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O N T H E B E H A V I O R O F R O T A T I N G H E L I C E S

R O B E R T J A R O S C H

Biological Research Division, Austrian Nitrate Works, Linz/Donau, Austria

I N T R O D U C T I O N

Several possibilities of t r a n s p o r t i n g substances have been devel- oped by m a n . One of them, t h e so-called "spiral of A r c h i m e d e s " (Fig.

1), h a s been used for m a n y centuries for farm irrigation. B y a simple d y n a m i c process (revolution) of a relatively complex s t r u c t u r e (the helix), w a t e r is t r a n s p o r t e d against a g r a d i e n t in energy. Because of its primitive mechanics, this principle m a y be applied to all orders

FIG 1. T h e "spiral of Archimedes," an old water pump.

of m a g n i t u d e , as well as a t the molecular level. T h e helical aspect of proteins invites us to a p p l y it to t h e t r a n s p o r t of substances in t h e living cell. T h e displacement caused b y t h e revolution of a rigid worm shaft is v e r y simple, b u t the motions along elastic helices, such as proteins, seem to be much more complicated.

T h e present paper describes some helical configurations in t h e p r o - toplasm, a n d t h e n a t t e m p t s to find t h e special conditions for substance t r a n s p o r t along these structures.

275

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276 ROBERT JAROSCH

C O N F I G U R A T I O N O F P R O T E I N H E L I C E S

Amino Acid—Sequence and Tertiary Structure

According to Crick [2] and P a u l i n g and Corey [18] a stable super- helix is superimposed on the α-helix if a special sequence of amino acids is continually repeated (Fig. 2 a ) . T h e gap between chemical and protoplasmic structure would be almost closed if the relation between t h e respective sequences of amino acids a n d t h e average pitch and diameter of these second-order helices could be calculated. T h e higher protein configuration are m a i n l y deduced from the lower ones by t h e screw-mechanic theory, as will be shown.

Intertwining of the Helices

I t was supposed for k e r a t i n t h a t the helices of t h e second order might intertwine (Fig. 2 a ) . T h e properties of intertwining m a y be ex- amined very closely by using helices m a d e of steel wire [ 1 2 ] .

Different Types of Intertwining A " n o n p e n e t r a t i n g intertwining'

7

is distinguished from a " p e n e t r a t - ing intertwining." T h e unstable, n o n p e n e t r a t i n g intertwining (Fig. 3 ) , which appears in t h e case of v e r y small pitches, does n o t seem to be very i m p o r t a n t for protoplasmic structures because t h e helices are deformed in a flexible m a n n e r . T h i s t y p e of intertwining obviously occurs on the chromatids in t h e chromosome (Fig. 2 1 ) . T h e more i m p o r t a n t p e n e t r a t i n g intertwining is either " n e g a t i v e " (Fig. 4) or

"positive" (Fig. 5 ) . N e g a t i v e intertwining does not show a correspon- dence of coils and is not stable. I t cannot produce a superhelix (Fig.

10b). Positive intertwining (Fig. 2 b ; Figs. 5 - 8 ) shows correspondence of coils and is stable. P i t c h differences cause a superhelix (Fig. 10c).

Possible Reasons for Intertwining

I n principle, there are three possibilities t h a t can lead to an inter- twining of helical structures, (a) M e c h a n i c a l contact between differ- ent helices. T w o similar coiled helices r o t a t i n g in t h e same direction show a tendency to intertwine if t h e y receive a mechanic contact [ 1 2 ] . (b) Polymerization in an intertwined position, (c) T h e Umschnappen ("refolding") of one a n d t h e same helix (Fig. 10).

T h i s process occurs if a strong torsional force t h a t cannot be released

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ON T H E BEHAVIOR OF ROTATING HELICES 277 quickly enough arises in the helix, e.g., if resistant forces in the surrounding medium are too strong. A torsional force connected with an increase of the pitch always leads to a negative intertwining (Fig.

10b). The torsional force connected with a pitch decrease produces a positive intertwining (Fig. 10c). Occasionally the Umschnappen can be directly observed in the microscope or is discernible by its charac- teristic forms of tension [9, 11, 1 2 ] .

