862:
973:
45:
1599:
999:
1066:). Vourc’h et al. (2020) showed that this biased motility stems from the averaged displacements during run periods, which is no longer random (as it was in the uniform illumination). They showed the bias is the result of the number of runs, which is greater toward the light source, and not of longer runs in this direction. Brought together, these results suggest distinct pathways for the recognition of light intensity and light direction in this prokaryotic microorganism. This effect can be used in the active control of bacterial flows.
1205:
885:
1594:{\displaystyle {\frac {\partial f(\mathbf {r} ,{\hat {\mathbf {s} }},t)}{\partial t}}+v_{0}\,{\hat {\mathbf {s} }}\cdot \nabla f(\mathbf {r} ,{\hat {\mathbf {s} }},t)=\xi ^{-1}\nabla \cdot (\nabla V(\mathbf {r} )f(\mathbf {r} ,{\hat {\mathbf {s} }},t))-\alpha f(\mathbf {r} ,{\hat {\mathbf {s} }},t)+{\frac {\alpha }{\Omega _{d}}}\int g({\hat {\mathbf {s} }}-{\hat {\mathbf {s} }}')f(\mathbf {r} ,{\hat {\mathbf {s} }}',t)d{\hat {\mathbf {s} }}'}
606:
900:
3441:
2421:
2350:
2370:
Cooper, Kendal G.; Chong, Audrey; Kari, Laszlo; Jeffrey, Brendan; Starr, Tregei; Martens, Craig; McClurg, Molly; Posada, Victoria R.; Laughlin, Richard C.; Whitfield-Cargile, Canaan; Garry Adams, L.; Bryan, Laura K.; Little, Sara V.; Krath, Mary; Lawhon, Sara D.; Steele-Mortimer, Olivia (2021-01-13).
915:
In a uniform medium, run-and-tumble trajectories appear as a sequence of nearly straight segments interspersed by erratic reorientation events, during which the bacterium remains stationary. The straight segments correspond to the runs, and the reorientation events correspond to the tumbles. Because
1047:
being in the run state randomly in all directions. This feature, however, vanishes after a typical characteristic time of about one hour, when the initial probability is recovered. These results were well described by a mathematical model based on a linear response theory proposed by Vourc’h et al.
852:
that pushes the cell in a forward run, parallel to the long axis of the cell. Clockwise rotation disassembles the bundle and the cell rotates randomly (tumbling). After the tumbling event, straight swimming is recovered in a new direction. That is, counterclockwise rotation results in steady motion
714:
pathways) for the bacterium to move in a directed manner along gradients and reach more favorable conditions for life. The direction of flagellar rotation is controlled by the type of molecules detected by the receptors on the surface of the cell: in the presence of an attractant gradient, the rate
809:
that controls the direction of the flagellar motor. This can result in a chemotaxis, where attractant gradients extend the length of time flagellar motors rotate CCW, resulting in more smooth swimming in a favourable direction, while repellents cause an increase of CW rotations, resulting in more
657:
and other microscopic agents. It consists of an alternating sequence of "runs" and "tumbles": during a run, the agent propels itself in a fixed (or slowly varying) direction, and during a tumble, it remains stationary while it reorients itself in preparation for the next run.
935:
in a uniform aqueous medium, the mean turn angle is about 70 degrees, with a relatively broad distribution. In more complex environments, the tumbling distribution and run duration may depend on the agent's local environment, which allows for goal-oriented navigation
1089:. Contrary to the run phase that can extend from a fraction of a second to several minutes, the tumble lasts only a fraction of a second. The tumbling phase is a clockwise rotation that allows the cell to change the motility direction of the next run.
1961:
2856:
Choi, Jong-Soon; Chung, Young-Ho; Moon, Yoon-Jung; Kim, Changhoon; Watanabe, Masakatsu; Song, Pill-Soon; Joe, Cheol-O; Bogorad, Lawrence; Park, Young Mok (1999). "Photomovement of the
Gliding Cyanobacterium Synechocystis sp. PCC 6803".
2059:
877:
which project in all directions. Clockwise (CW) rotation of flagellar motors results in random re-orientation for the bacterium, but counter-clockwise (CCW) rotation produces approximate straight-line motion.
3798:
Rosser, Gabriel; Fletcher, Alexander G.; Wilkinson, David A.; de Beyer, Jennifer A.; Yates, Christian A.; Armitage, Judith P.; Maini, Philip K.; Baker, Ruth E. (2013-10-24). Coombs, Daniel (ed.).
2661:
Schuergers, Nils; Lenn, Tchern; Kampmann, Ronald; Meissner, Markus V; Esteves, Tiago; Temerinac-Ott, Maja; Korvink, Jan G; Lowe, Alan R; Mullineaux, Conrad W; Wilde, Annegret (2016-02-09).
637:
3743:
Polin, Marco; Tuval, Idan; Drescher, Knut; Gollub, J. P.; Goldstein, Raymond E. (2009-07-23). "ChlamydomonasSwims with Two "Gears" in a
Eukaryotic Version of Run-and-Tumble Locomotion".
2088:
In real-world systems, more complex models may be required. In such cases, specialized analysis methods have been developed to infer model parameters from experimental trajectory data.
1069:
It has also been observed that very strong local illumination inactivates the motility apparatus. Increasing the light intensity of more than ~475 ÎĽmol m s reverses the direction of
853:
and clockwise rotation in tumbling; counterclockwise rotation in a given direction is maintained longer in the presence of molecules of interest (like sugars or aminoacids).
2124: – biologically propelled motion through a liquid medium; in contrast of passive swimming (floating); involves the expenditure of energy to travel to a desired location
1782:
861:
940:). For example, a tumbling distribution that depends on a chemical gradient can guide bacteria toward a food source or away from a repellant, a behavior referred to as
1010:
cyanobacterium. During run the cell moves quickly from one point to another, while during tumble it remains constrained in a given area and tends to change directions.
669:, which may depend on the organism's local environment (e.g., chemical gradients). The duration of a run is usually random in the same sense. An example is wild-type
1114:
Theoretically and computationally, run-and-tumble motion can be modeled as a stochastic process. One of the simplest models is based on the following assumptions:
706:
and—irrespective of species and type of flagellation—they have only two modes of operation: clockwise or counterclockwise rotation. Bacterial swimming is used in
4020:
Villa-Torrealba, Andrea; Chávez-Raby, Cristóbal; de Castro, Pablo; Soto, Rodrigo (2020-06-22). "Run-and-tumble bacteria slowly approaching the diffusive regime".
1972:
3920:
3861:
Seyrich, Maximilian; Alirezaeizanjani, Zahra; Beta, Carsten; Stark, Holger (2018-10-25). "Statistical parameter inference of bacterial swimming strategies".
3669:
Krell, Tino; Lacal, JesĂşs; Muñoz-MartĂnez, Francisco; Reyes-Darias, JosĂ© Antonio; Cadirci, Bilge Hilal; GarcĂa-Fontana, Cristina; Ramos, Juan Luis (2011).
3533:
2373:"Regulatory protein HilD stimulates Salmonella Typhimurium invasiveness by promoting smooth swimming via the methyl-accepting chemotaxis protein McpC"
623:
931:
In contrast with the more gradual effect of rotational diffusion, the change in orientation (turn angle) during a tumble is large; for an isolated
4079:
3603:
3461:
924:, so the runs can be approximated as constant velocity motion. The deviation of real-world runs from straight lines is usually attributed to
972:
2608:
Vourc'h, Thomas; Léopoldès, Julien; Peerhossaini, Hassan (2020-02-03). "Light
Control of the Diffusion Coefficient of Active Fluids".
1095:
is another scheme that allows an organism to move toward or away from gradients of nutrients or other chemical stimuli. Detecting by
630:
3623:
3918:
Solon, A. P.; Cates, M. E.; Tailleur, J. (2015). "Active brownian particles and run-and-tumble particles: A comparative study".
