Morphogenesis: Writhing, Folding, Close Packing, and Contractiont

Transcription

1 JOURNAL OF BACTERIOLOGY, July 1982, p Vol. 151, No /82/ $2./ Dynamics of Bacillus subtilis Helical Macrofiber Morphogenesis: Writhing, Folding, Close Packing, and Contractiont NEIL H. MENDELSON Department of Cellular and Developmental Biology and Graduate Committee on Genetics, University of Arizona, Tucson, Arizona Received 21 August 198/Accepted 15 March 1982 Helical Bacillus subtilis macrofibers are highly ordered structures consisting of individual cells packed in a geometry remarkably similar to that found in helically twisted yarns (G. A. Carnaby, in J. W. S. Hearle et al., ed., The Mechanics of Flexible Fibre Assemblies, p , 198; N. H. Mendelson, Proc. Natl. Acad. Sci. U.S.A. 75: , 1978). The growth and formation of macrofibers were studied with time-lapse microscopy methods. The basic growth mode consisted of fiber elongation, folding, and the helical wrapping together of the folded portion into a tight helical fiber. This sequence was reiterated at both ends of the structure, resulting in terminal loops. Macrofiber growth was accompanied by the helical turning of the structure along its long axis. Right-handed structures turned clockwise and left-handed ones turned counterclockwise when viewed along the length of a fiber looking toward a loop end. Helical turning forced the individual cellular filaments into a close-packing arrangement during growth. Tension was evident within the structures and they writhed as they elongated. Tension was relieved by folding, which occurred when writhing became so violent that the structure touched itself, forming a loop. When the multistranded structure produced by repeated folding cycles became too rigid for additional folding, the morphogenesis of a ball-like structure began. The dynamics of helical macrofiber formation are interpreted in terms of stress-strain deformations. In view of the similarities between macrofiber structures and those found in multifilament yarns and cables, the physics of helical macrofiber structure and also growth may be suitable for analysis developed in these fields concerning the mechanics of flexible fiber assemblies (C. P. Buckley; J. W. S. Hearle; and J. J. Thwaites, in J. W. S. Hearle et al., ed., The Mechanics of Flexible Fibre Assemblies, p. 1-97, 198). Bacillus subtilis macrofibers consist of highly ordered arrays of long, division-suppressed cell filaments arranged in a helical fashion. Their basic geometry is similar to that found in helically twisted multifilament yarns (2, 9). Bacterial macrofibers are produced by culturing low concentrations of cells under conditions that apparently lead to a reduction in autolytic enzyme activity. White threadlike structures, several millimeters in length, eventually arise, and because they are readily viewed with the naked eye, they have been termed macrofibers. The helical structure of macrofibers has been interpreted as a reflection of the helical organization of the individual cells that comprise the macrofiber (9). Thus, macrofibers provide an amplified view of individual cells and the study of macrofiber growth provides information about the t This paper is dedicated to the memory of my mother, Rose Kutner Mendelson, growth of individual cells, information that otherwise might be impossible to obtain. This communication is concerned with studies of macrofiber growth dynamics and illustrates the usefulness of the macrofiber system in studying aspects of the physics of cell growth. Helical macrofibers or their equivalent are not found solely in mutants of B. subtilis. Forty years ago publications described similar structures in related bacilli (5, 11). More recently, helical macrofibers have been found in cultures of "wild-type" bacilli grown at very low cell densities (14) and in strains of lactobacilli used in commercial cheese and yogurt production (V. Bottazzi et al., personal communication). The helical principle upon which macrofibers are built is probably widespread in the bacterial world. We have simply exploited this aspect of cell growth to provide a new system suitable for the study of growth by new approaches. Downloaded from on June 13, 218 by guest 438

2 VOL. 151, 1982 MATERIALS AND METHODS The techniques used to culture macrofibers have been previously described (9). Fluid TB medium containing 2,ug each of uracil and methionine per ml was utilized (8). Derivates of B. subtilis strain B1S were studied (8, 9). Strain 63SB was obtained after autolysis of a B1S macrofiber culture. A portion of the autolyzed culture was transferred to fresh TB medium. After incubation at 2 C, the newly produced macrostructures were isolated and cloned. Selection was for the most organized structures that persisted for the longest period when incubated in the usual manner at 2 C. Strain 63SB was obtained from one of these sublines. In comparison to the parent strain B1S, strain 63SB retains a highly ordered helical macrofiber structure for several days beyond the time when cell division resumes and the structure of B1S macrofibers undergoes decay. The autolytic enzymes have not, however, been examined directly in either strain. Strains BlS and 63SB both produce only right-handed helical macrofibers when cultured in the usual manner. Time-lapse films were produced by culturing cells in 5 to 1 ml of fluid medium contained in a plastic petri dish (1 by 15 mm) on the stage of a Nikon