas- sively transported into the cell, other questions still remain unanswered. These questions relate to energetic considerations dealing with the con- siderable amounts of ATP that must be trans- ported to and consumed in microvilli in order to mediate on one hand the myosin ATPase cata- lyzed translocation of myosin (7) and on the other hand the Na+-and- Kt -stimulated ATPase- catalyzed (3, 20) generation of a transmem- braneous electrochemical gradient of sodium and potassium. The sliding filament (7), the screwing filament ( 1 1) and the undulating filament (3 1) hypotheses are all unable to provide any physio- logical function to the observed contraction of brush border microvilli. The reason for this is that if any of these hypotheses is adapted, too complex and multiple interactions would be necessary in the binding of the filaments to the plasma membrane. In addition, any active me- chanism for the assumed cytoplasmic straming in brush border microvilli would yield energy-re- quiring frictional flow. One experimental fundament for the hypothesis that will be presented here is the original observa- tion that cytoplasmic particles move closely along the protoplasmic filaments of Characean algae without Brownian motion (9, 12). Only a mecha- nism capable to non-randomize and vectorize (structurize) this random motion can thus be as- sumed to be responsible for cytoplasmic stream- ing. Any active mechanism such as the myosin ATPase catalyzed sliding of filaments (7), pro- pelling of filaments (1 l), or undulation of fila- ments ( 3 1) must accordingly be rejected because it would on the contrary enhance Brownian motion in the vicinity of these filaments. Upsala J Med Sci 81 204 Erik Cervkn Thermal motion of solvent molecules can be absorbed.by proteins in small amounts resulting in e.g. strained bond angles (cJ.3). It is postulated in the present hypothesis that increased utilization of similar or other possibilities of storing thermo- dynamic energy results in a defined conformation of a protein. By further postulating that this energy-storing conformation of a protein in one single step reverts to a low energy conformation a possibility is created to structurize the Brownian motion of the surrounding solvent molecules. Since the thermodynamic energy is rejected as a pressure pulse when used for generating cyto- plamic streaming it must be assumed that a “con- densed” form of a protein equivalents its energy storing, low entropy conformation. This idea is compatible with calculations indicating that all components of a protein do not oscillate simul- taneousely in all degrees of freedom of motion of the protein (26). A protein oscillating between two main conformations may be considered to have one main degree of freedom of motion, at least represented by the difference of entropy between the “condensed” and the “loose” form. According to the present hypothesis, the one step release of thermodynamic energy from the low entropy conformation of a protein (or pro- teins) in the actin-containing filaments into the surrounding medium is brought about by the transfer to this conformation of the energy re- siding in a high energetic phosphate bond in an adjacent protein of the actin-containing filament. By this assumption a concept of propagating high energy equivalent to a phosphate bond in the actin-containing filament is introduced, which may explain why myosin apparently effects contraction of brush border microvilli at dis- tance and why ATP enhances cytoplasmic streaming in several other cells (12). This idea is not contradicted by recent reports that in actin, high energy may be stored in two interchangeable forms, bound ATP and a labile conformation of protein (1 6). Furthermore the idea is compatible with considerations indicating that the nucleotide- binding region of actin is located in a P-pleated sheet (16), because this conformation of a poly- peptide would be the most efficient in generating a pressure pulse. Since a low entropy conformation of a protein imposed by absorption of thermo- dynamic energy from the surrounding medium is labile and tends to reject this energy the postula- tion of such a conformation may be a require- ment for the concept of a unidirectional propa- gation of high energy pulses which will be “pulled” by the thermodynamically labile con- formation. It is further assumed in this hypothesis that a thermodynamically labile conformation of a protein that in addition binds phosphate in a high energetic bond tends to “push” the phosphate bond to adjacent proteins. It is inherent in the hypothesis that is outlined here that absorption of thermodynamic energy resulting in a defined low entropy conformation would confer