1

Differences in the Pitch and the Origin of Superhelices

In Fig. 2b six helical models t h a t are composed of one to six positively intertwined helices of the same shape are shown. Note t h a t the models with the 2, 3, and 4 helices show a play between the single elements. This play allows the occurrence of pitch differences on the single helices. These differences cause the origin of a tension which leads to a superhelix (Figs. 10c and 11a). Intertwined protein helices of the second order m a y produce helices of the third order in this way. The actin fibrils (Fig. 13b) consist of two positively intertwined helics of the second order which form a helix of the third order (pitch P3, Fig. 13a). Helices of the third order m a y also intertwine (Fig. 9) and pitch differences on the helices of the third order will form a helix of the fourth order; in a bacterial flagellum there are two or more helices of the third order positively intertwined (Fig. 14a and b ) . Thus the flagellar helix (Fig. 14c) is a helix of the fourth order. I t would appear t h a t the play in Fig. 14a and b is smaller than in the actin fibrils, as seen in Fig. 13b. According to an empirical approximation formula [6] the pitch difference of the intertwined helices is about 5 Â in the case of actin fibrils (using the data of Hanson and Lowy [3]) and about 20 Â in the case of bacterial flagella (using the d a t a of L a b a w and Mosley [ 1 4 ] ) .

I t is characteristic for the superhelices produced by pitch differ- ences t h a t the axes of the single helices coincide only on the ends.

A model of a superhelix (Fig. 11a) t h a t is divided in some portions changes its structure. The parts are strained only within themselves (Fig. l i b , left). The mechanical tension which was distributed at a long range is fully lost if the parts are very small. The bending disappears (Fig. l i b , right). This property is probably the main rea- son why the structural proteins of the protoplasm cannot be fixed or prepared very well: The tension of the native state becomes free 1

1 am indebted to Dr. Crane for telling me that the microvilli (see his paper in this volume) are constituted by Umschnappen [17a].

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FIG. 2 a. Protein helices of the second order of keratin. ( F r o m Pauling and Corey [ 1 8 ] . ) b. Similar configurations com- posed by helices made of steel wire. For details, see text.

278 ROBERT JAROSCH

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FIGS. 3-9. Models showing several kinds of intertwining between wire helices. For details, see text.

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280 ROBERT JAROSCH

Ρ Ρ

FIG. 10. The Umschnappen at point U (Fig. 10a) of a helix showing two different pitches (p and P ) leads to a "negative" intertwining (Figs. 10b and 4) when the helix is twisted against the direction of coiling. T h e "positive" inter- twining (Fig. 5) connected with the generation of a superhelix (Fig. 10c) is the consequence of a twisting in the direction of coiling.

a n d t h e structure is destroyed or d e n a t u r a t e d . T h u s , the single helical coils m a y a p p e a r as "globular s u b u n i t s . "

Origin of Tubules

I n Fig. 2b, t h e compound helix composed of six single helices does not show a n y more p l a y . A t u b u l e has been constituted a n d there is no space for a further helix. T h e cross-sections of t h e single helices a p p e a r more as ellipses when t h e inclination angle of t h e helices b e - comes smaller (Figs. 6 - 8 ) . T h e m a x i m a l n u m b e r of single helices

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ON T H E B E H A V I O R OF ROTATING H E L I C E S 281

FIG. 11. The existence of a superhelix (Fig. 11a) is dependent on the me- chanical tension distributed in a definite length of the superhelix. After dividing, small portions do not show the bending (Fig. l i b ) . FIG. 12. A lateral branch may show an acute angle (δ in Fig. 12c) either by additional winding of helices coming from one side (straight arrow in Fig. 12b) or by coiling away of single helices from a compound helix (Fig. 12d).

is determined by the proportions of the single helices: nm ax = Ρ cos a/d, where Ρ is the pitch, « the inclination angle, and d the diameter of the wire of the single helices. I t is also possible to calculate the pitch of the single helices by knowing the parameters of the cross-sec- tion of the tubule: Ρ = ηάΏπ[1/(D

2

TT

2

— n2d2)]$, where D is the average diameter of the tubule (average of the inner and outer diameter).

The appearance of tubules seems to be possible on helices of differ-

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FIGS. 13-14. Interpretations of several protein configurations with helical models. FIG. 13. Actin fibril. (Electron micrograph from Hanson and Lowy [3].) Period P2, 56 Â ; pitch of the third order, P3, about 700 A. FIG. 14 Bacterial flagella. (Electron micrographs from Labaw and Mosley [14].) P3 about 570 Â; D3 (diameter of one flagellum) about 140 Â; P4 (pitch of the flagellar helix in Fig. 14c) about 2.6 μ.