44:
3981:
2091:
The mathematical abstraction of run-and-tumble motion also appears outside of biology—for example, in idealized models of
1161:
3401:
666:
3480:
998:
884:
4126:
3804:
3675:
3621:
Guasto, Jeffrey S.; Rusconi, Roberto; Stocker, Roman (2012-01-21). "Fluid
Mechanics of Planktonic Microorganisms".
338:
1701:
1143:
748:
676:
462:
454:
343:
2154:
683:
537:
407:
263:
1664:
290:
3863:
782:
733:
610:
402:
301:
715:
of smooth swimming increases, while the presence of a repellent gradient increases the rate of tumbling.
4181:
548:
412:
1956:{\displaystyle \langle \mathbf {r} ^{2}\rangle ={\frac {2v_{0}^{2}}{\alpha ^{2}(1-\sigma _{1})}}\left}
797:, bacteria swim in a random pattern produced by alternating counterclockwise (CCW) and clockwise (CW)
4041:
3939:
3882:
3813:
3754:
3632:
3552:
3313:
3212:
3071:
2975:
2451:
1139:
1106:
is observed in a homogenous environment, and the direction of each run is identified after a tumble.
925:
569:
711:
584:
523:
472:
467:
3660:
Jensen, Oliver E. (2015), "Mathematical
Biomechanics", in Nicholas J. Higham; et al. (eds.),
4159:
4112:
4031:
4008:
3963:
3929:
3906:
3872:
3786:
3723:
3595:
3576:
3542:
3503:
3337:
3303:
3236:
3202:
3102:
2944:
2890:
2643:
2617:
2121:
2115:
2092:
806:
662:
487:
306:
96:
80:
69:
4077:
Wadhams, George H.; Armitage, Judith P. (2004). "Making sense of it all: bacterial chemotaxis".
698:
Many bacteria swim, propelled by rotation of the flagella outside the cell body. In contrast to
4151:
4143:
4124:
Wadhwa, Navish; Berg, Howard C. (2021-09-21). "Bacterial motility: machinery and mechanisms".
4104:
4096:
4065:
4057:
4022:
4000:
3955:
3898:
3849:
3831:
3778:
3770:
3745:
3731:
3694:
3648:
3609:
3599:
3568:
3519:
3467:
3457:
3430:
3395:
Bastos-Arrieta, Julio; Revilla-Guarinos, Ainhoa; Uspal, William E.; Simmchen, Juliane (2018).
3329:
3228:
3159:
3141:
3094:
3052:
3044:
3009:
2991:
2936:
2928:
2882:
2874:
2821:
2803:
2759:
2741:
2702:
2684:
2635:
2583:
2565:
2487:
2469:
2410:
2392:
2339:
2321:
2160:
2109:
2096:
921:
770:
739:
574:
482:
353:
196:
188:
101:
3564:
1035:, displaying an intermittent two phase motion; a high-motility run and a low-motility tumble
4135:
4088:
4049:
3990:
3947:
3890:
3839:
3821:
3800:"Novel Methods for Analysing Bacterial Tracks Reveal Persistence in Rhodobacter sphaeroides"
3762:
3715:
3684:
3640:
3589:
3560:
3511:
3495:
3420:
3410:
3321:
3220:
3149:
3133:
3086:
3036:
2999:
2983:
2920:
2866:
2811:
2793:
2749:
2733:
2692:
2674:
2627:
2573:
2557:
2477:
2459:
2400:
2384:
2329:
2311:
849:
828:
787:
699:
477:
85:
17:
3040:
2054:{\displaystyle \sigma _{1}=\int _{0}^{2\pi }g({\hat {\mathbf {s} }})(\cos \theta )d\theta }
1040:
917:
845:
579:
366:
258:
3706:
Paasschens, J. C. J. (1 July 1997). "Solution of the time-dependent
Boltzmann equation".
2240:
2238:
2236:
2234:
1054:
cells can also undergo biased motility under directional illumination. Under directional
4045:
3943:
3886:
3817:
3758:
3644:
3636:
3556:
3317:
3291:
3216:
2979:
2455:
2112: – Ability of many animals to find their way accurately without maps or instruments
3844:
3799:
3531:
Cates, Michael E.; Tailleur, Julien (2015-03-01). "Motility-Induced Phase
Separation".
3425:
3396:
3190:
3154:
3121:
3004:
2963:
2870:
2816:
2781:
2697:
2662:
2578:
2546:"Phototaxis Assays of Synechocystis sp. PCC 6803 at Macroscopic and Microscopic Scales"
2545:
2482:
2439:
2405:
2372:
2334:
2299:
2130:
1024:
841:
753:
507:
348:
270:
3090:
2754:
2721:
1757:. In two dimensions, the mean squared displacement corresponding to initial condition
4175:
4163:
4116:
3689:
3670:
3341:
3240:
2948:
2924:
2647:
2142:
1099:
1096:
1019:
1006:
980:
962:
826:
An archetype of bacterial swimming is represented by the well-studied model organism
812:
802:
757:
423:
333:
311:
248:
3967:
3910:
3790:
3580:
2894:
2737:
2163: – Memoryless continuous-time stochastic process that shows two distinct values
4012:
3106:
2316:
2136:
1131:
1055:
1032:
1031:
species can move in cell suspensions and on moist surfaces and by using retractile
989:
844:
swimming pattern, as shown in the diagrams below. Counterclockwise rotation of the
833:
724:
543:
532:
253:
233:
206:
201:
155:
143:
53:
3951:
1039:. The two phases can be modified under various external stressors. Increasing the
899:
3826:
3325:
2464:
1062:
cells perform phototactic motility and head toward the light source (in positive
4053:
3224:
2438:
Egbert, Matthew D.; Barandiaran, Xabier E.; Di Paolo, Ezequiel A. (2010-12-02).
1694:
1625:
1103:
1078:
589:
518:
243:
228:
173:
4139:
3894:
3445:
2425:
2388:
2354:
928:, which causes small fluctuations in the orientation over the course of a run.
3995:
3976:
3613:
3137:
2722:"Multiple Light Inputs Control Phototaxis in Synechocystis sp. Strain PCC6803"
1092:
1082:
1063:
941:
793:
778:
774:
387:
238:
161:
149:
137:
131:
4147:
4100:
4061:
3959:
3902:
3835:
3774:
3735:
3727:
3719:
3652:
3572:
3523:
3507:
3415:
3191:"Run-and-tumble particles in two dimensions: Marginal position distributions"
3145:
3048:
2995:
2932:
2878:
2807:
2745:
2688:
2639:
2569:
2473:
2396:
2325:
3766:
3471:
2561:
798:
703:
382:
167:
125:
4155:
4108:
4069:
4004:
3853:
3782:
3698:
3434:
3333:
3232:
3163:
3098:
3056:
3013:
2886:
2840:
Emergent phototactic responses of cyanobacteria under complex light regimes
2825:
2763:
2706:
2587:
2491:
2414:
2343:
2244:
2133: – Biological ability to detect and respond to cell population density
2940:
2798:
2424:
Modified material was copied from this source, which is available under a
2353:
Modified material was copied from this source, which is available under a
3515:
2148:
908:
874:
654:
564:
559:
2679:
2118: – Ability of bacteria to move independently using metabolic energy
682:
Run-and-tumble motion forms the basis of certain mathematical models of
3440:
3253:
2964:"Bacterial swarming: a model system for studying dynamic self-assembly"
2420:
2349:
1073:
cells to move away from the high levels of radiation source. Moreover,
869:
671:
512:
433:
397:
3499:
3481:"Existence and Uniqueness Theorems for the Neutron Transport Equation"
2911:
Parkinson, John S. (1993). "Signal transduction schemes of bacteria".