on the propagating high energy pulse the possibility of an equivalent active physiological function at equiva- lent sites along the actin-containing filaments. THE HYPOTHESIS It is postulated that components of the actin- containing filaments formed in vivo can exist in two low energy conformations, L,, L, and two L A ! I I Fig. 3. Energy content of proteins that are of the same magnitude of size as the proteins constituting the actin-con- taining filaments. (L,-LJ is equivalent to (HI-H,) and defines the energy content of a protein that is exchangeable with the surrounding medium as one thermodynamic quan- tum (Q), that is, a single pressure pulse or a defined region of increased thermal motion of solvent molecules. The capital H denotes a high energy content derived from and ex- changeable with a terminal phosphate bond of ATP. This high energy may reside in a protein in the form of a high energetic phosphate bond or an unstable conformation of a protein ( c j : 16). The.capital L denotes that a protein is lacking this particular form of high energy content. The lines in this figure denote possible but not obligate energy transi- tions of a protein submitted to the postulates of this hypo- thesis. Upsala J Med Sci 81 The Migrating Thermodynamic Quantum Hypothesis f o r Cell Biological Phenomena 205 high energy conformations, H,, H, (see Fig. 3 and page 209 for explanation of the notations used). The energetic difference Q (=one thermo- dynamic quantum) between L,, H, and L,, H,, respectively, is equal and exchangeable with the surrounding medium as described by the follow- ing reactions: L2p + Qs-+p (1 ) H2p + Qs -H2p The thermodynamic quantum is generated by the actin-containing filaments as a mainly uni- directional cytoplasmic pressure pulse which is equivalent to a defined region of increased thermal motion of cytoplasmic solvent molecules. The energetic difference between L,, L, and H,, HI, re- spectively is comparable to the energy content of the terminal phosphate bond of ATP. The main function of myosin is to transfer energy from ATP to the actin-containing filaments which as reflected by their polarity have the capability of propagating this energy in one direction. The un- idirectional propagation of high energy is a re- quirement for the generation of thermodynamic quanta. Mainly two combinations of energy con- tent in adjacent proteins of the actin-containing filament are unstable and responsible for the un- idirectional propagation of high energy as described by the following reactions: H2 (Xfl (Y) -+ L2 (X)H2 (Y) + Qs HI (Xf2 (Y) -+ L1 (X)H2 (Y) (3) (4) These reactions have a physiological signi- ficance at the junction between two adjacent actin-tropomyosin subunits where they are in- PI 5-c - A. Fig. 4 . A: schematic illustration of an actin-tropomyosin subunit. The equilibrium arrows indicate that the propagation of high energy in the intermediate part of the subunit not necessarily is unidirectional. B to C illustrate reaction (5). The notations used are explained on page 209. A B -+- C - D e E--F Fig. 5 . Schematic illustration of sodium pumping from a sodium-depleted (int) medium across a plasma membrane (m) to a sodium-enriched medium without reference to the pos- sible occurrence of proteins linking the carrier and the actin- containing filaments together. Filled circles represent sodium ions and empty circles represent carrier sites. The transloca- tion of the carrier sites as illustrated in this figure only indicate differential accessability to either side of the mem- brane without any preference of molecular mechanism for this phenomenon. A illustrate reaction ( 6 ) . B to C illustrate reaction (7). C to D illustrate reaction (8). D and E illustrate reaction (9). E to F illustrate reaction (10). The notations used are explained on page 209. volved in either the generation of cytoplasmic streaming or sodium carrier function. Cyto- plasmic streaming is generated as illustrated in Fig. 4 and can be described by reaction (3) in the following form (see Fig 4 B-C): H2 (DI)L1 (PII) -+ L2 (DI)H2 (PII) + 6s (5) In order to ascertain that the propagating high energy pulse does not give rise to any pressure pulse when transferred from a sodium carrier molecule to PI1 it must be assumed that reaction (2) is involved in this transfer. It is further postu- lated that association and dissociation of sodium to the carrier sites are equilibrium reactions and that each energy content according to Fig. 3 of the carrier is preferentially represented by a sodium-associated or -dissociated carrier mole- cule exposing its carrier sites to either a sodium- depleted or sodium-enriched medium. By applying reactions (1) to (4), the consequences