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FIG. 15. "Microtubules" in the protoplasm of a young plant cell and their imitation with helical models. (Electron micrographs from Ledbetter and Porter [15, 16].) The cross-section (Fig. 15c) shows addition of contrast substance (reproduction by the Markham-test). The model contains 15 helices instead of 13. P3 about 1220 A; Diameter of the tube, Dh about 230 Â . FIG. 16.

Extended "polysheath" of a phage tail (electron micrograph from Kellenberger [13].) The models also show the contracted state. Ps about 180 Â; diameter D3 about 260 A.

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FIG. 17. Possible genesis of a "crossed texture" of cellulose microfibrils in a plant cell. (Electron micrograph from Pres- ton [19].)When no gap exists the microfibrils lie parallel to the microtubules (Fig. 17a). FIGS. 18-20. Extracellular pro- tein helices in animal-tissue culture. (Phase-contrast micrographs from Rose [20].) Compare the helical model in Fig. 17b.

Figure 20 shows four phases of increasing the pitch and diameter, photographed within a period of 2 hours. C indi- cates a particle fixed on the rotating end of the helix. FIG. 21. Chromosome of a h u m a n leucocyte. (Electron micro- graph from Yasuzumi et al. [22].)

284 ROBERT JAROSCH

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ON T H E B E H A V I O R O F R O T A T I N G H E L I C E S 285 ent order. T h e well-known " m i c r o t u b u l e s " revealed b y t h e electron microscope (Fig. 15c a n d d) are p r e s u m a b l y compound helices of t h e t h i r d order (Fig. 15a and b ) ,

2

as are the bacterial flagella (Fig.

14) a n d t h e tail of a phage (Fig. 1 6 d ) . T h e extracellular tubules described by Rose [20, 21] with t h e light microscope (Figs. 18-20) are p r e s u m a b l y compound helices of a high order. T h e helices of chromosomes (Fig. 21) also seem to be helices of a high order.

I n s t e a d of t h e p l a y (Fig. 2b) only a single i n t e r m e d i a t e space can exist if t h e single helices lie parallel and adhere together. (Molecu- lar forces t h a t are p r e s u m a b l y involved cannot be i m i t a t e d in t h e models.) An i n t e r m e d i a t e space of this kind m u s t a p p e a r after an increase of t h e pitch (Fig. 16a a n d b ) . T h e t a i l of a phage a p p e a r s either in the extended (Fig. 16d) or contracted form. Rose [20]

directly observed t h e growth of t h e pitch (Fig. 2 0 ) . T h i s process is connected with a v a r i a t i o n of t h e diameter. T h e same occurs on t h e phage tail [ 1 3 a ] . T h i s v a r i a t i o n of pitch a n d d i a m e t e r shows a higher extension in helices of higher order t h a n in lower ones. R e c e n t l y two different helical configurations h a v e also been found in bacterial flagella [ 1 6 a ] .

D u r i n g t h e generation of t h e torsional force protein helices of t h e t h i r d a n d higher orders m a y also change their direction of coiling (Fig. 16b, c ) . Similar processes in t h e microtubules are p r e s u m a b l y connected with diurnal r h y t h m s [10, 1 1 ] ; for example, t h e directed crystallization of cellulose microfibrils in the secondary wall of m a n y p l a n t cells (Fig. 17), and t h e generation of fibrillar p a t t e r n s in the skin of animals [21a, 1 3 b ] .

I t should also be mentioned t h a t the b r a n c h i n g of protoplasmic structures or cell processes m a y be explained by intertwined helices.

A branching occurs by the Umschnappen (Fig. l O a - c ) , by a combina- tion of t h e Umschnappen a n d winding (Fig. 1 2 a - c ) , or by uncoiling

(Fig. 1 2 d ) ] . T h e acute angle (δ in Fig. 12c), which sometimes arises during t h e b r a n c h i n g process, is a l w a y s opposed to t h e source (point of fixation) of t h e helices.

B r a n c h i n g a n d other processes connected with protoplasmic m e m - branes m a y be explained by t h e assumption t h a t helices of t h e second a n d t h i r d orders exist as s t r u c t u r a l elements in t h e m e m b r a n e s [ 1 2 ] . Therefore, t h e a r r a n g e m e n t of proteins in t h e m e m b r a n e models should be modified for t h e description of t h e n a t i v e s t a t e . 2

I t should be mentioned t h a t already in 1962 Harris [3a] supposed a model for the microtubules of the mitotic spindle in terms of a tightly coiled spring.