inverted microscope. The microscope was positioned so that its photo tube was aligned with a Wild cinetube focusing device that was attached to a Bolex 16-mm movie camera. A motorized device attached to the camera drove the film advance and shutter release mechanisms. An electronic rate controller was used to maintain a 6-s interval between frames and an exposure of.15 s per frame (Lafayette Instrument Co., Lafayette, Ind.). The entire device was isolated from vibration in a manner to be described elsewhere. All of the instrumentation was maintained at 22 C. An optical bench was constructed that enables the image from a stop-action 16-mm film projector to be placed via a front surface mirror onto a horizontal surface. A Numonics graphic calculator (Numonics Corp., Lansdale, Pa.) was used to transfer contour length data from the film images to a North Star Horizon II microcomputer (North Star Computers Inc., Berkeley, Calif.). Because of the usefulness of this system for the study of cell growth in large fluid cultures, a separate publication will be prepared describing both the system used to produce films and that used for their analysis (Mendelson, manuscript in preparation). Some of the data described here were derived from a film sequence that is available through the University of Arizona Film Library. To describe the complex dynamics of helical macrofiber morphogenesis, a number of terms not usually applied to microbial systems have been used in this manuscript. Some of these terms have been taken from those used in the description of analogous phenomena in macromolecules such as DNA. Others, however, are specific to the helical macrofiber system. To avoid having to repeat lengthy definitions in the text of this paper, terms and conventions used will be defined here. Helical macrofibers are multicellular structures consisting of division-suppressed cellular filaments tightly packed together into a long helically twisted fiber. Right- or left-handed helical macrofibers refer to the direction of twist followed by the individual cellular HELICAL STRUCTURE DYNAMICS 439 filaments packed into a helical macrofiber. In righthanded structures the cellular filaments twist in a clockwise manner when viewed from the end of a structure looking along the length of the macrofiber. Rotational turning about the long axis of a fiber means that the entire fiber turns along its length as would a speedometer cable. A right-handed helical macrofiber turns during growth in a clockwise direction when viewed from either end of the structure along the length of the macrofiber. Rotational turning of the fiber axis refers to the fact that the entire fiber changes its orientation in space, much as would a rotating speedometer cable if its ends were free and it could move about while still spinning. Writhing refers to whiplike motions that distort a macrofiber from its predominantly cylindrical shape into contorted shapes. In helical macrofibers, writhing motions cause waves to propagate along the length of the structure and eventually cause the fiber to touch itself. Folding of a macrofiber refers to the reduction in length caused by the touching of a fiber to itself as a result of violent writhing. An effective contact means that the touching of a macrofiber to itself leads to the helical wrapping together of the folded structure so created and to the formation of a new tightly wrapped structure. Loop closure is the term given to the reduction of a loop created by folding as a result of the helical wrapping together of the new structure. Immediately after a fold, an effective contact results in formation of a large loop that progressively becomes smaller and smaller as the structure wraps together from the point of contact toward the distal portion of the loop furthest from the point of effective contact. The rate of loop closure was determined by measuring the distance from the point of effective contact to the most distal portion of the loop at various times after the establishment of an effective contact. Unincorporated tail structures arise when a structure folds but wraps together only that portion of the fiber from the point of effective contact toward the loop and not the portion from the point of effective contact towards the ends of the previous structure. U-shaped and J-shaped folds refer to the relative proportions of a fiber that become involved in wrapping together after a fold. A U-shaped fold effectively reduces the length of a fiber in half. J-shaped folds occur toward the ends of a structure and may involve only a portion of the entire length of the fiber. To close a loop created by the fold of a fiber, the loop must rotate faster than the entire fiber rotating about its long axis. We refer to the basic fiber rotation not concerned with loop closure as shaft rotation. The contour length of fibers is measured from the center of a terminal loop to the distalmost point at the opposite end of the structure. Hexagonal close packing refers to the tightest clustering of circles to one another in which a minimum of space is occupied. Classically, this consists of a single circle surrounded by six evenly spaced circles, which in turn are each positioned so that they too are surrounded by six circles touching one another. The same geometry applies to the close packing of cylinders parallel to one another. Contraction refers to the shortening of a helical Downloaded from on June 13, 218 by guest