of these postulates for the sequential mode of action of a sodium carrier molecule will be described by the following reactions (see Fig. 5 , and appendix for deduction). NaLt + L1 (C) 2 Id2 (C, Naifnl) + Qs ( 6 ) (7) + L1 (C) + Naint L2 (C, NaLt) + Qs (D1)L2 ('9 NaLt) L1 (DI)H2 (C, Na+ ext ) (8) (9) t "2 (C, NalXt) + Qs "t H1 (C) + Naext HI (Cf2 (PII) -+ L1 (C)H2 (PII) (10) Upsala J Med Sci 81 206 Erik Cervbn By the reactions (7) to (10) one cycle of the carrier is completed leading to expulsion of sodium ions and the propagation of one high energy pulse in the distal direction. In order to ascertain a sodium carrier function it must be assumed that the high energy pulse is preferenti- ally transferred to a carrier which is associated with sodium as described in reaction (8). This property is inherent in the sequence of reactions that have been described in that the high energy pulse leaves the carrier in a sodium-dissociated L, conformation (reaction (10)) which according to reaction (7) (see appendix for interpretation) has a high affinity for sodium. Since Ll0, is unstable, efficient pumping of potassium would be impossible if this ion were to associate with an L, conformation of the carrier in a potassium depleted external medium. By making the same postulates as were made for sodium, relating to different conformations of the carrier, the following transitions will operate in potassium pumping, in the sequence correspond- ing to the reactions ( 6 ) to (9): (see appendix for additional evidence). Since ouabain-binding is involved in reaction (9b) (see appendix) electrogenic action of the carrier is ascertained in the present hypothesis by competition of endogenous ouabain (1, 18, 35) with the potassium-binding sites when these are exposed to the external side of the plasma mem- brane. This view is further supported by the find- ing that high external potassium ‘concentrations result in a diminished transmembraneous poten- tial (32). The “field” of migrating thermodynamic quanta generated by the actin-containing fila- ments will induce unusual properties of the sur- rounding medium as exemplified by the behaviour of proteins in solution that are capable of oscil- lating in harmony with the quantized flow. Ac- cording to Boltzmanns law, S=k In a($: 5), highly ordered states are less probable, and there- fore accumulation of either high entropy forms or Upsah J Med Sci 81 low entropy forms in adjacent coordinates (x-1), (x), (x+ 1) of the field is not favoured. Some con- sequences of this statement for proteins in solu- tion, capable of storing the energy represented by Q are described by the following reactions where the sequence of notations indicate adjacent loca- tion in the direction of quantized cytoplasmic flow. -? -+ (Q, + LZP) - Qs + -- Q, (1 1) These reactions are all unidirectional because they occur in a field of migrating thermodynamic quanta. Fusion of the energy components in parenthesis in reaction (1 1 ) to (14) is either ac- companied by migration of the protein in the backward direction or by extension of the quan- tized field. DISCUSSION According to this hypothesis ATP enhances cytoplasmic streaming (12) by increasing the number of high energy pulses per filament length while filamentous myosin probably influences cytoplasmic streaming by increasing synchrony in the quantized field surrounding the actin-con- taining filaments. A tendency of the protoplasmic fibrils of Characeae to join in circles (9, 12) is explained partly from considerations of fuel economy since only thermodynamic energy would be required to maintain the rotation of such circles provided the propagation of high energy pulses is unrestricted. There are profound energetic differences be- tween on one hand the present hypothesis and on the other hand the sliding filament hypothesis for myosin-actin interaction (7) and the Na’ - and - K + -stimulated ATPase hypothesis for generation of a transmembraneous sodium gradient (cf.: 1, 3). These differences are illustrated by the follow- ing calculations which are based on an estimated number of 50 actin-tropomyosin subunits, (cf.: 24) The Migrating Thermodynamic Quantum Hypothesis f o r Cell Biological Phenomena 201 each containing 13 actin monomers ( 2 2 ) in their turn constituting spheres with a diameter of 5 5 8, (22), in one actin-containing filament along the entire length of one microvillus. According to the present hypothesis the hydrolysis of 2 ATP mole- cules optimally results in 50 cycles of the sodium carrier, and depending on the degree of quantiza- tion and on the magnitude of the oscillations of the proteins involved in generating a pressure pulse, results in a cytoplasmic translocation (flow) perhaps