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286 R O B E R T J A R O S C H

R O T A T I O N S O F P R O T E I N H E L I C E S Torsional Force

All configurations shown in Figs. 13-21, as well as protein helices of a lower organization, m a y r o t a t e if a n i n t e r n a l torsional force is generated. As m a y easily be observed in model helices, it is a mechanical consequence t h a t each pitch change is definitely con- nected with t h e arising of a torsional force [5, 7 ] . According to P a u l - ing and Corey, changes in t h e n a t u r e of t h e side-chain groups m a y cause small v a r i a t i o n s in t h e proportion of t h e α-helix. T h e processes occurring here are not quite clear. B u t there is evidence t h a t the splitting of adenosine t r i p h o s p h a t e ( A T P ) is t h e energy source and t h a t cations are also involved. T h e energy m u s t be p u m p e d into the α-helices as a torsional force a t precisely t h e m o m e n t when t h e process on t h e side chains occurs. P e r h a p s t h e S—H groups are essentially involved because m a n y protoplasmic motions m a y be i n t e r r u p t e d in a reverse m a n n e r with t h e specific sulfhydryl r e a g e n t p-chloromercuri- benzoate (Abe [ 1 ] ) .

Speed of Revolutions

According to M e t z n e r [ 1 7 ] , flagella show rotations up to 40/sec and bacterial flagella up to 90/sec. These flagella are bundles of large helices of t h e fourth order. T h e i r revolution m u s t generate strong resisting forces in t h e surrounding medium. W h e n t h e helix is small there will be less resistance and t h e speed will be increased. F o r p r o t o - plasmic s t r e a m i n g one can calculate values u p t o 500/sec for t h e revolutions of the helices of t h e t h i r d order [ 8 ] . Helices of t h e second order a n d free α-helices p r e s u m a b l y will r o t a t e more quickly.

I n special cases helices of higher orders (cellular helices) cannot r o t a t e because t h e resisting forces are too strong. T h e y m a y show a r o t a t i o n of a lower order b y deforming t h e highest order in a flexible m a n n e r [ 9 ] . Because of t h e same resisting forces, elongation growth is p r e s u m a b l y based on slow revolutions [ 1 1 ] .

Relation between Length of Helices and Revolution

W h e n a protein helix is longer, more processes in t h e side chains m a y occur a n d its torsional c a p a c i t y will be higher. I t is calculated t h a t a n α-helix 1 cm long can r o t a t e a p p r o x i m a t e l y 1 hour if t h e average speed is 70 revolutions per second. An α-helix 10 cm long will r o t a t e 11 hours [ 8 ] . Very short α-helices m a y show torsional

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ON T H E B E H A V I O R O F ROTATING H E L I C E S 287 revolutions of a high frequency with a period of about TÔVÔ second.

T h u s all periodic processes occurring with the helices are dependent on their length. However, along with the length of a protein helix, resisting forces must be reckoned with. If a wire helix fixed on the rotating axis of a weak electric motor is gradually immersed in a vessel filled with honey, the rotation becomes slower and a t last stops.

When the motor is strong enough the helix m a y umschnappen and branch. Very long protein helices like "neurotubules" consequently would not show any rotation at all if a suitable lubricant able to reduce the friction were not present. I n the case of the living cells, the lipids are this lubricant. If a protoplasmic droplet is squeezed out of the characeous cell into the cell sap one can observe t h a t each

FIG. 2 2 . Passive motions in the surface of an extruded protoplasmic droplet caused by external streamings in the surrounding fluid [4].

streaming in the surrounding fluid causes a streaming together on the surface of the droplet—sometimes even a small eddy motion (Fig.

22). I t is known t h a t the surface of the protoplasmic droplet consists of a lipid m e m b r a n e ; hence the outstanding property of lipids, namely, to compensate friction forces between two substrates similar to a fric- tion bearing, is well demonstrated. The relation between the content of myelin and speed of conduction in the nerves is also in agreement with this concept. I t becomes clear t h a t the damage of the myelin sheath in the case of multiple sclerosis must suppress the rotations of the neurotubules and also the ability to conduct (see below).