3 44 MENDELSON macrofiber. As a result of constraint of rotation about the long axis of the macrofiber, the structure is forced into a positive supercoil and consequently the two ends of the macrofiber are brought closer together much as is a coiled spring when allowed to relax after stretching. Negative twist is used here as in the case of supercoiled DNA. In macrofibers, negative twist amounts to forcing a structure in which an established helix hand is present and somewhat rigidly maintained to turn about its long axis in the opposite direction to effectively unwind the structure to some degree. Negative twist or its equivalent is required to drive folding in a manner that results in the same helix hand in the newly formed structure as was present in the initial structure. Folding threshold refers to an amount of energy required to force a macrostructure into an effective contact, hence folding. Folding generations refer to the sequential repetitions of folding cycles during the morphogenesis of an individual helical macrofiber. Each folding cycle results in a helical macrofiber with a given number of cellular filaments. The term helix order has been applied to represent each of the intermediate structures produced during the morphogenesis of a fiber. Thus, a new helix order of higher number is created by each folding cycle. RESULTS Although helical macrofiber cultures may be initiated from spores, individual cells, or multicellular fragments from large macrofibers, we routinely seeded 5-ml cultures at very low cell densities with macrofiber fragments. Depending upon strain and the size of the inoculum, a typical culture yielded 1 to 3 structures when incubated at 2 C for 8 to 24 h. The population of helical macrofibers consisted of structures of various lengths and widths. These variations correspond to macrofiber age and the particular route of morphogenesis followed by each fiber. The youngest fibers corresponding to the thinnest, and often the longest, in the population were transferred to fresh medium of sufficient volume to permit unrestricted motions during morphogenesis. Under the growth conditions used for microcinematography, structures interact therefore only with the fluid environment, the bottom of the petri dish, or one another. The primary interaction is with the viscous drag of the fluid environment. The young fibers selected for cinematography consisted of multistrand helical structures. As young fibers grew, they underwent complex movements that involved: (i) rotational turning about the long axis of the fiber; (ii) rotational turning of the fiber axis; (iii) writhing motions which contort the fiber into U- or J-shaped configurations; and (iv) folding events that serve to reduce the contour length of the fibers and increase their thickness. Some examples of J. BACTERIOL. these events are shown in Fig. 1. This sequence represents one folding generation that occurred at a late stage of fiber morphogenesis. Four folding generations were recorded before the time shown in frame. The entire film sequence is available for study as described in Materials and Methods. The reiteration of folding sequences serves to build large macrofibers. Although the basic folding geometry is always the same, there are a variety of folding topologies possible. Some of these are illustrated in Fig. 2, which represents the six-fold sequence from which Fig. 1 was taken. The initial structure shown above as a single line represents a young multistranded helical fiber of too few strands to permit resolution of the loop ends. The initial fold recorded was an uneven or J-shaped fold involving one end of the fiber. As the folded structure continued to grow, the loop created by the fold became smaller and smaller. At the same time the opposite end of the fiber also folded, resulting in a structure with loops at both ends. In this particular fiber, the two original ends of the starting fiber happened to meet after the second fold and to wrap themselves together to form a small protruding stalk that could be used as a landmark in subsequent folding generations. This is shown in the seventh diagram from the top as a cross toward the center of the structure. The third folding generation was also a J-shaped fold which served to position the protruding stalk to the newly created loop at the left of the figure. As this folding order was in the process of wrapping together, the fiber underwent its fourth-generation fold at the opposite end, this time in a manner so as to overlap the previously folded section (see line 9, Fig. 2). For purposes of simplification, the first two folding orders, which by this time had become completely tightened together into a single structure, are represented only as a single line. Notice that the overlapping fold serves to wrap together two sections of fiber that contain different numbers of strands. Fiber width, therefore, does not always double with each folding. Whenever a fiber folds unevenly (J-shaped folds) the previous tip of the fiber comes to lie along the shaft of the fiber. This tip may later become buried in the interior of the fiber as subsequent folds encompass the region of the fiber where the tip now resides. The third fold in Fig. 2 illustrates how a J-shaped fold positions the loop at the tip of a fiber so that it eventually becomes part of the fiber interior. As new helix orders wrap tightly into a compact structure, internal irregularities such as these buried loops cannot readily be detected on the surface of the fiber. Internal irregularities may function, however, like faults in a crystal as places of structur- Downloaded from on June 13, 218 by guest