2631:
2987:
1138:, i.e., the number of tumbling events in a given time interval has a
438:
428:
392:
4092:
2225:
4036:
3934:
3877:
3308:
3207:
2622:
2157: – Model of self-propelled motion in a dissipative environment
988:. These cells lack flagella, but achieve motility using retractile
805:
detect attractants or repellents and stimulate responses through a
3547:
1689:. The integral is taken over all possible unit vectors, i.e., the
985:
937:
898:
816:
uses run-and-tumbling in a manner which can result in phototaxis.
117:
3444:
Material was copied from this source, which is available under a
3277:
3027:
Mattick, John S. (2002). "Type IV Pili and
Twitching Motility".
744:
3265:
2298:
Mehdizadeh Allaf, Malihe; Peerhossaini, Hassan (2022-03-24).
944:. Tumbles are typically faster than runs: tumbling events of
1156:
Interactions with other agents are negligible (dilute limit)
2780:
Moon, Yoon-Jung; Kim, Seung; Chung, Young-Ho (2012-12-03).
1195:
is the unit vector in the direction of its orientation. In
948:
last about 0.1 seconds, compared to ~ 1 second for a run.
675:
in a dilute aqueous medium, for which the run duration is
2663:"Cyanobacteria use micro-optics to sense light direction"
1043:, uniformly over the space, increases the probability of
3122:"Responding to chemical gradients: bacterial chemotaxis"
2720:
Ng, Wing-On; Grossman, Arthur R.; Bhaya, Devaki (2003).
2544:
Jakob, Annik; Schuergers, Nils; Wilde, Annegret (2017).
2268:
781:, to optimally navigate through complex environments or
1102: the microorganism performs a three-dimensional
769:
Genetically diverse groups of microorganisms rely upon
686:, in which case the particles themselves may be called
3446:
Creative
Commons Attribution 4.0 International License
2426:
Creative
Commons Attribution 4.0 International License
2355:
Creative Commons Attribution 4.0 International License
810:
tumbling and changes in direction. The cyanobacterium
661:
The tumbling is erratic or "random" in the sense of a
1975:
1785:
1208:
1118:
Runs are straight and performed at constant velocity
707:
2256:
2126:
Pages displaying wikidata descriptions as a fallback
1164:
can be derived for the probability density function
1081:
radiation as an effective escape mechanism to avoid
1027:. Cyanobacterium do not have flagella. Nonetheless,
3292:"Active Brownian motion with directional reversals"
2383:(1). Springer Science and Business Media LLC: 348.
3176:
2603:
2601:
2599:
2597:
2185:
2183:
2181:
2179:
2177:
2053:
1955:
1593:
920:, bacteria starting at rest quickly reach a fixed
2962:Copeland, Matthew F.; Weibel, Douglas B. (2009).
2782:"Sensing and Responding to UV-A in Cyanobacteria"
2139: – Microscopic object able to traverse fluid
2906:
2904:
2440:"A Minimal Model of Metabolism-Based Chemotaxis"
2300:"Cyanobacteria: Model Microorganisms and Beyond"
2293:
2291:
2289:
2287:
2285:
2283:
2281:
2279:
2277:
1077:cells show a negative phototaxis behavior under
3070:Webre, D.J.; Wolanin, P.M; Stock, J.B. (2003).
2838:Chau, R.M.W., Bhaya, D. and Huang, K.C., 2017.
2504:
3664:, Princeton University Press, pp. 609–616
3662:The Princeton Companion to Applied Mathematics
665:—that is, the new direction is sampled from a
3479:Case, K. M.; Zweifel, P. F. (November 1963).
3354:
2201:
1160:With a few other simplifying assumptions, an
631:
8:
3921:The European Physical Journal Special Topics
2539:
2537:
2365:
2363:
1801:
1786:
3975:Sowa, Yoshiyuki; Berry, Richard M. (2008).
3366:
2786:International Journal of Molecular Sciences
2775:
2773:
653:is a movement pattern exhibited by certain
3378:
2528:
1142:. This implies that the run durations are
638:
624:
29:
4035:
3994:
3933:
3876:
3843:
3825:
3688:
3546:
3534:Annual Review of Condensed Matter Physics
3424:
3414:
3307:
3206:
3153:
3120:Sourjik, Victor; Wingreen, Ned S (2012).
3003:
2815:
2797:
2753:
2696:
2678:
2621:
2577:
2481:
2463:
2404:
2333:
2315:
2213:
2016:
2014:
2013:
1998:
1993:
1980:
1974:
1939:
1907:
1887:
1880:
1873:
1853:
1834:
1822:
1817:
1807:
1795:
1790:
1784:
1700:In free space (far from boundaries), the
1576:
1574:
1573:
1545:
1543:
1542:
1533:
1509:
1507:
1506:
1491:
1489:
1488:
1471:
1462:
1439:
1437:
1436:
1428:
1393:
1391:
1390:
1382:
1368:
1341:
1314:
1312:
1311:
1303:
1280:
1278:
1277:
1276:
1270:
1232:
1230:
1229:
1221:
1209:
1207:
3671:"Diversity at its best: Bacterial taxis"
3565:10.1146/annurev-conmatphys-031214-014710
3290:Santra; Basu; Sabhapandit (2021-07-13).
3189:Santra; Basu; Sabhapandit (2020-06-15).
1667:describing transitions from orientation
2173:
2145: – Matter behavior at system scale
723:Run-and-tumble motion is found in many
37:
3041:10.1146/annurev.micro.56.012302.160938
2516:
891:Run-and-tumble swimming pattern
785:host tissues. In the model organisms
4080:Nature Reviews Molecular Cell Biology
7:
3588:Chandrasekhar, Subrahmanyan (1960).
2189:
710:(mediated by specific receptors and
3645:10.1146/annurev-fluid-120710-101156
3397:"Bacterial Biohybrid Microswimmers"
1127:(initial speed-up is instantaneous)
743:. It has also been observed in the
2871:10.1111/j.1751-1097.1999.tb01954.x
2257:Guasto, Rusconi & Stocker 2012
1645:is the friction, and the function
1468:
1359:
1350:
1294:
1254:
1212:
25:
1085:and other cellular components of
3690:10.1111/j.1462-2920.2010.02383.x
3624:Annual Review of Fluid Mechanics
3439:
3177:Solon, Cates & Tailleur 2015
2419:
2348:
2017:
1791:
1577:
1546:
1534:
1510:
1492:
1440:
1429:
1394:
1383:
1369:
1315:
1304:
1281:
1233:
1222:
997:
971:
883:
860:
605:
604:
43:
3982:Quarterly Reviews of Biophysics
3488:Journal of Mathematical Physics
3126:Current Opinion in Cell Biology
2859:Photochemistry and Photobiology
2738:10.1128/jb.185.5.1599-1607.2003
2151: – Model in fluid dynamics
679:with a mean of about 1 second.