in the range of l O A to 50xlOA. The latter estimation is based on the difference of width of the interchain cleft between tetrameric oxy- and deoxyhemoglobin (MW: 64 500) which is 7 8, (29) and which may be representative of the magnitude of oscillations of a protein of approximately that molecular weight (MWactin: 42000). On the contrary, in order to bring about a comparable physiological effect according to the sliding filament and the Na+-and- Kt stimulated ATPase hypotheses, lOAI55A (0.2) to 50 x 10/55 (9.1) ATP molecules (see text to Fig. 3 and ref. 7) and 50 ATP molecules, respectively, are hydrolyzed (&: 7). The present hypothesis does not contradict the idea that a Na' -and-K' -stimulated ATPase molecule is responsible for generation of an elec- trochemical gradient, but extends this idea in that it includes a mechanism for the reutilization of high energetic phosphate bonds. This consider- ably increases the efficiency for generation of an electrochemical gradient of sodium and potas- sium. It is notable that when the sequential mode of action of the carrier is deduced from the postulates of this hypothesis one "solution" (see appendix) is compatible with several experimental data. In addition this solution is also compatible with fundamental thermodynamic principles in that a low entropy form of the carrier is as- sociated with potassium and dissociated from sodium on the potassium-depleted and sodium- enriched side of the membrane. This is a less probable state and should represent lower en- tropy according to Boltzmanns law S = k Inn. A high affinity for internal sodium is also accounted for in the present hypothesis since the low entropy form, L,, is more unstable when adjacent to a high energetic phosphate bond in accordance with the same fundamental thermodynamic prin- ciples. The finding that mitochondria may be located in horizontal planes at the level of the Z-band of striated muscle (2) is compatible with the postu- late of the present hypothesis that high energetic phosphate bonds propagate towards regions en- riched in a-actinin when combined with the generally held view that mitochondria are found where they are best needed. Since the propagating high energy would leave the filament at this site, low energetic phosphate metabolites would ac- cumulate resulting in positive chemotaxis of mito- chondria. In skeletal muscle, the length of an actin- tropomyosin subunit determined by X-ray dif- fraction is approximately 365 A (7) and the inter- crosslink distance of equivalent spatial orientation between actin and myosin filaments is 429 8, (7). This diff'erence of length is interpreted in the pre- sent hypothesis to indicate that myosin is ar- ranged in the myofilaments so to, as far as pos- sible, avoid contact with equivalent sites on the actin-containing filaments. This arrangement would guarantee, firstly minimal interference with the quantum flow generating mechanism located between adjacent actin-tropomyosin subunits, and secondly, transfer of ATP from myosin to the actin-containing filaments irrespective of their spatial orientation and the degree of shortening. This application of the present hypothesis is, in contrast with the sliding filament model for mus- cular contraction, compatible with the repetedly demonstrated fact that ATP weakens the inter- action between myosin and actin (&: 2 2 ) . The contraction of regenerated actomyosin containing conversely oriented actin filaments (6) is explained by reactions (1 1) to (14) according to which proteins capable of storing the energy represented by Q are able to migrate opposite to the quantized flow generated by the actin-con- taining filaments. These reactions imply that con- versely oriented actin-containing filaments slide past each other inside the regenerated actomyosin threads (cf.: 6) where the degree of quantization is high. The reassembly of myosin filaments simul- Upsala J Med Sci 81 208 Erik CervPn taneously with contraction in regenerated acto- myosin ( 6 ) and the tendency of myosin molecules to join in the A-band of striated muscle proximal (see notations, page 209) to the actin-containing filaments is explained by postulating that myosin molecules are capable of storing the energy repre- sented by Q . By this assumption the occurrence of myosin-like filaments in the I-band proximal to the Z-band (30) and the apparent migration of mate- rial from the I-band to the A-band during contrac- tion (30) would also be explained. The present hypothesis gives an alternative ex- planation to the phenomenon that the ATP level remains unchanged after contraction in skeletal muscle (cf.: 18). It is further suggested that creatine and phosphocreatine interconversion