4 VOL. 151, 1982 HELICAL STRUCTURE DYNAMICS /.._ J-" k I :4 5 6A, (N\E 7 8 I >r : Irlo.::kN',.../ FIG. 1. B. subtilis 63SB macrofiber formation. Time-lapse film sequence of a structure grown at 24 C. The initial structure shown in frame is a multistranded right-handed helix. Writhing configurations precede folding. Nucleation of the wrapping together of the next hierarchy of the helix occurs in frame 4. The loop created toward the left of the figure closes with subsequent wrapping together of the two arms of the hairpinlike structure. Five additional folding sequences were recorded subsequently in this clone. Exposure was.15 s per frame, and time-lapse interval between frames was 6 s. Bar = 1 mm. The entire sequence represents approximately 16 min in real time. al weakness and may influence the places where future folds occur. Not all J-shaped folds result in the internalization of loop ends, however. When, for example, the point of effective contact during folding involves not the very tip of a fiber touching back to the fiber shaft but rather a contact between a section of fiber some distance from the tip touching the shaft, the subsequent tightening together of the new helix order may proceed only from the point of contact toward the newly created loop, leaving the tails free. The protruding tail may itself later interact with the fiber to form a higher-order structure. These dynamics are illustrated in Fig. 1 and 2. The contour length of fibers during growth has been measured, and a representative sequence in which at least 1 folds occurred is shown in Fig. 3. Macrofibers increase in length at an exponential rate but periodically reduce their length by folding. The total reduction in length achieved by any given fold indicates whether the fold is even, uneven, or overlapping. Most of the folds shown in Fig. 3 are uneven or J-shaped.9, 5.'i. %..,.. A;..., *I, 155 1) folds, and consequently they reduce the fiber length to a value greater than half that at the time of folding. J-shaped folds frequently occur in pairs involving first one end of the fiber and then the other. This is not universal, however, as indicated in the legend to Fig. 3. Similarly, the total fiber length achieved at folding often, though not always, falls within a narrow range for a given strain and set of environmental conditions. Older fibers, those that have undergone many folding generations, enter a phase where the length at folding progressively decreases with additional folds. This stage marks the beginning of the transition from helical fiber to compact ball structure, and the fibers by this time consist of highly constrained multistranded structures. A series of experiments were performed in which the effects of growth inhibition by drugs on macrofiber dynamics were examined (Fig. 4). The addition of 1 [Lg of chloramphenicol per ml does not result in the immediate cessation of growth. When chloramphenicol is added during 4 Downloaded from on June 13, 218 by guest

5 442 MENDELSON loop closure after a fold (see Fig. 4), residual growth is sufficient to permit the completion of loop closure and the initiation of another folding cycle. The decrease in growth rate at the time of the second fold is accompanied by a great reduction in the rate of loop closure after the fold. The legend to Fig. 4 indicates that loop and shaft rotation rates are also reduced by inhibition of growth. Similar results are shown in Table 1, which summarizes a series of experiments involving the addition of chloramphenicol at various stages of the folding cycle. These data indicate that growth is necessary for macrofiber rotation and folding cycles to occur. The rotation that accompanies macrofiber growth may be used to drive various physical ~ ~ ~ ~ ~ ~ ~ ~ O processes (Fig. 5). When, during fiber growth, one end of a macrofiber encountered a second structure that happened to move into the vicinity of the first, an effective fiber-fiber interaction occurred which resulted in the contraction of both fibers and their folding into a compact balllike structure. The initial fiber whose rotation was blocked responded by the development of a positive supercoil. This is a fundamentally different geometry than that concerned with the normal folding cycle. Numerous other fiberfiber interactions have also been observed. Some of these serve to induce one of the interacting fibers to touch itself and thus initiate a fold of the normal folding cycle topology. The latter usually results from the interaction of a 2k NW~ ~~ rn r\low %,\1.V k.../ A.- N--:k dm e.q al. dc-.a N,Wor- -\-=/ J. BACTERIOL I I Downloaded from on June 13, 218 by guest -U' _,I FIG. 2. Folding pattern during macrofiber morphogenesis. Diagram drawn to scale from time-lapse film sequence of B. subtilis 63SB (right-handed helix) grown in fluid culture at 24 C. The initial structure shown at the top of the figure consisted of a young multistranded helical macrofiber. To simplify the diagram, the initial two folding sequences, when thoroughly wrapped together, are shown as a single line in the 9th structure from the top. Similarly, the 11th structure, shown as a single line, represents the completion of wrapping together after folds 3 and 4. Bar at left = 1. mm.

