Also published as: Biological Bulletin 159 (1980): 459-460Last year we reported on time-of-transit experiments in which magnetically
orienting bacteria crossed a 1-mm stretch in the direction of a uniform
magnetic field. The bacteria were found to behave as tiny self-propelled
compass needles subject both to magnetic field alignment and to the randomizing
effect of thermal agitation. In strong fields, magnetic bacteria are
held in tight aligment; in weaker fields, their swimming paths meander more
and transit times are greater. Paul Langevin derived an expression for the distribution of orientation in
an ensemble of free-moving dipole particles as a function of ambient field
strength. His theory becomes applicable to our experiments when bacterial
migration is analyzed as a sequence of short steps during each of which the
cell swims in a direction randomly selected from the Langevin distribution .
The duration of each step, Δt, is actually a time constant of the cell's loss
of directionality due to thermal agitation. By thus treating the migration
as a process of random walk with drift, we are able to predict the mean and
variance of the time of transit across a 1-mm stretch.Prepared for the Office of Naval Research under Contract
N00014-79-C-0071

Gilson, Michael

Kalmijn, Adrianus J.

Woods Hole Open Access Server

,, -,.,., [J ::r ,.,., - U") ~ [J :!:_o :::a_o m-~ r-'l -Cl ,.,., Cl -Cl WHOI -81-32 STATISTICAL MECHANICS OF GEOMAGNETI C ORIENTATION IN SEDI MENT BACTERIA by Michael K. Gi lson and Ad . J . Kalmi jn WOODS HOLE OCEANOGRAPHIC INSTITUTION Woods Hole , Mass achusett s 0254 3 Ap ril 1981 TECHNICAL REPORT Prepared for the Office of Naval Research under Contract N00014-?9- C-00?1. Reproduction in whole or in part is permitted for any pur-pose of the United States Government. In citing this report in a bibliography~ the reference given should be to: The Biological Bulletin 159(2): 459-460 (October 1980). Approved for public release; distribution unlimited. Approved for Di st ri buti on: George D. Gri ce, Chairman Depart ment of Biology ,.. Reprinted from The Biological Bulletin, Vol. 159, No. 2, pp. 459-460, October 1980 Printed in U. S. A. Statistical 1necha.nics of geomagnetic orientation in sediment bacteria. MrcHAEL K. GILSON AND Ao. J. KALl\IIJN. Last year we reported on time-of-transit experiments in which magnetically orienting bacteria crossed a 1-mm stretch in the direction of a uniform magnetic field. The bacteria were found to behave as tiny self-propelled compass needles subject both to magnetic field alignment and to the randomizing effect of thermal agitation. In strong fi elds, magnetic bacteria are held in tight alignment ; in weaker fields, thei r swimming paths meander more and transit times arc g reater. Paul Langevin derived an expression for the distribution of orientation in an ensemble of free-moving dipole particles as a function of ambient field strength. His theory becomes applicable to our experiments when bacterial migration is analyzed as a sequence of short steps during each of which the cell swims in a direction randomly selected from the Langevin distribution. The duration of each step. ~t. is actually a time constant of the cell's loss of directionality due to thermal agitation. By thus treating the migration as a process of random walk with drift, we are able to predict the mean and variance of the time of transit across a 1-mm stretch. The behavior of the model depends on three parameters: the randomization time .:lt, the cell's intrinsic dipole moment m, and the speed of propulsion Vo. We use nonlinear regression analysis to estimate these parameters and to fit the behavior of the model to that of the bacteria. We also determine the goodness of fi t of