If a helix rotates there are two possibilities of motion which are dependent on the stability of the surrounding medium. When the me- dium is immovable or fixed (Fig. 23a and b) the helix moves through-

c

Modifications" of Revolution

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288 R O B E R T J A R O S C H

FIG. 2 4 . Explanation of the "figure of rotation." For details, see text.

u υ c α

FIG. 2 3 . Two extreme cases occurring during the rotation of a helix, a and b : Rotation without apparent waves; the medium is immovable, c and d:

Rotation with apparent waves ; the medium is movable

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ON T H E B E H A V I O R O F R O T A T I N G H E L I C E S 289 out t h e m e d i u m (rotation w i t h o u t " a p p a r e n t w a v e s " ) . W h e n it is movable (Fig. 23c a n d d) t h e helix remains in t h e same position a n d t h e " a p p a r e n t w a v e s " m a y shift t h e surrounding m e d i u m ( r o t a - tion with " a p p a r e n t w a v e s " ) . T h e r e are, of course, t r a n s i t i o n stages between these two extreme cases (Fig. 3 9 ) .

Oscillation

D u r i n g r o t a t i o n with a p p a r e n t waves oscillations will also occur on t h e elastic helix [ 8 ] . I t is t h e n a t u r e of a helix t h a t its mass is distributed excentrically around t h e axis. D u r i n g r o t a t i o n this m a s s acts as a flywheel m a s s a n d causes a c t u a l s t a n d i n g waves with v i b r a - tion nodes (Fig. 27, a r r o w s ) . As a result certain sections of t h e helix—

in each case t h e section between two neighboring v i b r a t i o n nodes—

r o t a t e excentrically. I n this section t h e geometric axis of t h e helix, S - S ' (Fig. 2 4 a ) , r o t a t e s round t h e m a i n axis, Α - Α ' . Because of t h e course of t h e a p p a r e n t w a v e s t h e oscillation is superposed b y t h e a p p a r e n t waves and a characteristic figure of r o t a t i o n arises (Fig.

2 4 a ) . T h e positions of a coil V, 2', 3'. . . correspond to t h e positions of t h e helical axis 1, 2, 3 . . . .

T h e location of t h e figure of r o t a t i o n was v e r y u n s t a b l e in t h e experiments with homogeneous helical models. I t could be displaced b y small changes such as bending t h e helical axis. W i t h heterogeneous helices, which indicate a special bending a n d distribution of mass, it m a y be expected t h a t the " n o d e s " of t h e figure lie more stable a t defined sites of t h e helix.

T h e frequency of t h e oscillation is in agreement with t h e n u m b e r of revolutions if t h e helix r o t a t e s w i t h o u t disturbance ( " p r i m a r y oscil- l a t i o n " ) . D u r i n g a disturbance, for instance, b y touching with the fingers, t h e figure of r o t a t i o n changes similarly to t h e generation of harmonic oscillations in a chord because of increasing t h e frequency (Fig. 24b and c ) . T h i s process a p p e a r s more striking a t t h e nodes of v i b r a t i o n t h a n a t t h e w a v e crests (Fig. 2 8 ) . T h e changed s t a t e of t h e oscillation m a y p r o p a g a t e along t h e entire helix a n d t h e speed is increased with the n u m b e r of revolutions per second and t h e angle of inclination. This h a s been assumed for t h e p r i m a r y process for conduction [ 8 ] .

Movement of the Surrounding Medium

As a consequence of t h e oscillations, t h e motion of t h e surrounding medium becomes v e r y complicated. A superposition of t h e shearing

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290 R O B E R T J A R O S C H

forces with t h e forces produced by t h e standing waves occurs. Since a theoretical t r e a t m e n t of these processes is v e r y intricate, we h a v e to rely on t h e model experiments. Figure 31 shows 16 helices of differ- ent proportions whose revolutions h a v e been examined in glycerin.

T h r e e zones m a y be distinguished.

FIG. 25. T h e resting helix. FIGS. 26 and 27. T h e figure of rotation, photographed in dark and bright field, arrows: node of vibration (21 rps in glycerin).

I n zone A it was characteristic for phenomena to occur w i t h o u t reference to t h e direction of t h e revolution or p r o p a g a t i o n of t h e a p - p a r e n t waves. T h e m e d i u m was twisted a r o u n d t h e helix u p to a definite distance (Figs. 32 and 3 8 a ) . Air bubbles moved characteristi- cally in a to-and-fro motion (Glitschbewegung or agitation) on t h e

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ON T H E B E H A V I O R O F R O T A T I N G H E L I C E S 291 surface of t h e figure of r o t a t i o n . N o s t a t e of equilibrium was reached.