constitute a mechanism for recycling of the high energy pulse when it leaves the distal ends of the actin-containing filaments. The main effect of ATP hydrolysis in muscular contraction would consequently be to supply energy in the form of thermal motion of cytoplasmic solvent molecules. Since no possibilities for restreaming close to the Z-band of the sarcomere of skeletal muscle can be discerned the propagation of high energy pulses along the actin-containing filaments in this system only results in the establishment of a quantized field without accompanying quantized cyto- plasmic flow. Contraction of skeletal muscle will therefore be described by the following reaction: H2(D1)L1(P11)(x)~ L2(DI)H2(PII)(x-1) (15) The ubiquity of actin and actin-like proteins in animal and plant kingdoms (cf. : 15) suggests that the evolution of many proteins has occurred under the influence of the quantum-generating mecha- nism described here. These conditions would counteract the establishment of protein mutants that do not oscillate in harmony with the quan- tum flow generated by actin-containing filaments, because the presence of such “distorsion” mole- cules would render impossible the optimal func- tion of cellular enzymes, adapted to a quantized environment millions of years ago. Experimental support for this assumption is again found in electron-microscopic studies on brush border Upsala J Med Sci 81 microvilli. In some of these studies the actin-core supposed to carry cytoplasmic flow in the distal direction apparently originates in the cell body (29). Since cytoplasmic enzymes are of the same size as the proteins constituting the actin core they would tend to obstruct the flow if they were to follow with it. However, the reaction (1 1) im- plies that proteins oscillating in harmony with the quantized flow are either stationary or translo- cated in the opposite direction. Entrance into microvilli of cytoplasmic enzymes adapted to a quantized flow would then be counteracted by both the central actin core and the terminal web, a network of actin-containing (29) quantum-gene- rating filaments situated in the distal part of the cell but proximal to microvilli (see Fig. 1). These considerations thus seem to be compa- tible with the view that actin-containing filaments in generating thermodynamic quanta constitute a pace-maker for cellular life and evolution and pro- foundly influence the behaviour of most cellular proteins. SUMMARY STATEMENTS A hypothesis for cell biological phenomena is presented according to which: 1. “Condensed”, low entropy forms of a protein are capable of generating a pressure pulse when reverting in one single step to high entropy forms. 2. The actin-containing filaments generate vectorial pressure pulses each representing a de- fined thermodynamic energy content, thus explain- ing cytoplasmic streaming. 3. Proteins of actin-containing filaments gene- rate vectorial pressure pulses in connection with the vectorial propagation of protein-bound high energy pulses along the filament. These pheno- mena are mutually dependent. 4. The evolution of many proteins has occurred under the influence of the quantum flow generated by the actin-containing filaments, making them capable of oscillating in a quantized field, storing and rejecting the thermodynamic energy repre- sented by the pressure pulse. 5 . The protein(s) responsible for generation of a transmembraneous gradient of sodium and potas- sium is (are) in this sence adapted to a quantized environment. 6 . A sequential mode of action of a sodium and potassium carrier molecule can be deduced from the postulates of the hypothesis. One of four solu- tions in this deduction is compatible with experi- mental data and fundamental thermodynamic principles. 8. A physiological significance is ascribed to the contraction of brush border microvilli. Con- cominantly with contraction, sodium ions are pumped out of the cell thus creating an electro- chemical gradient which is necessary for sodium- dependent transport of certain metabolites across the microvillous plasma membrane. When reach- ing the intracellular space the transported meta- bolites are carried further into the cell by a sub- membraneous cytoplasmic flow in the microvilli. 9. The high energetic phosphate bond of ATP is reutilized several times for sodium pumping when propagated along an actin-containing filament bound to carriers in the plasma membrane, thus considerably increasing the efficiency of the sodium- and potassium-pumping mechanism. 