the model in its enti rety, and the approximate confidence limits of the parameter estimates. The estimated ran-domization times are in accord with preliminary calculations of rotational diffusion rates. The dipole strengths agree well with those expected on the basis of the number and size range of the bacteria's intracellular magnetite crystals. Our values are slightly lower due to the inevitable impurities and imperfections in alignment of the crystals, and to additional agitation resulting from swimming movements. In short, the dipole moments direct the bacteria magnetically despite thermal agitation and swimming noise. As statistical mechanics suffice to expla in the orientation of magnetic bacteria, there is no need to invoke an active orientation mechanism. ( Kalmij n's project on electric and magnetic detection operates under the auspices of the Office of Naval Research, Oceanic Biology Program, r\00014-79-C-0071. ) MANDATORY DISTRIBUTION LIST FOR UNCLASSIFIED TECHNICAL REPORTS, REPRINTS, AND FINAL REPORTS PUBLISHED BY OCEANOGRAPHIC CONTRACTORS OF THE OCEAN SCIENCE AND TECHNOLOGY DIVISION OF THE OFFICE OF NAVAL RESEARCH (REVISED NOVEMBER 1978) Deputy Under Secretary of Defense (Research and Advanced Technology) Military Assistant for Environmental Science Room 3Dl29 Washington, D.C. 20301 Office of Naval Research 800 North Quincy Street Arlington, VA 22217 3 ATTN: Code· 483 1 ATTN : Code 460 2 ATTN: 102B CDR J. C. Harlett, (USN) ONR Representative Woods Hole Oceanographic Inst. Woods Hole, MA 02543 Commanding Officer Naval Research Laboratory Washington, D.C. 20375 6 ATTN: Library, Code 2627 12 Defense Documentation Center Came ron Station Alexandria, VA 22314 ATTN: DCA Commander Naval Oceanographic Office NSTL Station Bay St . Louis, MS 39522 1 ATTN: Code 8100 1 ATTN: Code 6000 1 ATTN: Code 3300 NO DC/NOAA Code D781 Wisconsin Avenue, N.W. Washington, D.C . 20235 UN CLASS I FlED 4/81 SECURITY C LASSIFICATION OF THIS PAGE ( When Data Entered) REPORT DOCUMENT AT ION PAGE READ INSTRUCTIONS BEFORE COMPLETING FORM 1. REPORT NUMBER r· GOVT ACCESSION NO. 3 . RECIPIENT'S CATALOG NUMBER WHOI-81-32 4 . TITLE (and Subtitle) 5 . ·TYP E OF REPORT & PERIOD COVERED STATISTICAL MECHANICS OF GEOMAGNETIC ORIENTATION Technical IN SEDIMENT BACTERIA 6 . PERFORMING ORG. REPORT NUMBER 7 . AU TH O R(a) 8 . CONTRACT OR GRANT NUMBER(a) Michae l K. Gilson and Ad J. Kalmijn N00014-79-C-007l 9 . PERFORMING ORGAN IZ AT I ON NAME AN D ADDRESS 10. PROG RAM ELEMENT. PROJECT, TASK AREA & WORK UNIT NUMBERS Woods Hole Oceanographic Institution Woods Hole, Massachusetts 02543 11. CONTROLLING OFFI CE NAME AND ADDRESS 12. REPO RT D ATE NORDA/National Space Technology Laboratory Aoril 1981 Bay St. Louis , MS 39529 13. NUMBER OF PAGES 14. MONITORING AGENCY N AME 6 ADDRESS(II dllferent /tom ControlllnQ 0//lce) 15. SECURITY CLASS. (of thla report) Unclassified 15a. DECLASSIFICATION/ DOWNGRADING SCHEDULE 16. DI STRIBUTION STATEM.ENT (o f thl e Report) Approved for public release; distribution unlimited. 17. D ISTRIBUTION STATEMENT (o f the abattact entered In Bloclc ::10, II dllfetent /tom Repott) 18. SUPPLEMENTARY NOTES Reprinted from: The Biological Bulletin 159(2} : 459-460 (October 1980). 