38:Microbial and microbot movement
2317:10.3390/microorganisms10040696
2042:
2030:
2027:
2021:
2010:
1913:
1894:
1859:
1840:
1682:. For complete reorientation,
1581:
1566:
1550:
1530:
1524:
1514:
1496:
1485:
1456:
1444:
1425:
1413:
1410:
1398:
1379:
1373:
1365:
1356:
1331:
1319:
1300:
1285:
1249:
1237:
1218:
1199:-dimensions, this equation is
1:
3091:10.1016/S0960-9822(02)01424-0
3029:Annual Review of Microbiology
2610:Journal of Fluids Engineering
1189:is the particle position and
1162:integro-differential equation
1153:Tumble duration is negligible
3827:10.1371/journal.pcbi.1003276
3402:Frontiers in Robotics and AI
3326:10.1103/PhysRevE.104.L012601
2925:10.1016/0092-8674(93)90267-t
2465:10.1371/journal.pcbi.1001004
911:projecting in all directions
667:probability density function
18:Synechocystis run-and-tumble
4127:Nature Reviews Microbiology
4054:10.1103/physreve.101.062607
3977:"Bacterial flagellar motor"
3952:10.1140/epjst/e2015-02457-0
3254:Villa-Torrealba et al. 2020
3225:10.1103/PhysRevE.101.062120
2505:Wadhams & Armitage 2004
1004:Run-and-tumble motion of a
4198:
4140:10.1038/s41579-021-00626-4
3805:PLOS Computational Biology
3676:Environmental Microbiology
2444:PLOS Computational Biology
2389:10.1038/s41467-020-20558-6
2245:Bastos-Arrieta et al. 2018
1639:is an external potential,
1134:and occur at average rate
850:flagellar bundle formation
339:Bacteria collective motion
3996:10.1017/S0033583508004691
3138:10.1016/j.ceb.2011.11.008
2202:Cates & Tailleur 2015
1702:mean squared displacement
1144:exponentially distributed
765:Directed motility (taxis)
749:Chlamydomonas reinhardtii
702:, bacterial flagella are
677:exponentially distributed
463:Synthetic molecular motor
344:Collective cell migration
3895:10.1088/1367-2630/aae72c
3720:10.1103/PhysRevE.56.1135
3416:10.3389/frobt.2018.00097
2155:Active Brownian particle
1665:scattering cross section
688:run-and-tumble particles
684:self-propelled particles
264:Self-propelled particles
27:Type of bacterial motion
3767:10.1126/science.1172667
3367:Case & Zweifel 1963
2726:Journal of Bacteriology
2562:10.21769/bioprotoc.2328
291:Biohybrid microswimmers
222:Microbots and particles
3864:New Journal of Physics
3456:. New York: Springer.
3072:"Bacterial chemotaxis"
2529:Wadhwa & Berg 2021
2055:
1957:
1715:generically scales as
1595:
912:
734:Salmonella typhimurium
3452:Berg, Howard (2004).
2799:10.3390/ijms131216303
2377:Nature Communications
2214:Sowa & Berry 2008
2056:
1958:
1596:
1110:Mathematical modeling
902:
651:Run-and-tumble motion
549:cytoplasmic streaming
1973:
1783:
1206:
1140:Poisson distribution
1130:Tumbling events are
926:rotational diffusion
727:bacteria, including
570:Molecular biophysics
302:bacterial biohybrids
4046:2020PhRvE.101f2607V
3944:2015EPJST.224.1231S
3887:2018NJPh...20j3033S
3818:2013PLSCB...9E3276R
3759:2009Sci...325..487P
3637:2012AnRFM..44..373G
3557:2015ARCMP...6..219C
3318:2021PhRvE.104a2601S
3278:Seyrich et al. 2018
3217:2020PhRvE.101f2120S
2980:2009SMat....5.1174C
2792:(12): 16303–16332.
2680:10.7554/elife.12620
2456:2010PLSCB...6E1004E
2006:
1827:
1017:Another example is
978:Cross section of a
719:Biological examples
712:signal transduction
585:Non-motile bacteria
524:Axophilic migration
473:Molecular propeller
468:Molecular modelling
33:Part of a series on
3596:Dover Publications
3591:Radiative Transfer
3355:Chandrasekhar 1960
3266:Rosser et al. 2013
2122:Aquatic locomotion
2116:Bacterial motility
2093:radiative transfer
2051:
1989:
1953:
1813:
1591:
916:they exist at low
913:
807:signalling cascade
799:flagellar rotation
663:stochastic process
488:Molecular tweezers
307:protist biohybrids
146:(electric current)
97:Protist locomotion
70:Bacterial motility
4087:(12): 1024–1037.
4023:Physical Review E
3753:(5939): 487–490.
3708:Physical Review E
3605:978-0-486-31845-5
3500:10.1063/1.1703916
3494:(11): 1376–1385.
3463:978-0-387-21638-6
3454:E. coli in motion
3296:Physical Review E
3195:Physical Review E
2632:10.1115/1.4045951
2269:Polin et al. 2009
2226:Krell et al. 2011
2161:Telegraph process
2110:Animal navigation
2097:neutron transport
2024:
1946:
1863:
1584:
1553:
1517:
1499:
1477:
1447:
1401:
1322:
1288:
1261:
1240:
922:terminal velocity
773:(taxis), such as
771:directed motility
740:Bacillus subtilis
648:
647:
575:Molecular machine
483:molecular shuttle
376:Biological motors
354:Swarming motility
327:Collective motion
16:(Redirected from
4189:
4167:
4120:
4073:
4039:
4016:
3998:
3971:
3937:
3928:(7): 1231–1262.
3914:
3880:
3857:
3847:
3829:
3812:(10): e1003276.
3794:
3739:
3714:(1): 1135–1141.
3702:
3692:
3683:(5): 1115–1124.
3665:
3656:
3617:
3584:
3550:
3527:
3485:
3475:
3443:
3438:
3428:
3418:
3382:
3376:
3370:
3364:
3358:
3352:
3346:
3345:
3311:
3287:
3281:
3275:
3269:
3263:
3257:
3251:
3245:
3244:
3210:
3186:
3180:
3174:
3168:
3167:
3157:
3117:
3111:
3110:
3076:
3067:
3061:
3060:
3024:
3018:
3017:
3007:
2988:10.1039/b812146j
2974:(6): 1174–1187.
2959:
2953:
2952:
2908:
2899:
2898:
2853:
2847:
2836:
2830:
2829:
2819:
2801:
2777:
2768:
2767:
2757:
2732:(5): 1599–1607.
2717:
2711:
2710:
2700:
2682:
2658:
2652:
2651:
2625:
2605:
2592:
2591:
2581:
2541:
2532:
2526:
2520:
2514:
2508:
2502:
2496:
2495:
2485:
2467:
2450:(12): e1001004.
2435:
2429:
2423:
2418:
2408:
2367:
2358:
2352:
2347:
2337:
2319:
2295:
2272:
2266:
2260:
2254:
2248:
2242:
2229:
2223:
2217:
2211:
2205:
2199:
2193:
2187:
2127:
2084:
2070:parametrized as
2069:
2060:
2058:
2057:
2052:
2026:
2025:
2020:
2015:
2005:
1997:
1985:
1984:
1962:
1960:
1959:
1954:
1952:
1948:
1947:
1945:
1944:
1943:
1927:
1920:
1919:
1912:
1911:
1881:
1864:
1862:
1858:
1857:
1839:
1838:
1828:
1826:
1821:
1808:
1800:
1799:
1794:
1775:
1756:
1750:
1735:
1729:
1714:
1692:
1688:
1681:
1675:
1674:
1662:
1660:
1644:
1638:
1623:
1617:
1600:
1598:
1597:
1592:
1590:
1586:
1585:
1580:
1575:
1559:
1555:
1554:
1549:
1544:
1537:
1523:
1519:
1518:
1513:
1508:
1501:
1500:
1495:
1490:
1478:
1476:
1475:
1463:
1449:
1448:
1443:
1438:
1432:
1403:
1402:
1397:
1392:
1386:
1372:
1349:
1348:
1324:
1323:
1318:
1313:
1307:
1290:
1289:
1284:
1279:
1275:
1274:
1262:
1260:
1252:
1242:
1241:
1236:
1231:
1225:
1210:
1198:
1194:
1188:
1182:
1149:
1137:
1126:
1001:
975:
887:
864:
846:flagellar motors
829:Escherichia coli
821:Escherichia coli
788:Escherichia coli
700:protist flagella
640:
633:
626:
613:
608:
607:
478:molecular sensor
455:Synthetic motors
367:Molecular motors
158:(magnetic field)
47:
30:
21:
4197:
4196:
4192:
4191:
4190:
4188:
4187:
4186:
4172:
4171:
4170:
4123:
4093:10.1038/nrm1524
4076:
4019:
3974:
3917:
3860:
3797:
3742:
3705:
3668:
3659:
3620:
3606:
3587:
3530:
3483:
3478:
3464:
3451:
3394:
3390:
3385:
3379:Paasschens 1997
3377:
3373:
3365:
3361:
3353:
3349:
3289:
3288:
3284:
3276:
3272:
3264:
3260:
3252:
3248:
3188:
3187:
3183:
3175:
3171:
3119:
3118:
3114:
3079:Current Biology
3074:
3069:
3068:
3064:
3026:
3025:
3021:
2961:
2960:
2956:
2910:
2909:
2902:
2855:
2854:
2850:
2837:
2833:
2779:
2778:
2771:
2719:
2718:
2714:
2660:
2659:
2655:
2607:
2606:
2595:
2543:
2542:
2535:
2527:
2523:
2515:
2511:
2503:
2499:
2437:
2436:
2432:
2369:
2368:
2361:
2297:
2296:
2275:
2267:
2263:
2255:
2251:
2243:
2232:
2224:
2220:
2212:
2208:
2200:
2196:
2188:
2175:
2171:
2166:
2125:
2105:
2071:
2065:
1976:
1971:
1970:
1935:
1928:
1903:
1883:
1882:
1869:
1865:
1849:
1830:
1829:
1809:
1789:
1781:
1780:
1758:
1752:
1737:
1731:
1716:
1704:
1690:
1683:
1677:
1672:
1668:
1658:
1646:
1640:
1629:
1619:
1611:
1605:
1572:
1541:
1505:
1467:
1337:
1266:
1253:
1211:
1204:
1203:
1196:
1190:
1184:
1165:
1147:
1135:
1125:
1119:
1112:
1041:light intensity
1015:
1014:
1013:
1012:
1011:
1002:
994:
993:
976:
967:
966:
956:
918:Reynolds number
897:
896:
895:
894:
893:
892:
888:
880:
879:
878:
865:
824:
767:
721:
708:bacterial taxis
696:
644:
603:
596:
595:
594:
580:Nanoengineering
555:
540:
528:
515:
502:
494:
493:
492:
457:
447:
446:
445:
419:
377:
360:
359:
358:
328:
320:
319:
318:
295:
285:
277:
276:
275:
259:Janus particles
223:
215:
214:
213:
191:
181:
180:
179:
120:
110:
109:
108:
92:
72:
64:
28:
23:
22:
15:
12:
11:
5:
4195:
4193:
4185:
4184:
4174:
4173:
4169:
4168:
4134:(3): 161–173.