E a c h disturbance (e.g., touching) caused an increase of t h e range of motion. Increasing t h e n u m b e r of revolutions increased t h e frequency a n d the speed of this motion. F r o m the sites a t which air bubbles were a t t a c h e d to t h e surface, air was continuously pushed

FIG. 2 8 . Increase of frequency caused by touching. FIGS. 2 9 and 3 0 . Periodic condensations of air bubbles appear in a glass tube corresponding to the pitch.

out. E a c h particle fixed on t h e helix has the same effect because it produces a wave crest.

Inside t h e figure of r o t a t i o n a continous filling with air occurs during faster r o t a t i o n s . As a consequence of t h e higher a m p l i t u d e of t h e oscillation, t h e inside air becomes displaced externally so t h a t t h e figure of r o t a t i o n appears enclosed by an aerial body. I t s surface

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292 R O B E R T J A R O S C H

sometimes shows a r h y t h m i c wavelike motion if t h e r o t a t i n g helix is touched in a specific m a n n e r . T h e motion resembles t h e " p u m p i n g "

motion described for cell surfaces.

I n zone Β (Fig. 31) a strong tendency to displace the m e d i u m along t h e axis occurred in addition to t h e twisting motion (Figs. 33 a n d 3 8 b ) . T h e particles move inside t h e figure of r o t a t i o n as well as a t its surface in t h e direction of t h e a p p a r e n t waves a n d were pushed out a t t h e end of t h e helix. G r e a t a m o u n t s of air m a y be t r a n s p o r t e d in this w a y (Fig. 3 6 ) . T r a n s p o r t occurs a t its p e a k inside the figure of r o t a t i o n (Fig. 38b) b u t it is always slower t h a n t h e

A

" A g i t a t i o n "

ΙΟ II 12 13 14 15 16 Β

T r a n s p o r t in the direction of the a p p a r e n t w a v e s

C Stable a rrangement

FIG. 31. Helices of different proportions whose rotations have been examined in glycerin. Three zones (A, B, and C) are distinguished. See text.

motion of a p p a r e n t waves. L a r g e bubbles of air sometimes show j e r k y motion in steps of a single pitch. A t certain points t h e bubbles hesitate a little. T h e speed increases with the n u m b e r of revolutions a n d t h e inclination angle. Outside t h e figure of rotation t h e particles move in helical t r a c e s ; t h e y move more quickly when t h e y are closer to the helix. Large bubbles of air, sometimes a t t a c h e d on t h e surface of t h e figure of rotation, occasionally show spontaneous quick motions in t h e opposite direction of t h e a p p a r e n t waves.

Compound helices did n o t favor t r a n s p o r t . W i t h completely closed tubules (Figs. 7, 8, 15a, 1 6 a ) , no t r a n s p o r t could be observed in the model experiments. T r a n s p o r t inside t h e figure of rotation becomes possible only if more t h a n half of t h e single helices have been removed.

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FIGS. 32-33. Investigation of the movement of the medium by observing the traces of small air bubbles in dark field. F o r details, see text.

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FIGS. 34-37. Investigation of the movement of the medium by observing the traces of small air bubbles in dark field. For details, see text.

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295

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FIG. 38. Schematic descriptions of the traces in Figs. 32-35. I n t h e case of a high amplitude (Fig. 35), Fig. 38d indicates the theoretically expected positions of "active sites" (AS).

296 ROBERT JAROSCH

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ON T H E B E H A V I O R O F R O T A T I N G H E L I C E S 297 On t h e other h a n d , t h e filling of t h e inside with air during fast revolutions w a s favored by using compound helices.

F i n a l l y , zone C was characterized by t h e prevalence of standing waves a n d a r a t h e r stable a r r a n g e m e n t of air inside t h e figure of r o t a t i o n . Only touching caused a displacement. A lateral emergence of air was striking. W h e n limited by t h e walls of a flat glass cuvette the medium obtained a r a t h e r t u r b u l e n t motion (Fig. 34) depending on t h e a m p l i t u d e of t h e oscillation (the a m p l i t u d e is the distance

between S-S' a n d Α-Α', Fig. 2 4 a ) . I n t h e case of a r a t h e r small a m p l i t u d e two helical streamings could be observed (Fig. 3 8 c ) . Increasing the a m p l i t u d e a l w a y s leads to an emergence of particles from t h e " w a v e c r e s t s " of t h e figure of r o t a t i o n (Figs. 35, 3 8 d ) . T h e y describe curves which are modifications or residues of t h e two streamings described in Fig. 38c, and then are pushed to t h e nodes of the figure of rotation. A condensation of particles occurs (as in Fig.