6 VOL. 151, 1982 HELICAL STRUCTURE DYNAMICS a 3- C 2- w -j w goiool U TIME (FRAMES X 1) FIG. 3. Contour length measurements of macrofiber growth. B. subtilis 63SB macrofiber grown in fluid at 24 C. Measurements were obtained from time-lapse film images, using a Numonics graphics calculator interfaced to a North Star Horizon II computer. Filming details are as in the legend to Fig. 1. Eleven folds are shown. Most of the folds are J rather than U configurations. If we designate the loop end created by the first fold as A, then the following J-folds occur in order near ends: B, B, A, B, A, A, then a U-fold. The remaining three folds involve complicated geometry and positive supercoiling. Note that the absolute fiber length achieved at the time of folding is fairly uniform over most of the folding sequence. The complicated last folds illustrate the reduction in length at time of folding characteristic of large multiple helix order fibers progressing toward the production of a ball structure. The entire sequence represents approximately 8.8 h in real time. young fiber with a larger structure. Several examples are found on the film described earlier that is available for study. The sequence represented in Fig. 5 is also present on this film. This sequence illustrates that the rules governing the conservation of angular momentum can drive a unique kind of contraction and folding of a multistrand helical system. This principle may be of use in a number of biological contexts. The combination of shaft rotation and loop rotation leads to the tightening together of the two fiber arms brought into contact by folding. As loop closure continues, the individual cellular strands that comprise the loop are squeezed into a tight single structure. Because all folding orders always follow the same helix hand, the individual cellular filaments can nestle together in a close-packed array that approximates hexagonal close packing. The exact form of the packing arrangement is complex and will be considered in detail elsewhere. Figure 6 illustrates the basic structure. In this cross section several previous orders are seen under an array of surface elements representing the most recent folding order. The helical nature of the macrofiber is evident in the progressive elliptical cross sections of cells lying closer to the surface which correspond to the changing surface pitch angles found in fibers of different diameters (9). The close-packed regions toward the center of the macrofiber illustrate that the wrapping together of folding orders obliterates the geometry of each order by virtue of compressing all of the cellular strands into new close associations. The dynamic nature of the system, however, means that there is no equilibrium structure, only a continuously changing one; hence, the packing imperfections noted are to be expected. DISCUSSION Helical macrofibers of B. subtilis provide a unique system for the study of dynamic structure and helical geometry. They are produced when cells are cultured under conditions of division suppression and consequent autolysin deficiency (4, 9, 12, 14). The strategy of growth leading to their formation involves length extension accompanied by rotation of the growing structure around its long axis, followed by repeated cycles of folding. Each fold reduces the length of the structure, and the subsequent wrapping together of the folded structure into a single fiber increases the number of cellular filaments in the fiber. The diameter of fibers is a function, therefore, of the number of folding cycles that have occurred in the fiber's history. Usually the frequency of folding as a function of time during growth is fairly constant; thus, we refer to fibers as either young or old on the basis of their diameter. Using microcinematography techniques, we have been able to document the details of macrofiber morphogenesis and have come to understand the static structures observed by light and electron microscopy in a new Downloaded from on June 13, 218 by guest

7 444 MENDELSON 4 +CAM 63SB ON TB) 22C ±CAM J. BACTERIOL. IL 3. o 1 o. 8 w - m ~ D~,, TME RAMES X 1) FIG. 4. Chloramphenicol inhibition of macrofiber dynamics. A B. subtilis 63SB macrofiber was cultured in the usual manner for microcinematography in fluid TB medium at 22 C. A 1-pLg/ml concentration (final) of chloramphenicol (CAM) was added at the time indicated by the arrow on the upper curve. Contour lengths were measured from film images as described in the text. The average rate of shaft rotation (per 18 turn) before addition of the drug was 16.3 frames. The average rate of loop rotation (per 18 turn) before addition of the drug was 11.5 frames. The average rate of shaft rotation during the initial 2 frames (after addition of the drug was 12.8 and 1.9 frames near the two ends of the fiber. The average rate of loop rotation during this period was 6.1 frames. One folding sequence is shown after the addition of chloramphenicol. After this fold, the average rate of shaft rotation was 33.7 frames, and the average rate of loop rotation was frames. The loop closure rates shown below represent a measurement of the linear distance from the farthest point on the newly formed terminal loop to the point where the loop joins the fiber shaft. perspective. We find that helical macrofibers are constantly in a state of change during growth. There is no true equilibrium structure. Instead, an interplay of forces created during growth governs the cellular organization present at any moment; to