4121:
4074:
4017:
3989:(2): 103–132.
3972:
3915:
3871:(10): 103033.
3858:
3795:
3740:
3703:
3666:
3657:
3631:(1): 373–400.
3618:
3604:
3585:
3541:(1): 219–244.
3528:
3476:
3462:
3449:
3391:
3389:
3386:
3384:
3383:
3371:
3359:
3347:
3302:(1): L012601.
3282:
3270:
3258:
3246:
3181:
3169:
3132:(2): 262–268.
3112:
3085:(2): R47–R49.
3062:
3035:(1): 289–314.
3019:
2954:
2919:(5): 857–871.
2900:
2848:
2831:
2769:
2712:
2653:
2593:
2533:
2521:
2509:
2497:
2430:
2359:
2304:Microorganisms
2273:
2261:
2249:
2230:
2218:
2206:
2194:
2172:
2170:
2167:
2165:
2164:
2158:
2152:
2146:
2140:
2134:
2131:Quorum sensing
2128:
2119:
2113:
2106:
2104:
2101:
2062:
2061:
2050:
2047:
2044:
2041:
2038:
2035:
2032:
2029:
2023:
2019:
2012:
2009:
2004:
2001:
1996:
1992:
1988:
1983:
1979:
1964:
1963:
1951:
1942:
1938:
1934:
1931:
1926:
1923:
1918:
1915:
1910:
1906:
1902:
1899:
1896:
1893:
1890:
1886:
1879:
1876:
1872:
1868:
1861:
1856:
1852:
1848:
1845:
1842:
1837:
1833:
1825:
1820:
1816:
1812:
1806:
1803:
1798:
1793:
1788:
1607:
1602:
1601:
1589:
1583:
1579:
1571:
1568:
1565:
1562:
1558:
1552:
1548:
1540:
1536:
1532:
1529:
1526:
1522:
1516:
1512:
1504:
1498:
1494:
1487:
1484:
1481:
1474:
1470:
1466:
1461:
1458:
1455:
1452:
1446:
1442:
1435:
1431:
1427:
1424:
1421:
1418:
1415:
1412:
1409:
1406:
1400:
1396:
1389:
1385:
1381:
1378:
1375:
1371:
1367:
1364:
1361:
1358:
1355:
1352:
1347:
1344:
1340:
1336:
1333:
1330:
1327:
1321:
1317:
1310:
1306:
1302:
1299:
1296:
1293:
1287:
1283:
1273:
1269:
1265:
1259:
1256:
1251:
1248:
1245:
1239:
1235:
1228:
1224:
1220:
1217:
1214:
1158:
1157:
1154:
1151:
1128:
1123:
1111:
1108:
1100:chemoreceptors
1025:cyanobacterium
1003:
996:
995:
977:
970:
969:
968:
960:
959:
958:
957:
955:
950:
890:
889:
882:
881:
867:
866:
859:
858:
857:
856:
855:
842:run-and-tumble
836:flagellation,
823:
818:
803:Chemoreceptors
766:
763:
754:cyanobacterium
720:
717:
695:
692:
646:
645:
643:
642:
635:
628:
620:
617:
616:
615:
614:
598:
597:
593:
592:
587:
582:
577:
572:
567:
562:
556:
554:
553:
552:
551:
546:
541:
529:
527:
526:
521:
516:
510:
508:Brownian motor
504:
503:
500:
499:
496:
495:
491:
490:
485:
480:
475:
470:
465:
459:
458:
453:
452:
449:
448:
444:
443:
442:
441:
436:
431:
424:Motor proteins
420:
418:
417:
416:
415:
410:
408:intraflagellar
405:
400:
395:
390:
379:
378:
375:
374:
371:
370:
362:
361:
357:
356:
351:
349:Quorum sensing
346:
341:
336:
330:
329:
326:
325:
322:
321:
317:
316:
315:
314:
309:
304:
296:
294:
293:
287:
286:
283:
282:
279:
278:
274:
273:
271:Swarm robotics
268:
267:
266:
261:
256:
246:
241:
236:
231:
225:
224:
221:
220:
217:
216:
212:
211:
210:
209:
204:
193:
192:
187:
186:
183:
182:
178:
177:
171:
165:
159:
153:
147:
141:
135:
129:
122:
121:
116:
115:
112:
111:
107:
106:
105:
104:
93:
91:
90:
89:
88:
83:
78:
76:run-and-tumble
66:
65:
62:
61:
58:
57:
49:
48:
40:
39:
35:
34:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4194:
4183:
4180:
4179:
4177:
4165:
4161:
4157:
4153:
4149:
4145:
4141:
4137:
4133:
4129:
4128:
4122:
4118:
4114:
4110:
4106:
4102:
4098:
4094:
4090:
4086:
4082:
4081:
4075:
4071:
4067:
4063:
4059:
4055:
4051:
4047:
4043:
4038:
4033:
4030:(6): 062607.