10. The main effect of ATP hydrolysis in muscu- lar contraction is to supply energy in the form of thermal motion of cytoplasmic solvent molecules. NOTATIONS L,, L,, HI, and H,: energy content of proteins as defined in Fig. 3. The sequence of these denotions indicate the vectorial propagation of a high energy pulse. Q: The thermodynamic quantum, that is, the energy differnce (L, - L2) rejected as a pres- sure pulse from actin-containing filaments in connection with the unidirectional propaga- tion of high energy residing in a labile phos- phate bond of ATP. -Q: The energy difference (L,-L,) 0: A sign denoting energy comparable to and exchangeable with the energy residing in a terminal phosphate bond of ATP. p: Index denoting the energy that resides in pro- tein s: Index denoting the energy that resides in solu- tion (x-1), (x) and (x+ 1): Indices occurring after p and s and denoting coordinates in a field om mig- rating thermodynamic quanta in the direction of quantized cytoplasmic streaming. +: Migration of energy in the direction of quanti- zed cytoplasmic streaming (= forward, distal) +: Migration of energy in the direction opposite to quantized cytoplasmic streaming (=back- ward, proximal) P: Proximal part (in the direction of quantized cytoplasmic streaming) of an actin-tropmyo- sin subunit. The part of an actin-containing filament located immediately distal to a bind- ing site of the filament to the plasma mem- brane in brush border microvilli. D : Distal part (in the direction of quantized cyto- plasmic streaming) of an actin-tropomyosin subunit. The part of an actin-containing fila- ment located immediately proximal to a bind- ing site of the filament to the plasma mem- brane in brush border microvilli. I: The intermediate part of an actin-tropomyosin subunit. C: Sodium and potassium carrier molecule lo- cated in a biological membrane. (X), (Y): Indices denoting location of energy or ions. I, 11: Sequence of actin-tropomyosin subunits in The Migrating Thermodynamic Quantum Hypothesis f o r Cell Biological Phenomena 209 Upsala J Med Sci 81 210 Erik Cervth the direction of quantized cytoplasmic streaming. (C,Na:,,), (C,Na:,,): indices denoting asso- ciation of ions to the carrier sites when ex- posed to the sodium-depleted (int) or the sodium-enriched (ext) side of a membrane. APPENDIX The reactions (6) to (10) are deduced as follows. Since H,~c~L2~plr~+Ll~c~Hz~p~l~ is the final re- action, the sequence of transitions of the carrier must be L2+H2+Hl-+Ll. Since adsorption of so- dium is an equilibrium reaction H,(c)+Hl(c) is either accompanied by adsorption of Nati,, or dislocation of Na:,,. In the former case Ll& associated with Na:,,and LI(c)+Lz(c)or HzLI(C)-*L2Hz(C) is necessary for its dislocation. L1(C,I.la+e,t) is thus on average thermodynamically unstable. On the contrary, when HZ(C)+HI(C) is accompanied by dislocation of Na:,t(c), L,(,, is an interior sodium-dissociated form. The thermo- dynamically spontaneous transition H2L,(,)-+ L2H2(,-) is then impossible because H2(C) is as- sociated with Na:,,. On average L1(,, will therefore be unstable increasing the affinity of the carrier for sodium when the carrier sites are exposed to the cell interior. This sequential mode of action of the sodium carrier is illustrated in reactions (6) to (10) because it is compatible with several expe- rimental findings and interpretations made by re- searchers in this field as given by the following statements (1): 1. A single cation carrier has an absolute requirement for Na’ to go to its ‘‘acti- vated” form. 2. External ATP is not hydrolyzed. 3. The temperature dependent step is neither the phosphorylation nor the dephosphorylation step (reaction (8) and (10)). 4. Carriers have inwardly oriented cation sites of high affinity for Na’. When a corresponding deduction is made for potassium pumping, one “solution” is rejected because in that case the L, conformation is labile, making potassium accumulation from a potas- sium depleted medium improbable. This sequen- also improbable according to Boltzmanns law, ce, L1(C)+L2(C,Natint Kiext)+HZ(C,Natext Kqnt)sH1(C)iS Upsala J Med Sci 81 S=k I&, which implies that highly ordered states are not favoured. The other solution which is illustrated in the text as the sequence (6b) to (9b) is compatible with inter alia the following experi- mental findings and interpretations (1): 1. The cation carrier can return to its inactivated state either as a free carrier or in combination with K+. 2. K + but not Na’ decreases labeling with 32P from AT32P at low temperatures (re- action (6), (6b), (8) and (8b)). In this case K + but not Na’ stabilizes L,(,,, and the terminal phos- phate bond is looked upon as corresponding to Oubain competitively inhibits potassium-bind- ing (18, 35) when the carrier sites for this ion are exposed to the external side of the plasma mem- brane (1 8) indicating that oubain-binding is in- volved in reaction (9b). This is compatible with experimental data indicating that oubain binds to a phosphorylated form of the enzyme (34). Hl(DX).)