understand this organization, one must examine the rules of physics responsible for the particular geometry that macrofibers assume. The helical properties of macrofibers must reflect aspects of the organization of the cell surfaces and the manner in which surface growth takes place just as the helical properties of twisted multifilament yarns reflect the tension of the individual filaments introduced by mechanical twisting (6, 13). Previously, helical growth morphology was interpreted in terms of tension and the concomitant distortion of a basic cylinder (8). The cell surface was visualized as consisting of helically arranged elements, and growth was presumed to result in rotation in accordance with this pitch angle. The analysis of films presented in this communication contributes several additional facts to our overall understanding of the helical growth system. First, rotation around the long axis of the cell cylinder as previously predicted is documented. In macrofibers, two components of this rotation are revealed: rotation of the fiber shaft, and a more rapid rotation associated with the closure of loops created by folding. Using suitable landmarks such as projecting unincorporated cellular filaments or other visible irregularities along the macrofiber shaft, we have been able to observe Downloaded from on June 13, 218 by guest

8 VOL. 151, 1982 HELICAL STRUCTURE DYNAMICS 445 ZH o X o -4 a, CL -1 R --h 1-" -" C) 8 8 O O C 7- ( k 8 = > B n 4.. (D CD o" CD < _. ( ( CDcn B 3 t_ ~ (. * 'o "' (Q o - CD x t ( Lf cl3 ' gi~~~~~~~c O~ - CD o o C"o o o ~~~~~~r cns ~ o> a ( ( + -- (D 7 wj U.) Ij C - r C4 (A -_ k LA c,. 1 " WO - U.) CN-1-4 o - S. r_ r* I _,_- C4 c, I- s O1- ON w i -_ r. cn c) _ t - _ s \~tj -.J. ON W k _ O v-~\ I~ 3 ( CD CD n.6 la. c, =:, = B I - z o: It CA _e r m - n ' -o3 _ B la - _F. C- n -1 ' e. ' F : E3 Xl CD P: o _. OC 11 3 ow Cr Downloaded from on June 13, 218 by guest I - U.) 'I 1-4 II :a 3 i 1-" Z 4 _4 _ I4. -P o- oo -4 " I- r- I-- / _ - r r- - w

9 446 MENDELSON J. BACTERIOL. At.41* Is I. t ".. S rw 1_....: :..v. 4...'-..! m. i wlyt \ _~~~~~ I I * et,t. I1,.4 I/., a' Downloaded from FIG. 5. Fiber-fiber interaction sequence involving helical macrofibers of B. subtilis 63SB fluid grown at 24 C. Sequence begins at upper left. A ball structure is associated with one of the two interacting fibers. Contact of the thin distal end of the central fiber with the fiber located near the bottom of the frame occurs in frame 4, the third shown in this sequence. The block to rotation resulting from contact leads to a positive supercoil contraction of the central fiber. The lower fiber is also drawn and contracted into association with the central fiber. Eventually the ensemble forms a ball-like structure. Filming details are as in the legend to Fig. 4. Frame numbers shown =, 2, 4, 5, 7, 8, 85, 95, 1, 15, 11, 115, 117, 118, 119, 12, 125, 13, 14, 145, 15, 155, 165, 175. Bar = 2. mm. The entire sequence represents approximately 18 min in real time. on June 13, 218 by guest and quantitate the rate of shaft rotation with growth. The rate of rotation associated with loop closure has also been quantitated. The direction of rotation has been determined and found to depend upon the helix hand of the macrofibers. In right-handed structures, as discussed in this paper, the apparent direction of rotation as seen by an observer inside the fiber looking toward either end of the fiber is always clockwise. Lefthanded macrofibers appear to rotate in the opposite direction, i.e., counterclockwise. This means that in any given fiber all cells must have their surfaces organized in the same helix hand. Throughout the entire sequence of macrofiber morphogenesis from young to old fibers, during folding, loop closure, writhing, or any other geometrical contortions the fiber may undergo, the direction of rotation does not change. Only in the special case of helix hand inversion, not encountered during normal macrofiber morphogenesis, is this rule violated. Macrofiber rotation during growth serves to tighten the helical superstructure and force all cellular filaments into a close-packing arrange-

10 VOL. 1 51, HELICAL STRUCTURE DYNAMICS 447 t "144-ou. U D- Go * *.. S Downloaded from FIG. 6. Cellular organization of B. subtilis macrofibers. Sectioned perpendicular to the long axis of the fiber, the packing arrangements of individual cellular filaments are evident. Several domains represent arms of a folded structure that have not yet become completely amalgamated. Close packing is present in some regions but cellcell contacts are not frequent. The alignment of cells in shells is illustrated. Helical twist is responsible for the progressive elliptical cross section shapes found at greater distances from the center of the structure. Bar = 2,um. Methods of preparation and electron microscopy are as in reference 3. 4, on June 13, 218 by guest ment. Since all cellular filaments are of the same helix hand, they can be packed almost perfectly into a minimum space, that is, into a cylindrical space of minimum diameter to accommodate all filaments. The packing arrangement in macrofibers approximates hexagonal close packing. Three complicating factors are responsible for deviations from this ideal, however. (i) Helical twist distorts the individual cellular filaments, causing those furthest from the center to deviate progressively in their cross section geometry from a circle to an ellipse. (ii) The folding cycle strategy and the complexity of topologies that may be followed result in fibers that do not have the perfect numbers of strands required to fill shells according to hexagonal close packing geometry. The latter requires 1, 7, 19, 37, 61, etc., elements to form structures with completely filled shells. Unless these "perfect" numbers are present in the packing array, the outermost shell will have unoccupied spaces, and elements located in this shell need not pack as uniformly as those in the inner shells. Measurements of pitch angle as a function of macrofiber diameter