4029:
4025:
4024:
4018:
4014:
4010:
4006:
4002:
3997:
3992:
3988:
3984:
3983:
3978:
3973:
3969:
3965:
3961:
3957:
3953:
3949:
3945:
3941:
3936:
3931:
3927:
3923:
3922:
3916:
3912:
3908:
3904:
3900:
3896:
3892:
3888:
3884:
3879:
3874:
3870:
3866:
3865:
3859:
3855:
3851:
3846:
3841:
3837:
3833:
3828:
3823:
3819:
3815:
3811:
3807:
3806:
3801:
3796:
3792:
3788:
3784:
3780:
3776:
3772:
3768:
3764:
3760:
3756:
3752:
3748:
3747:
3741:
3737:
3733:
3729:
3725:
3721:
3717:
3713:
3709:
3704:
3700:
3696:
3691:
3686:
3682:
3678:
3677:
3672:
3667:
3663:
3658:
3654:
3650:
3646:
3642:
3638:
3634:
3630:
3626:
3625:
3619:
3615:
3611:
3607:
3601:
3597:
3593:
3592:
3586:
3582:
3578:
3574:
3570:
3566:
3562:
3558:
3554:
3549:
3544:
3540:
3536:
3535:
3529:
3525:
3521:
3517:
3516:2027.42/70329
3513:
3509:
3505:
3501:
3497:
3493:
3489:
3482:
3477:
3473:
3469:
3465:
3459:
3455:
3450:
3447:
3442:
3436:
3432:
3427:
3422:
3417:
3412:
3408:
3404:
3403:
3398:
3393:
3392:
3387:
3380:
3375:
3372:
3368:
3363:
3360:
3356:
3351:
3348:
3343:
3339:
3335:
3331:
3327:
3323:
3319:
3315:
3310:
3305:
3301:
3297:
3293:
3286:
3283:
3279:
3274:
3271:
3267:
3262:
3259:
3255:
3250:
3247:
3242:
3238:
3234:
3230:
3226:
3222:
3218:
3214:
3209:
3204:
3201:(6): 062120.
3200:
3196:
3192:
3185:
3182:
3178:
3173:
3170:
3165:
3161:
3156:
3151:
3147:
3143:
3139:
3135:
3131:
3127:
3123:
3116:
3113:
3108:
3104:
3100:
3096:
3092:
3088:
3084:
3080:
3073:
3066:
3063:
3058:
3054:
3050:
3046:
3042:
3038:
3034:
3030:
3023:
3020:
3015:
3011:
3006:
3001:
2997:
2993:
2989:
2985:
2981:
2977:
2973:
2969:
2965:
2958:
2955:
2950:
2946:
2942:
2938:
2934:
2930:
2926:
2922:
2918:
2914:
2907:
2905:
2901:
2896:
2892:
2888:
2884:
2880:
2876:
2872:
2868:
2865:(1): 95–102.
2864:
2860:
2852:
2849:
2845:
2841:
2835:
2832:
2827:
2823:
2818:
2813:
2809:
2805:
2800:
2795:
2791:
2787:
2783:
2776:
2774:
2770:
2765:
2761:
2756:
2751:
2747:
2743:
2739:
2735:
2731:
2727:
2723:
2716:
2713:
2708:
2704:
2699:
2694:
2690:
2686:
2681:
2676:
2672:
2668:
2664:
2657:
2654:
2649:
2645:
2641:
2637:
2633:
2629:
2624:
2619:
2615:
2611:
2604:
2602:
2600:
2598:
2594:
2589:
2585:
2580:
2575:
2571:
2567:
2563:
2559:
2556:(11): e2328.
2555:
2551:
2547:
2540:
2538:
2534:
2530:
2525:
2522:
2518:
2513:
2510:
2506:
2501:
2498:
2493:
2489:
2484:
2479:
2475:
2471:
2466:
2461:
2457:
2453:
2449:
2445:
2441:
2434:
2431:
2427:
2422:
2416:
2412:
2407:
2402:
2398:
2394:
2390:
2386:
2382:
2378:
2374:
2366:
2364:
2360:
2356:
2351:
2345:
2341:
2336:
2331:
2327:
2323:
2318:
2313:
2309:
2305:
2301:
2294:
2292:
2290:
2288:
2286:
2284:
2282:
2280:
2278:
2274:
2270:
2265:
2262:
2258:
2253:
2250:
2246:
2241:
2239:
2237:
2235:
2231:
2227:
2222:
2219:
2215:
2210:
2207:
2203:
2198:
2195:
2191:
2186:
2184:
2182:
2180:
2178:
2174:
2168:
2162:
2159:
2156:
2153:
2150:
2147:
2144:
2143:Active matter
2141:
2138:
2135:
2132:
2129:
2123:
2120:
2117:
2114:
2111:
2108:
2107:
2102:
2100:
2098:
2094:
2089:
2086:
2082:
2078:
2074:
2068:
2048:
2045:
2039:
2036:
2033:
2007:
2002:
1999:
1994:
1990:
1986:
1981:
1977:
1969:
1968:
1967:
1949:
1940:
1936:
1932:
1929:
1924:
1921:
1916:
1908:
1904:
1900:
1897:
1891:
1888:
1884:
1877:
1874:
1870:
1866:
1854:
1850:
1846:
1843:
1835:
1831:
1823:
1818:
1814:
1810:
1804:
1796:
1779:
1778:
1777:
1773:
1769:
1765:
1761:
1755:
1749:
1745:
1741:
1734:
1728:
1724:
1720:
1712:
1708:
1703:
1698:
1696:
1693:-dimensional
1686:
1680:
1671:
1666:
1657:
1653:
1649:
1643:
1636:
1632:
1627:
1624:-dimensional
1622:
1615:
1610:
1587:
1569:
1563:
1560:
1556:
1538:
1527:
1520:
1502:
1482:
1479:
1472:
1464:
1459:
1453:
1450:
1433:
1422:
1419:
1416:
1407:
1404:
1387:
1376:
1362:
1353:
1345:
1342:
1338:
1334:
1328:
1325:
1308:
1297:
1291:
1271:
1267:
1263:
1257:
1246:
1243:
1226:
1215:
1202:
1201:
1200:
1193:
1187:
1180:
1176:
1172:
1168:
1163:
1155:
1152:
1145:
1141:
1133:
1129:
1122:
1117:
1116:
1115:
1109:
1107:
1105:
1101:
1098:
1097:transmembrane
1094:
1090:
1088:
1087:Synechocystis
1084:
1083:damage to DNA
1080:
1076:
1075:Synechocystis
1072:
1071:Synechocystis
1067:
1065:
1061:
1060:Synehcocystis
1057:
1053:
1052:Synechocystis
1049:
1046:
1045:Synechocystis
1042:
1038:
1037:(see diagram)
1034:
1030:
1029:Synechocystis
1026:
1023:, a genus of
1022:
1021:
1020:Synechocystis
1009:
1008:
1007:Synechocystis
1000:
991:
987:
983:
982:
981:Synechocystis
974:
965:
964:
963:Synechocystis
954:
953:Synechocystis
951:
949:
947:
943:
939:
934:
929:
927:
923:
919:
910:
906:
901:
886:
876:
872:
871:
863:
854:
851:
847:
843:
839:
835:
831:
830:
822:
819:
817:
815:
814:
813:Synechocystis
808:
804:
800:
796:
795:
790:
789:
784:
780:
776:
772:
764:
762:
760:
759:
758:Synechocystis
755:
751:
750:
746:
742:
741:
736:
735:
730:
726:
718:
716:
713:
709:
705:
701:
693:
691:
689:
685:
680:
678:
674:
673:
668:
664:
659:
656:
652:
641:
636:
634:
629:
627:
622:
621:
619:
618:
612:
602:
601:
600:
599:
591:
588:
586:
583:
581:
578:
576:
573:
571:
568:
566:
563:
561:
558:
557:
550:
547:
545:
542:
539:
536:
535:
534:
531:
530:
525:
522:
520:
517:
514:
511:
509:
506:
505:
498:
497:
489:
486:
484:
481:
479:
476:
474:
471:
469:
466:
464:
461:
460:
456:
451:
450:
440:
437:
435:
432:
430:
427:
426:
425:
422:
421:
414:
411:
409:
406:
404:
401:
399:
396:
394:
391:
389:
386:
385:
384:
381:
380:
373:
372:
369:
368:
364:
363:
355:
352:
350:
347:
345:
342:
340:
337:
335:
334:Active matter
332:
331:
324:
323:
313:
312:robotic sperm
310:
308:
305:
303:
300:
299:
298:
297:
292:
289:
288:
281:
280:
272:
269:
265:
262:
260:
257:
255:
252:
251:
250:
249:Microparticle
247:
245:
242:
240:
237:
235:
232:
230:
227:
226:
219:
218:
208:
205:
203:
200:
199:
198:
195:
194:
190:
185:
184:
176:(temperature)
175:
172:
169:
166:
163:
160:
157:
154:
151:
148:
145:
142:
139:
136:
133:
130:
127:
124:
123:
119:
114:
113:
103:
100:
99:
98:
95:
94:
87:
84:
82:
79:
77:
74:
73:
71:
68:
67:
60:
59:
56:
55:
54:Microswimmers
51:
50:
46:
42:
41:
36:
32:
31:
19:
4182:Bacteriology
4131:
4125:
4084:
4078:
4027:
4021:
3986:
3980:
3925:
3919:
3868:
3862:
3809:
3803:
3750:
3744:
3711:
3707:
3680:
3674:
3661:
3628:
3622:
3590:
3538:
3532:
3491:
3487:
3453:
3406:
3400:
3374:
3362:
3350:
3299:
3295:
3285:
3273:
3261:
3249:
3198:
3194:
3184:
3172:
3129:
3125:
3115:
3082:
3078:
3065:
3032:
3028:
3022:
2971:
2967:
2957:
2916:
2912:
2862:
2858:
2851:
2846:: e02330-16.