38d) which can be observed better in a glass t u b e (Fig. 3 0 ) .

Helices of zones Β a n d A also produce condensations, b u t their demonstration is more difficult. I n principle it is shown by the s t a n d i n g

Apporent waves

I No

oscillation I oscillation

I I

I I I

I

I

1 No apparent woves

x I I I

I

I I

I I I I

tension

tong distonce Active sheoring Growth Dressure

forces forces

FIG, 39, Diagram showing the different possibilities that may occur during

the rotation of helices (see Fig. 23), Also see text.

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298 R O B E R T J A R O S C H

waves of t h e whole helix: T h e particles emerge from the wave crests and move to t h e nodes (Fig. 3 7 ) . I t is d e m o n s t r a t e d here also t h a t the zone of influence around t h e helix arises with t h e a m p l i t u d e of t h e oscillation: I n t h e case of a small a m p l i t u d e , e.g., in Figs. 32 a n d 33, t h e d i a m e t e r of this zone is three to four times t h e diameter of t h e helix. AVith a higher a m p l i t u d e , e.g., in Figs. 34 a n d 35, it becomes a b o u t 5-fold, and with t h e extreme oscillation of Fig. 37, a p p r o x i m a t e l y 20-fold.

Summary in a Diagram

I n Fig. 39 t h e possibilities occurring during t h e revolution of helices are summarized in a diagram. T h e arrows t h a t lead up from the axis a-b d e m o n s t r a t e the displacement of t h e helices. T h e arrows lower t h a n this axis describe t h e displacement of t h e surrounding medium (see Fig. 2 3 ) . I n the direction from a to b it is assumed t h a t the resistance forces in t h e surroundings of t h e helix arise.

Although the significance of the helical shape (see Fig. 31) has not been expressed, t h e d i a g r a m provides a survey of t h e different processes t h a t m a y occur with r o t a t i n g helices. I t should also be noted t h a t there are t r a n s i t i o n stages between t h e single possibilities.

S O M E P O S S I B L E A P P L I C A T I O N S

M u c h caution should be employed in transferring considerations derived from model experiments to the molecular level. B u t there is no reason why similar processes should not occur on r o t a t i n g protein helices. T h u s it is supposed t h a t t h e displacement of t h e helices or microtubules during their rotation w i t h o u t a p p a r e n t waves is t h e cause of the progressive m o v e m e n t of t h e tips, which occurs during elonga- tion growth. T h e Umschnappen and branching are always associated with this kind of motion. I n t e r n a l tensions m a y arise, producing growth pressure.

F o r different kinds of protoplasmic motions active shearing forces were required. These m u s t arise during t h e r o t a t i o n with a p p a r e n t waves. T h e Glitschbewegung or agitation in t h e protoplasm, especially of y o u n g p l a n t cells, m a y be based on t h e revolutions of densely coiled or contracted microtubules. T h e n o r m a l protoplasmic streaming in the increased cells m a y be explained by t h e r o t a t i o n of more stretched helices. T h e strong twisting effect occurring in the medium during t h e r o t a t i o n of densely coiled helices, as applied to neurotu- bules, could be responsible for t h e enveloping of the axon by the m e m - brane of t h e Schwann cell.

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ON T H E B E H A V I O R O F R O T A T I N G H E L I C E S 299 Similar to a self-lubricating engine, t h e forces generated during t h e r o t a t i o n of protein helices of a low order m i g h t well be responsible for t h e distribution of lipids in t h e cell. T h e i r adhesion to t h e n a t i v e proteins of t h e p r o t o p l a s m m a y be similar to t h e d y n a m i c support of t h e air surface occurring in t h e model experiments on the surface of t h e figure of r o t a t i o n . T h e existence of this surface was dependent on t h e density of coils in t h e helix a n d t h e speed of revolution.

A polar t r a n s p o r t of substances such as t h e active t r a n s p o r t along microvilli (see t h e paper of D r . C r a n e , this volume) or t h e motion of sugar from t h e tip to the root in t h e sieve tubes of higher p l a n t s m a y also be caused by a p p a r e n t waves connected with the r o t a t i o n of microfibrils or microtubules. T h a t t h e t r a n s p o r t is t e m p o r a r y only during t h e night m a y be based on diurnal changes in t h e helical proportion (see Fig. 16a a n d b ) . A related example could be t h e motion of secretion substance in or a t t h e surface of " n e u r o t u b u l e s "

or "neurofibrils." An additional example m a y be t h e injection of deoxyribonucleic acid ( D N A ) into t h e bacterial cell t h r o u g h t h e tail-core of a phage.