11 448 MENDELSON are affected by this geometrical situation. (iii) The dynamic motions that occur in macrofibers involve the sliding of individual cellular filaments along one another as well as the rotations of individual cellular filaments along their long axes. These motions produce deviations in packing arrangements and hence prevent the attainment of any idealized static structure. Nevertheless, the structure obtained is remarkably similar to that found in helically twisted multifilament yarns. Compare, for example, Fig. 6 in this communication with Fig. 1 in reference 2. The development of tension in macrofibers is an integral component of the folding cycle. As fiber rotation forces tightening of the structure, tension builds and writhing occurs. This is true regardless of the age or helix hand of the fiber and apparently reflects a situation at the individual cellular level. As fibers progress through a series of folds, the number of cellular filaments packed parallel to one another increases, and writhing motions appear to diminish proportionally. This reduction in motion is likely to reflect an increase in torsional stiffness of the structures resulting from the increase in the number of cellular filaments in the array. Eventually fibers reach a point where they are unable to undergo further folds. This marks the initiation of ballstructure formation and apparently reflects the point when the energy available to drive folding cannot overcome the stiffness of the macrofiber. We are interested in learning how tension is introduced during growth into macrofibers at the level of individual cells. A new model of helical cell surface growth in which the pitch angle of strands in the cell surface reorients during growth is discussed elsewhere (1). This new model provides a way in which cells may use stress that builds in the cell surface during growth to time events in the cell cycle. Tension in macrofibers and the processes that tension drives (writhing, folding, quasi-close packing, and the contraction described after fiber-fiber interactions) may eventually be traced to the development of stress in the individual cell surfaces. The details of how such stress arises are not yet thoroughly understood; however, we have reason to believe that cell wall peptidoglycan is involved in retention of the helical deformation. This belief is based upon recent observations that exogenous addition of lysozyme or autolytic enzymes to helical macrofibers results in specific relaxation motions. Details of these findings will be documented in another publication (N. H. Mendelson, M. M. Briehl, and D. Favre, manuscript in preparation). The exact moment of macrofiber folding rests to some extent upon the time at which an effective contact occurs. Writhing distortions are responsible for bringing the fiber into posi- J. BACTERIOL. tion where it may touch itself, but the exact time when this happens and the exact places where contact is made are random. The pattern of folding in terms of the times when progressive folds occur in individual fibers reflects this randomness to some degree, but there are nevertheless some aspects of regularity in these data and also in the topology of folding. The length to which macrofibers grow before folding is not random but rather appears to center around some ideal length throughout most of the fiber folding cycles. Fibers approximately double their length between folds. This suggests that all of the cells in a fiber must undergo about one cell cycle from fold to fold. Folding appears, therefore, to be a cell cycle event and may be driven when this event is achieved by a critical number of cells in the macrofiber. Folding is the macrofiber's equivalent of division and, for reasons discussed below, it is not unreasonable to assume that the cell cycle event responsible for folding is indeed cell septation. That folding always results in the wrapping together of a new helix order in the same helix hand as all previous orders means that writhing and folding are neither random processes driven by tension in the growing structure nor the result of simply overwinding the helical structure. Only the equivalent of negative twist, as achieved by unwinding the structure, can drive writhing, which leads always to the kind of folding that macrofibers undergo. Since we never detect any unwinding of either the macrofiber shaft or its terminal loops, negative twist must be introduced by events below the resolution of the microscopy system being used. It has been suggested, therefore, that negative twist arises when cell septa are produced within macrofibers (1). If so, then at every place where a septum is constructed, a small amount of negative twist is introduced. The total amount of negative twist in a macrofiber would reflect, therefore, the number of septa present. It is possible that a folding threshold exists that consists of some required amount of negative twist representing the amount of energy needed to force a macrofiber into a writhing distortion that results in an effective contact and folding. The folding threshold would then correspond to the attainment of a certain number of septa. We plan to test this hypothesis through the construction of appropriate mutants in which the production of septa may be blocked conditionally. Such mutants should have no way to generate negative twist and consequently to use the tension developed during growth to drive folding. Additional insight to the folding mechanism is being sought in studies of the helix hand inversion and also in studies concerning the action of lysozyme and other enzymes that cleave wall polymers. Downloaded from on June 13, 218 by guest