2843:
2839:
2834:
2789:
2785:
2729:
2725:
2715:
2670:
2666:
2656:
2613:
2609:
2553:
2550:Bio-Protocol
2549:
2524:
2512:
2500:
2447:
2443:
2433:
2380:
2376:
2307:
2303:
2264:
2252:
2221:
2209:
2197:
2137:Microswimmer
2090:
2087:
2080:
2076:
2072:
2066:
2063:
1965:
1771:
1767:
1763:
1759:
1753:
1747:
1743:
1739:
1732:
1726:
1722:
1718:
1710:
1706:
1699:
1684:
1678:
1669:
1655:
1651:
1647:
1641:
1634:
1630:
1620:
1613:
1608:
1603:
1191:
1185:
1178:
1174:
1170:
1166:
1159:
1132:uncorrelated
1120:
1113:
1091:
1086:
1074:
1070:
1068:
1059:
1051:
1050:
1044:
1036:
1033:type IV pili
1028:
1018:
1016:
1005:
990:type IV pili
979:
961:
952:
945:
932:
930:
914:
904:
868:
837:
834:peritrichous
827:
825:
820:
811:
792:
786:
768:
756:
747:
738:
732:
728:
725:peritrichous
722:
697:
687:
681:
670:
660:
650:
649:
533:Cytoskeleton
403:motor switch
365:
254:Nanoparticle
234:Nanorobotics
207:photokinesis
202:chemokinesis
170:(fluid flow)
156:Magnetotaxis
144:Electrotaxis
75:
52:
2968:Soft Matter
2517:Jensen 2015
1695:unit sphere
1626:solid angle
1104:random walk
1079:ultraviolet
903:Diagram of
840:performs a
832:. With its
694:Description
590:Virophysics
538:prokaryotic
519:Endocytosis
244:DNA machine
229:Microbotics
174:Thermotaxis
140:(chemicals)
4037:2002.02872
3935:1504.07391
3878:1805.08860
3614:1084019191
3309:2101.11327
3208:2004.07562
2623:2003.02207
2310:(4): 696.
1751:for large
1730:for small
1146:with mean
1093:Chemotaxis
1064:phototaxis
1056:light flux
984:cell with
942:chemotaxis
794:Salmonella
779:phototaxis
775:chemotaxis
544:eukaryotic
388:archaellum
284:Biohybrids
239:Nanomotors
162:Phototaxis
150:Gravitaxis
138:Chemotaxis
132:Anemotaxis
4164:237595932
4148:1740-1526
4117:205493118
4101:1471-0072
4062:2470-0045
3960:1951-6355
3903:1367-2630
3836:1553-7358
3775:0036-8075
3736:1063-651X
3728:1095-3787
3653:0066-4189
3573:1947-5454
3548:1406.3533
3524:0022-2488
3508:1089-7658
3342:231718971
3241:219636018
3146:0955-0674
3049:0066-4227
2996:1744-683X
2949:205020855
2933:0092-8674
2879:0031-8655
2808:1422-0067
2746:0021-9193
2689:2050-084X
2648:211987677
2640:0098-2202
2570:2331-8325
2474:1553-7358
2397:2041-1723
2326:2076-2607
2190:Berg 2004
2049:θ
2040:θ
2037:
2022:^
2003:π
1991:∫
1978:σ
1937:σ
1933:−
1922:−
1905:σ
1901:−
1892:α
1889:−
1871:α
1851:σ
1847:−
1832:α
1802:⟩
1787:⟨
1770:, 0) = δ(
1582:^
1551:^
1515:^
1503:−
1497:^
1480:∫
1469:Ω
1465:α
1445:^
1420:α
1417:−
1399:^
1360:∇
1354:⋅
1351:∇
1343:−
1339:ξ
1320:^
1295:∇
1292:⋅
1286:^
1255:∂
1238:^
1213:∂
848:leads to
413:evolution
383:Flagellum
168:Rheotaxis
152:(gravity)
126:Aerotaxis
102:amoeboids
81:twitching
4176:Category
4156:34548639
4109:15573139
4070:32688514
4005:18812014
3968:53057662
3911:51455869
3854:24204227
3791:10530835
3783:19628868
3699:21087385
3581:15672131
3472:56124142
3435:33500976
3334:34412243
3233:32688530
3164:22169400
3099:12546801
3057:12142488
3014:23926448
2895:25364218
2887:10420848
2826:23208372
2764:12591877
2707:26858197
2588:34541089
2492:21170312
2415:33441540
2344:35456747
2149:Squirmer
2103:See also
1588:′
1557:′
1521:′
1183:, where
909:flagella
875:flagella
783:colonise
752:and the
655:bacteria
611:Category
565:Mucilage
560:Gray goo
128:(oxygen)
4042:Bibcode
4013:3297704
3940:Bibcode
3883:Bibcode
3845:3812076
3814:Bibcode
3755:Bibcode
3746:Science
3633:Bibcode
3553:Bibcode
3426:7805739
3388:Sources
3314:Bibcode
3213:Bibcode
3155:3320702
3107:3203488
3005:3733279
2976:Bibcode
2941:8098993
2817:3546692
2698:4758948
2579:8410341
2483:3000427
2452:Bibcode
2406:7806825
2335:9025173
2075:= (cos
1966:where
1618:is the
1612:= 2π/Γ(
992:
946:E. Coli
933:E. Coli
907:, with
905:E. coli
870:E. coli
838:E. coli
729:E. coli
672:E. coli
513:Biochip
501:Related
434:kinesin
398:axoneme
197:Kinesis
189:Kinesis
164:(light)
86:gliding
4162:
4154:
4146:
4115:
4107:
4099:
4068:
4060:
4011:
4003:
3966:
3958:
3909:
3901:
3852:
3842:
3834:
3789:
3781:
3773:
3734:
3726:
3697:
3651:
3612:
3602:
3579:
3571:
3522:
3506:
3470:
3460:
3433:
3423:
3409:: 97.
3340:
3332:
3239:
3231:
3162:
3152:
3144:
3105:
3097:
3055:
3047:
3012:
3002:
2994:
2947:
2939:
2931:
2893:
2885:
2877:
2844:mBio 8
2824:
2814:
2806:
2762:
2755:148062
2752:
2744:
2705:
2695:
2687:
2646:
2638:
2586:
2576:
2568:
2490:
2480:
2472:
2413:
2403:
2395:
2342:
2332:
2324:
2079:, sin
1774:)/(2Ď€)
1604:where
737:, and
704:rotors
609:
439:dynein
429:myosin
393:cilium
134:(wind)
4160:S2CID
4113:S2CID
4032:arXiv
4009:S2CID
3964:S2CID
3930:arXiv
3907:S2CID
3873:arXiv
3787:S2CID
3724:eISSN
3577:S2CID
3543:arXiv
3504:eISSN
3484:(PDF)
3338:S2CID
3304:arXiv
3237:S2CID
3203:arXiv
3103:S2CID
3075:(PDF)
2945:S2CID
2891:S2CID
2667:eLife
2644:S2CID
2618:arXiv
2616:(3).