* ADDENDUM Possible application of the present hypothesis to anabolic phosphorylation of A D P Each actin-tropomyosin subunit in an actin-con- taining filament is considered to represent a func- tional unit attached to a sodium carrier molecule in the plasma membrane. When the concentration of Na’,, is high and Na:,, is low, the L2(e) and Hl(,, conformations are favoured. Under these conditions, a high ATP/ADP ratio will favour the generation of a transmembraneous gradient be- cause of imposed unidirectional components for transitions of the carrier as illustrated by the On the contrary, if Na’,,, is high and Na’,, is low, the H1(,, and L,(,, conformations will be stabilized. Under these conditions, a low ATP/ADP ratio will favour the reverse action of the carrier as illustrated by another sequence of transitions, L~,,, liil(c, Nt H , ( ~ , -+ L,(,, C L ~ ( ~ ) . The actin-tropomyosin subunit may thus oe re- garded as a coupling factor (cJ: IS), the main function of which could be to bind ADP and ortophosphate in an optimal spatial relationship ATP sequence L,(,, + K ( C ) Z H l ( C ) + L X , L 2 ( C ) . A D P + P , ’ The Migrating Thermodynamic Quantum Hypothesis f o r Cell Biological Phenomena 2 1 1 to the carrier. When the carrier associated with a coupling factor is operating in reverse due to a high transmembraneous gradient of the trans- ported ions, ATP will be formed from ADP and ortophosphate. These functional considerations support the idea derived from structural similari- ties (1 6 ) that an actin-tropomyosin subunit is equivalent to the coupling factors of mitochondria (and chloroplasts). In both cases ATP is formed simultaneousely with the reflux of ions participat- ing in a transmembraneous gradient. These ions are evidently sodium (and potassium) in the plasma membrane and protons in the mito- chondrial membrane (cJ: chemiosmotic hypo- thesis for oxidative phosphorylation, 18). In addition to the already established photo- phosphorylation and the oxidative phosphoryla- tion of A D P the present hypothesis is theoreti- cally compatible with a third mechanism for generating ATP. This mechanism which may be denoted thermodynamic phosphorylation relates to the well-known tendency of actin filaments to depolymerize at high potassium concentrations (cJ: 6 ) . Thermodynamic phosphorylation implies that potassium is accumulated and sodium pumped out of a cell by means of a high energy pulse propagating along an actin filament. When a critical potassium concentration is reached the actin filaments are enzymatically depolymerized to single actin-tropomyosin subunits, still at- tached to the plasma membrane. The sodium- potassium gradient is then used for generation of ATP by the reverse action of the carrier mole- cules with their associated actin-tropomyosin coupling factors. At the critical potassium con- centration both polymerized and depolymerized actin-tropomyosin filaments may coexist and these mechanisms may be operating simultane- ously. This type of phosphorylation may be phylogenetically older than photophosphorylation and oxidative phosphorylation. The above considerations may be applicable to the phenomena that tumor cells can survive in a low oxygen environment practically devoid of fuel for conventional generation of ATP (36) and that fibroblasts exposed to a low oxygen tension begin to move about (d: 12, 36). ACKNOWLEDGEMENT This work was supported by grants from the Swedish Medical Research Council (project B77-13X-228- 13B), the University of Uppsala and a personal grant from Uddeholms AB. I would like to thank Drs. Gunnar Agren and Gunnar Ronquist for generous support and valuable criticizm. REFERENCES 1. 2. 3. 4. 5 . 6. 7. 8. 9. 10. 11. 12. Albers, R.W.: Biochemical Aspects of Active Transport. I n Ann rev Biochem. Vol 36 Part I1 (ed. P.D. Boyer), pp 727-756 Ann Rev Inc, Palo Alto, California, 1967. Bennett, H.S.: The Structure of Striated Muscle As Seen by the Electron Microscope. I n The Struc- ture and Function of Muscle, Volume I (ed. G.H. Bourne)p 150, Academic Press New York and London, 1960. Christensen, H.N.: Biological Transport, second edition, W.A. Benjamin, Inc., London, Amster- dam, Don Mills, Ontario, Sydney, Tokyo, 1975. Clarke, M., Schatten, G., Mazia, D. & Spudich, I.A. : Visualization of Actin Fibers Associated with the Cell Membrane in Amoebae of Dictyostelium discoideum. Proc Nat Acad Sci USA 72: 1958- 1962, 1975. Daniels, F. & Alberty, R.A.: Physical Chemistry. Wiley International Edition. John Wiley and Sons, Inc., New York, London and Sydney, 