19. KEY WORDS (Continue on reverae aida II neceeeary and Identity by blocl< nUI11bet) 1. Statistical mechanics 2. Geomagnetic orientation 3. Sediment bacteria 20. ABSTR AC T (Continue on reveree el de II neceeeary and Identity by blocl< nUI11bet) Last year we reported on time-of-transit experiments in which magnetic-ally orienting bacteria crossed a 1-mm stretch in the direction of a uni form magnetic field. The bacteria were found to behave as tiny self-propelled compass needles subject both to magnetic field ali gnment and to the randomiz-ing effect of thermal agitation. In strong fields, magnetic bacteria are held i n tight aligment; in weaker fields , their swi mmi ng paths meander more and transit times are greater. DO FORM 1 J AN 73 1473 E DITI ON OF 1 NOV 611 I S OBSOLETE S;N 0 102·014•660 1 1 (continued on back) UNCLASSIFIE D 4/81 SECURITY CLASSIFICATION OF THIS PAGII!: (""an Data .nteted) UNCLASSIFIED ~ "-C.URITY CLASSIFICATION OF THIS PAGE(When Data Entered) 20 . . Paul Langevin derived an expression for the distribution of orientation in an ensemble of free-moving dipole particles as a function of ambient field strength. His theory becomes applicable to our experiments when bacterial migration is analyzed as a sequence of short steps during each of which the cell swims in a direction randomly selected from the Langevin distribution . The duration of each step, bt, is actually a time constant of the cell •s loss of directionality due to thermal agitation. By thus treating the migration as a process of random walk with drift, we are able to predict the mean and variance of the time of transit across a 1-mm stretch. UNCLASSIFIED SECURITY CLASSI .. ICATION 0 .. THIS PAGE(W'Jien D a ta Entered) STATISTICAL MECHANICS OF GEOMAGNETIC ORIENTATION IN SEDIMENT BACTERIA by Michael K. G11son and Ad. J. Kalmijn. April 1981. Prepared for the Office of Naval Research under Contract N00014-79-C-0071. Last year we reported on time-of-transit experiments in >ol! ich magntically orienting bacteria crossed a 1- mm stretch in the direction of a uniform magnetic field. The bacteria were found to behave as tiny se lf-propelled compass needles subj ect both to magnetic field alignment and to the randomiz-ing •ffect on thermal agitation. In strong fi elds, magnet-ic ba<terh are held in tight alignment; in weaker fi elds , their swimming paths meander more and transit times are greater. Paul Langevin derived an expression for the dis-tribution of orientation in an ensemble of free-moving di-pole particles as a function of ambient field strength. His theory becomes applicable to our experiments when bac-terial migration is analyzed as a sequence of s hort steps during each of which the cell swims In a di rection randomly select ed from the Langevin distribution. The duration of each step. At, 1s actually a time constant of the cel l's loss of di rectionality due to thermal agitation. By thus treating the migration as a process of random walk with drift, we are able t o predl ct t he mean and variance of the titre of t ransit across a 1-rrm stretch . Institut ion STATISTICAL MECHAN ICS OF GEOMAGNETIC ORIENTATION IN SEDIMENT BACTERIA by Michael K. G11son and Ad. J. Kalmijn. Apr11 1981. Prepared for the Office of Naval Research under Contrac t N00014-79-C-0071. Last year we reported on tfiTI!-of- transit experiments in >ol!lch magntlcally orienting bacteria crossed a 1-mm stretch in the direction of a uniform magnetic f ield. The bacter u were found to behave as tiny self-propelled compass needles subject both to magnetic field aligrvnent and to the randomiz-ing •ffect on thermal agitation. In strong fi el ds, magnet-Ic ba<terla are held in tight alignment; In weaker fields, thei r swimming paths meander more and t ransit times are great e r. Paul langevfn derived an expression for the dis -tribution of orientation In an ensemble of free-moving di -pole particles as a function of ambient field strength. HIs theory becomes applicable to our experiments when bac-terial migration is analyzed as a sequence of short steps during each of wh ich the cell swims In a direction randomly selected from the Langevin distribution. The duration of each step, at, Is actually a time constant of the cell's loss of directionality due to thermal agitation. By thus treating the mig ration as a process of random walk with dri ft, we are able to predict the mean and variance of the time of transit across a 1-mm stretch. L 1. 