2169:Notes
2064:with
1746:)âź© ~
1725:)âź© ~
1673:'
1663:is a
1659:'
938:taxis
873:have
118:Taxis
4152:PMID
4144:ISSN
4105:PMID
4097:ISSN
4066:PMID
4058:ISSN
4001:PMID
3956:ISSN
3899:ISSN
3850:PMID
3832:ISSN
3779:PMID
3771:ISSN
3732:ISSN
3695:PMID
3649:ISSN
3610:OCLC
3600:ISBN
3569:ISSN
3520:ISSN
3468:OCLC
3458:ISBN
3431:PMID
3330:PMID
3229:PMID
3160:PMID
3142:ISSN
3095:PMID
3053:PMID
3045:ISSN
3010:PMID
2992:ISSN
2937:PMID
2929:ISSN
2913:Cell
2883:PMID
2875:ISSN
2822:PMID
2804:ISSN
2760:PMID
2742:ISSN
2703:PMID
2685:ISSN
2636:ISSN
2584:PMID
2566:ISSN
2488:PMID
2470:ISSN
2411:PMID
2393:ISSN
2340:PMID
2322:ISSN
2095:and
1736:and
986:pili
791:and
745:alga
63:Taxa
4136:doi
4089:doi
4050:doi
4028:101
3991:doi
3948:doi
3926:224
3891:doi
3840:PMC
3822:doi
3763:doi
3751:325
3716:doi
3685:doi
3641:doi
3561:doi
3512:hdl
3496:doi
3421:PMC
3411:doi
3322:doi
3300:104
3221:doi
3199:101
3150:PMC
3134:doi
3087:doi
3037:doi
3000:PMC
2984:doi
2921:doi
2867:doi
2812:PMC
2794:doi
2750:PMC
2734:doi
2730:185
2693:PMC
2675:doi
2628:doi
2614:142
2574:PMC
2558:doi
2478:PMC
2460:doi
2401:PMC
2385:doi
2330:PMC
2312:doi
2034:cos
1776:is
1687:= 1
1676:to
1616:/2)
777:or
4178::
4158:.
4150:.
4142:.
4132:20
4130:.
4111:.
4103:.
4095:.
4083:.
4064:.
4056:.
4048:.
4040:.
4026:.
4007:.
3999:.
3987:41
3985:.
3979:.
3962:.
3954:.
3946:.
3938:.
3924:.
3905:.
3897:.
3889:.
3881:.
3869:20
3867:.
3848:.
3838:.
3830:.
3820:.
3808:.
3802:.
3785:.
3777:.
3769:.
3761:.
3749:.
3730:.
3722:.
3712:56
3710:.
3693:.
3681:13
3679:.
3673:.
3647:.
3639:.
3629:44
3627:.
3608:.
3598:.
3594:.
3575:.
3567:.
3559:.
3551:.
3537:.
3518:.
3510:.
3502:.
3490:.
3486:.
3466:.
3429:.
3419:.
3405:.
3399:.
3336:.
3328:.
3320:.
3312:.
3298:.
3294:.
3235:.
3227:.
3219:.
3211:.
3197:.
3193:.
3158:.
3148:.
3140:.
3130:24
3128:.
3124:.
3101:.
3093:.
3083:13
3081:.
3077:.
3051:.
3043:.
3033:56
3031:.
3008:.
2998:.
2990:.
2982:.
2970:.
2966:.
2943:.
2935:.
2927:.
2917:73
2915:.
2903:^
2889:.
2881:.
2873:.
2863:70
2861:.
2842:.
2820:.
2810:.
2802:.
2790:13
2788:.
2784:.
2772:^
2758:.
2748:.
2740:.
2728:.
2724:.
2701:.
2691:.
2683:.
2673:.
2669:.
2665:.
2642:.
2634:.
2626:.
2612:.
2596:^
2582:.
2572:.
2564:.
2552:.
2548:.
2536:^
2486:.
2476:.
2468:.
2458:.
2446:.
2442:.
2409:.
2399:.
2391:.
2381:12
2379:.
2375:.
2362:^
2338:.
2328:.
2320:.
2308:10
2306:.
2302:.
2276:^
2233:^
2176:^
2099:.
2085:.
1766:,
1713:)âź©
1697:.
1654:-
1628:,
1177:,
1173:,
1058:,
801:.
761:.
731:,
690:.
4166:.
4138::
4119:.
4091::
4085:5
4072:.
4052::
4044::
4034::
4015:.
3993::
3970:.
3950::
3942::
3932::
3913:.
3893::
3885::
3875::
3856:.
3824::
3816::
3810:9
3793:.
3765::
3757::
3738:.
3718::
3701:.
3687::
3655:.
3643::
3635::
3616:.
3583:.
3563::
3555::
3545::
3539:6
3526:.
3514::
3498::
3492:4
3474:.
3448:.
3437:.
3413::
3407:5
3381:.
3369:.
3357:.
3344:.
3324::
3316::
3306::
3280:.
3268:.
3256:.
3243:.
3223::
3215::
3205::
3179:.
3166:.
3136::
3109:.
3089::
3059:.
3039::
3016:.
2986::
2978::
2972:5
2951:.
2923::
2897:.
2869::
2828:.
2796::
2766:.
2736::
2709:.
2677::
2671:5
2650:.
2630::
2620::
2590:.
2560::
2554:7
2531:.
2519:.
2507:.
2494:.
2462::
2454::
2448:6
2428:.
2417:.
2387::
2357:.
2346:.
2314::
2271:.
2259:.
2247:.
2228:.
2216:.
2204:.
2192:.
2083:)
2081:θ
2077:θ
2073:Ĺť
2067:Ĺť
2046:d
2043:)
2031:(
2028:)
2018:s
2011:(
2008:g
2000:2
1995:0
1987:=
1982:1
1950:]
1941:1
1930:1
1925:1
1917:t
1914:)
1909:1
1898:1
1895:(
1885:e
1878:+
1875:t
1867:[
1860:)
1855:1
1844:1
1841:(
1836:2
1824:2
1819:0
1815:v
1811:2
1805:=
1797:2
1792:r
1772:r
1768:Ĺť
1764:r
1762:(
1760:f
1754:t
1748:t
1744:t
1742:(
1740:r
1738:⟨
1733:t
1727:t
1723:t
1721:(
1719:r
1717:⟨
1711:t
1709:(
1707:r
1705:⟨
1691:d
1685:g
1679:Ĺť
1670:Ĺť
1661:)
1656:Ĺť
1652:Ĺť
1650:(
1648:g
1642:Îľ
1637:)
1635:r
1633:(
1631:V
1621:d
1614:d
1609:d
1606:Ω
1578:s
1570:d
1567:)
1564:t
1561:,
1547:s
1539:,
1535:r
1531:(
1528:f
1525:)
1511:s
1493:s
1486:(
1483:g
1473:d
1460:+
1457:)
1454:t
1451:,
1441:s
1434:,
1430:r
1426:(
1423:f
1414:)
1411:)
1408:t
1405:,
1395:s
1388:,
1384:r
1380:(
1377:f
1374:)
1370:r
1366:(
1363:V
1357:(
1346:1
1335:=
1332:)
1329:t
1326:,
1316:s
1309:,
1305:r
1301:(
1298:f
1282:s
1272:0
1268:v
1264:+
1258:t
1250:)
1247:t
1244:,
1234:s
1227:,
1223:r
1219:(
1216:f
1197:d
1192:Ĺť
1186:r
1181:)
1179:t
1175:Ĺť
1171:r
1169:(
1167:f
1150:.
1148:α
1136:α
1124:0
1121:v
936:(
639:e
632:t
625:v
20:)
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