1967. D’Haese, I. & Komnick, H.: Fine Structure and Contraction of Isolated Muscle Actomyosin. Evidence for a Sliding Mechanism by means of Oligomeric Myosin. Z Zellforsch 134: 41 1-426, 1972. Huxley, H.E.: The Mechanism of Muscular Con- traction. Science 164: 1356-1366, 1969. Hiilser, D.F. & Frank, W.: Stimulation of Em- bryonic Rat Cells in Culture by a Protein Fraction Isolated from Fetal Calf Serum. Z Naturforsch Part B, 266: 1045-1048. Jarosch, R.: Plasmastromung und Chloroplasten- rotation bei Characeen. Phyton 6: 87-107, 1956. Jarosch, R.: Die Dynamik im Characeen-Proto- plasma. Phyton 1 5 : 43-66, 1960. Jarosch, R.: Screw-Mechanical Basis of Proto- plasmic Movement. In Primitive Motile Systems in Cell Biology (eds. R.D. Allen and N. Kamiya) pp 599-633. Academic Press New York & London, 1964. Kamiya, N.: Protoplasmic streaming. I n Proto- plasmalogia, Handbuch der Protoplasmaforschung Band 8:3:a (eds. L.V. Heilbrunn and F. Weber) Springer-Verlag, Wien, 1959. Upsala J Med Sci 81 2 12 Erik Cervkn 13. Karlson, P.: Kurzes Lehrbuch der Biochemie fur Mediziner und Natunvissenschafter. P 45 Georg Thieme Verlag, Stuttgart, 1967. 14. Kersey, Y.M., Hepler, P.K., Palevitz, B.A. & Wessels, N.K.: Polarity of Actin Filaments in Characean algae. Proc Acad Sci USA 73: 165- 167, 1976. 15. Laki, K.: Actin as an Ancient Nucleotide-Binding Protein. Int J Quant Chem: Quant Biol Symp No 16. Laki, K. & Ladik, I.: Protein Energy Converters. NATO Adv Study Inst; Ser B: 681-98, 1975. 17. Lazarides, E.: Actin, a-Actinin, and Tropomyosin Interaction in the Structural Organization of Actin Filaments in Nonmuscle Cells. J Cell Biol 68: 18. Lehninger, A.L.: Biochemistry, Worth Publishers, Inc. New York, 1970. 19. Metuzals, J. & Tasaki, I.: Scanning Electron Microscopy of Filamentous Network on the Cytoplasmic Face of the Axolemma. J Cell Biol 70 No. 2 Part 2 p 39a, 1976. 20. Minkoff, L. & Damadian, R.: Caloric Cata- strophe. Biophys J 13: 167-178, 1973. 21. Minkoff, L. & Damadian, R.: Actin-Like Proteins From Escherichia coli: Concept of Cytotonus as the Missing Link Between Cell Metabolism and the Biological Ion Exchange Resin. J Bacteriol 22. Moore, P.B., Huxley, H.E. & DeRosier, D.J.: Three-dimensional Reconstruction of F-Actin, Thin Filaments and Decorated Thin Filaments. I Mol Biol 50: 279-295, 1970. 23. Mooseker, M.S.: Brush Border Motility: Microvil- lar Contraction in Isolated Brusch Border Models. J Cell Biol 63 No. 2 Part 2, p 231a, 1974. 24. Mooseker, M.S. & Tilney, L.G.: Organization of an Actin Filament-Membrane Complex Filament Polarity and Membrane Attachment in the Micro- villi of Intestinal Epithelial Cells. J Cell Biol 67: 25. Murer, H., Sigrist-Nelson, K. & Hopfer, U.: On the Mechanism of Sugar and Amino Acid Inter- action in Intestinal Transport. J Biol Chem 250: 26. Netter, H.: Theoretische Biochemie. p. 531, Springer-Verlag, Berlin, Gottingen and Heidelberg, 1959. 27. Oplatka, A., Gadasi, H., Tirosh, R., Lamed, Y., Muhlrad, A. & Liron, N.: Demonstration of Me- chanochemical Coupling in Systems Containing Actin, ATP and Nonaggregating Active Myosin Derivatives. J Mechanochem Cell Motility 2: 28. Pollack, R., Osborn, M. & Weber, K.: Patterns of Organization of Actin and Myosin in Normal and Transformed Cultured Cells. Proc Nat Acad Sci 2 297-305, 1975. 202-219, 1976. 125: 353-365. 1975. 725-743, 1975. 7392-7396, 1975. 295-306, 1874. U~SQIQ J Med Sci 81 USA 72: 994-998, 1975. 29. Rodewald, R., Newman, S.B. & Karnovsky, M.J.: Contraction of Isolated Brush Borders from the Intestinal Epithelium. J Cell Biol 70: 541-554, 1976. 30. Sjostrand, F.S. & Andersson-Cedergren, E.: The Ultrastructure of the Skeletal Muscle Myofila- ments at Various States of Shortening. J Ultra- struct Res 1: 74-108, 1957. 3 1. Stromgren-Allen, N. : Endoplasmic Filaments Generate the Motive Force for Rotational stream- ing in Nitella. J Cell Biol 63: 270-287, 1974. 32. Tasaki, I.: Nerve Excitation. A Macromolecular Approach. Charles C. Thomas Publisher, Spring- field and Illinois, 1968. 33. Tilney, L.G. & Detmers, P.: Actin in Erythrocyte Ghosts and Its Association with Spectrin. J Cell Biol 66: 508-520, 1975. 34. Tobin, T., Akera, T., Lee, C.Y. & Brody, T.M.: Oubain Binding to (Na+ + K+)-ATPase. Effects of Nucleotide Analogues and Ethacrynic Acid. Bio- chim Biophys Acta, 345: 102-1 17, 1974. 35. Tobin, T. & Sen, A.K.: Stability and Ligand Sen- sitivity of 'H Oubain Binding to (Nat + K')- ATPase. Biochim et Biophys Acta 198: 120-131, 1975. 36. Warburg, 0.: On the Origin of Cancer Cells. Science 123: 309-314, 1956. Received November 15, I976 Address for reprints: E. Cerven institute of Medical and Physiological Chemistry Biomedical Center University of Uppsala Box 575 S-751 23 Uppsala Sweden