W i t h t h e help of t h e oscillations associated with t h e a p p a r e n t waves different processes m a y be explained for which long-distance forces h a v e been supposed. T h e higher concentration of particles on definite points of a r o t a t i n g helix m a y indicate " a c t i v e sites," which h a v e been found in connection with t h e c a t a l y t i c function of proteins (see Figs. 35 and 3 8 d ) . Periodic structures, such as t h e cross bridges between fibrils, t h e a r r a n g e m e n t of t h e Z-discs during t h e development of muscle, "desmosomes," the "nodes of R a n v i e r , " a n d t h e p a t t e r n for t h e addition of cell wall substance in y o u n g p l a n t cells, m a y h a v e similar explanations. I t is hoped t h a t an examination and p e r h a p s verification of this concept m i g h t become possible in t h e future.

S U M M A R Y

T h e configurations of some microscopic a n d submicroscopic protein structures h a v e been interpreted with t h e help of helical models. I t h a s been shown t h a t because of t h e r o t a t i o n s of these or similar s t r u c - tures t h e possibility arises of explaining either a t r a n s p o r t of s u b - stances t h r o u g h t h e cell or their concentration a t defined positions.

REFERENCES

1. Abe, S., Biol. Bull 124, 107 (1963).

2. Crick, F . H . C , Nature 170, 882 (1952).

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300 R O B E R T J A R O S C H

3. Hanson, J., and Lowy, J., J. Mol. Biol. 6, 46 (1963).

3a. Harris, P., J. Cell Biol. 14, 475 (1962).

4. Jarosch, R., P h . D . Thesis, University of Vienna (1955).

5. Jarosch, R., Protoplasma 57, 448 (1963).

6. Jarosch, R., J. Theoret. Biol. 7, 171 (1964).

7. Jarosch, R., in "Primitive Motile Systems in Cell Biology" (R. D . Allen and N . Kamiya, eds.), p. 599, Academic Press, New York, 1964.

8. Jarosch, R., Biorheology 2, 37 (1964).

9. Jarosch, R., Osterr. Botan. Z. I l l , 143 (1964).

10. Jarosch, R., Osterr. Botan. Z. I l l , 173 (1964).

11. Jarosch, R., Osterr. Botan. Z. I l l , 291 (1964).

12. Jarosch, R., Osterr. Botan. Z. 112, 449 (1965).

13. Kellenberger, E., In "New Perspectives in Biology" ( M . Sela, ed.), p. 234.

Elsevier, Amsterdam, (1964).

13a, Kellenberger, E., and Boy de la Tour, E., J. Ultrastructure Res. 11, 545 (1964).

13b. K e m p . N.E., Developmental Biol. 1, 459 (1959).

14. Labaw, L. W., and Mosley, V. M., Biochim. Biophys. Acta 17, 322 (1955).

15. Ledbetter, M . C , and Porter, K. R., J. Cell Biol. 19, 239 (1963).

16. Ledbetter, M. C , and Porter, K. R., Science 144, 872 (1964).

16a. Lowy, J., and Hanson, J., J. Mol. Biol. 11, 293 (1965).

17. Metzner, P., Naturwissenschaften 11, 365 (1923).

17a. Overton, J., Eichholz, Α., and Crane, R. K. J. Cell Biol. 26, 693 (1965).

18. Pauling, L., and Corey, R. B., Nature 171, 59 (1953).

19. Preston, R. D., Endeavour 23, 153 (1964).

20. Rose, G. G., J. Roy. Microscop. Soc. 83, 97 (1964).

21. Rose, G. G., Cancer Res. 24, 1159 (1964).

21a. Weiss, P., J. Cellular and Comp. Physiol. 49, Suppl. 1, 105 (1957).

22. Yasuzumi, G., Miyao, G., Yamamoto, Y., and Yokoyama, J., Chromosoma 4, 359 (1951).

Ábra

FIG 1.  T h e "spiral of Archimedes," an old water pump.
FIG. 2 a. Protein helices of the second order of keratin.  ( F r o m Pauling and Corey  [ 1 8 ]
FIG. 10. The Umschnappen at point U (Fig. 10a) of a helix showing two  different pitches (p and  P ) leads to a "negative" intertwining (Figs
FIG. 11. The existence of a superhelix (Fig. 11a) is dependent on the me- me-chanical tension distributed in a definite length of the superhelix
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