12 VOL. 1 51, B. subtilis helical macrofibers provide a new model system in which to explore the physical basis of cell growth, morphogenesis, and regulation. The physical writhing motions that macrofibers undergo and the fact that negative twist must drive folding suggest that the macrofiber system obeys some of the general rules governing helical systems previously studied. Some of the tension introduced by growth of macrofibers is apparently relieved by writhing and by folding. The energy associated with negative twist is apparently used for loop closure after a fold and for at least the initial stages of forcing the cellular strands into close packing. The helical deformation of cell shape is maintained by peptidoglycan but the source of stress responsible for the deformation that arises during growth has not yet been identified. We are currently studying the effects of selective cleavage of peptidoglycan in intact macrofibers, using specific hydrolytic enzymes to determine the relationship of peptidoglycan structure to helical growth dynamics and helical structure. In addition, we plan to obtain actual physical measurements of the magnitude offorces at play in the macrofiber system and to relate these to events that go on in the individual cells. The present communication illustrates the manner in which macrofibers may be used to probe cellular events that cannot readily be examined in individual cells. Although this paper focuses on the dynamic properties of helical macrofibers and suggests that these properties reflect events that go on in the individual cells that comprise the macrofibers, the relationship of helical growth to that of normal cells is not discussed. Elsewhere in two theoretical papers (8, 1), I have suggested how normal growth may utilize principles of helical geometry during growth and have developed a theory concerning cell cycle clocks that is based upon these rules. More recently, I have found that the helix clock theory may be applied in a simple and direct manner to provide a mechanism for the segregation of daughter genomes during the cell cycle. A detailed discussion of these concepts will be the subject of a review article. All of these models show that a basic plan of helical growth is compatible with the manner in which normal cells grow and with many facts known about the bacterial cell cycle. These considerations coupled with the fact that wild-type strains of B. subtilis grown under certain conditions produce helical macrofibers indicate that the helical growth system is not purely an aberrant or mutant growth form but rather is a system that reveals subtle aspects of normal growth not readily apparent in the study of conventional cultures. Experimental proof of HELICAL STRUCTURE DYNAMICS 449 this contention is currently being sought by an analysis of the relationship of cell cycle events to helical growth and by molecular studies of the cell surface components responsible for cell shape and growth regulation. ACKNOWLEDGMENTS I am grateful to Roger M. Cole and T. J. Popkin for help with electron microscopy and to D. Karamata for assistance in my initial attempts to determine macrofiber internal structure by electron microscopy. S. L. Keener provided excellent technical assistance. I am indebted to J.. Kessler for bringing to my attention the engineering and physics work being done on flexible fiber assemblies. I appreciate the support of a Public Health Service research grant from the National Institute of General Medical Sciences and a University of Arizona Biomedical Research Support Grant. LITERATURE CITED 1. Buckley, C. P Review of the mechanical properties of fibers, p In J. W. S. Hearle, J. J. Thwaites, and J. Amirbayat (ed.), The mechanics of flexible fibre assemblies. Sijthoff & Noordhoff, Germantown, Md. 2. Carnaby, G. A The compression of fibrous assemblies, with applications to yarn mechanics, p In J. W. S. Hearle, J. J. Thwaites, and J. Amirbayat (ed.), The mechanics of flexible fibre assemblies. Sijthoff & Noordhoff, Germantown, Md. 3. Cole, R. M., T. J. Popkin, R. J. Boylan, and N. H. Mendelson Ultrastructure of a temperature-sensitive rod- mutant of Bacillus subtilis. J. Bacteriol. 13: Fein, J. 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Biol. 94: Roberts, J. L Evidence of a rotational growth factor in Bacillus mycoides. Science 87: Rogers, H. J., and P. F. Thurman Double mutants of Bacillus subtilis growing as helices. J. Bacteriol. 133: Thwaites, J. J A continuum model for yarn mechanics, p In J. W. S. Hearle, J. J. Thwaites, and J. Amirbayat (ed.), The mechanics of flexible fibre assemblies. Sijthoff & Noordhoff, Germantown, Md. 14. Zaritski, A. H., and R. M. Macnab Effects of lipophilic cations on motility and other physiological properties of Bacillus subtilis. J Bacteriol. 147: Downloaded from on June 13, 218 by guest