2. 3. I. II. I ll. 1. 2. 3. I. I I. Ill. Statistical mechanics Geomagnetic orientation Sediment bacteria Gflson , Michael K. Ka lmljn , Ad. J. N00014- 79-C-0071 This card Is UNCLASSIFIED Statistical mechanics Geomagnetic orientat i on Sediment bacteri a Gil son, Mi chae 1 K. Kalmljn , Ad. J . N00014- 7g-C-0071 This card is UNCLASSIFIED - ~od:::le Oceanographic Institution WHOI -81-32 STATISTICAL MECHANICS OF GEOMAGNETIC OR!EtiTATION I N SEDIMENT BACTER IA by Michae l K. Gi lson and Ad. J. Ka lmijn. April 1g91. Prepared fo r the Offi ce of Naval Research under Contract N00014-79-C-0071. last year we reported on time-of- t ransit experiments in which magntlcally or ienting bacter ia crossed a 1-mm stretch in the direction of a uniform magnetic field. The bacteri a were f ound to behave as t iny self- propelled compass needles subject both to magnetic field alignment and to the randomiz-i ng • ffect on thermal agitation. In strong fields, magnet-ic ba<teria are held in tight alfgnment; In weaker fields , their swimming paths meander more and transit times are greater. Paul Langevin derived an expression fo r the dis -t ribution of orientation in an ensemble of free-m::~ving di-pole pa r ticles as a function of ambient field strength. Hi s theory becomes applicable to our experiments when bac-terial migration fs analyzed as a sequence of short steps dur ing each of which the cell swims in a direction randomly sel ected from the Langevin distribution. The duration of each step , 6t. is actually a time constant of the cell's loss of directionality due to therma l agitation. By thus treat ing the mig rat ion as a process of random walk with drift , we are able t o predict the mean and variance of the t ime of t ransi t across a 1-nm stretch. STATI STI CAL MECHANICS OF GEOMAGNETIC OR IENTATION IN SEDIMENT BACTERIA by Michael K. G11son and Ad. J . Kalmijn . April 1981. Prepared for the Offi ce of Naval Research under Contract N0001 4-79-C-0071 . last year we reported on time-of-transit experiments in \oitlich magntically orienting bacteria crossed a 1-nrn str-et ch In the direction of a uniform magnetic field. The bacter ia were foun d to behave as tiny self- propelled compass needles subject both to magnetic field aligrvnent and to the randomiz-ing •ffect on thermal agitation. In strong fields, magnet-ic bac.:teria are held fn tight alignment; in weaker fields, the ir swiming paths meander 100re and transit times are greater . Paul Langevin derived an expression for t he dis-tribution of orientation fn an ensemble of free - moving di -pole particles as a function of ambient field strength. His theory becomes applicable to our experiments when bac-teri al migration is analyzed as a sequence of short steps during each of which the cell swims in a direction randomly selected from the Langevin distribution. The duration of each step , at, is actually a time constant of the cell's loss of directionality due to thermal agitation. By thus treat ing the mfgratfon as a process of random walk with drift, we are able to predict the mean and variance of the time of t ransit across a 1-nm stretch. 1. 2. 3. I. II. Il l. 1. 2. 3. I. ll . I ll. Stat istica l mechanics I Geomagnetic orientation I Sediment bacteria Gilson, Michael K. Kal mi j n, Ad. J. N00014-79-C-0071 This ca rd Is UNCLASSIF!EO St at istical mechanics Ge omagnetic orientation Sedimen t bacteria Gilson, Mi chae 1 K. Ka lmij n, Ad. J. N00014- 79-C-0071 This card Is UNCLASSIFIED J 

Statistical mechanics of geomagnetic orientation in sediment bacteria

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