Dimensionality and Dynamics in the Behavior of C. elegans

A major challenge in analyzing animal behavior is to discover some underlying simplicity in complex motor actions. Here, we show that the space of shapes adopted by the nematode Caenorhabditis elegans is low dimensional, with just four dimensions accounting for 95% of the shape variance. These dimensions provide a quantitative description of worm behavior, and we partially reconstruct “equations of motion” for the dynamics in this space. These dynamics have multiple attractors, and we find that the worm visits these in a rapid and almost completely deterministic response to weak thermal stimuli. Stimulus-dependent correlations among the different modes suggest that one can generate more reliable behaviors by synchronizing stimuli to the state of the worm in shape space. We confirm this prediction, effectively “steering” the worm in real time.

[1]  Friedrich,et al.  How to quantify deterministic and random influences on the statistics of the foreign exchange market , 1999, Physical review letters.

[2]  J. Sulston,et al.  The DNA of Caenorhabditis elegans. , 1974, Genetics.

[3]  Christopher J. Cronin,et al.  An automated system for measuring parameters of nematode sinusoidal movement , 2005 .

[4]  N. Munakata.  [Genetics of Caenorhabditis elegans]. , 1989, Tanpakushitsu kakusan koso. Protein, nucleic acid, enzyme.

[5]  Howard C. Berg,et al.  E. coli in Motion , 2003 .

[6]  Henrik Flyvbjerg,et al.  Cell motility as persistent random motion: theories from experiments. , 2005, Biophysical journal.

[7]  S. Brenner,et al.  The neural circuit for touch sensitivity in Caenorhabditis elegans , 1985, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[8]  L. Vosshall,et al.  Influence of odorant receptor repertoire on odor perception in humans and fruit flies , 2007, Proceedings of the National Academy of Sciences.

[9]  C. Rankin,et al.  Effects of aging on habituation in the nematode Caenorhabditis elegans , 1993, Behavioural Processes.

[10]  S. Brenner,et al.  The structure of the nervous system of the nematode Caenorhabditis elegans. , 1986, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[11]  Christopher J. Cronin,et al.  Conservation rules, their breakdown, and optimality in Caenorhabditis sinusoidal locomotion. , 2006, Journal of theoretical biology.

[12]  N. Wittenburg,et al.  Thermal avoidance in Caenorhabditis elegans: an approach to the study of nociception. , 1999, Proceedings of the National Academy of Sciences of the United States of America.

[13]  D. Sherrington.  Stochastic Processes in Physics and Chemistry , 1983 .

[14]  W. Ebeling.  Stochastic Processes in Physics and Chemistry , 1995 .

[15]  J. F. Soechting,et al.  Postural Hand Synergies for Tool Use , 1998, The Journal of Neuroscience.

[16]  D. M. Green,et al.  Signal detection theory and psychophysics , 1966 .

[17]  Aravinthan D. T. Samuel,et al.  Sensorimotor control during isothermal tracking in Caenorhabditis elegans , 2006, Journal of Experimental Biology.

[18]  T D Sanger,et al.  Human Arm Movements Described by a Low-Dimensional Superposition of Principal Components , 2000, The Journal of Neuroscience.

[19]  R. L. Russell,et al.  Normal and mutant thermotaxis in the nematode Caenorhabditis elegans. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[20]  E. Bizzi,et al.  Low dimensionality of supraspinally induced force fields. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[21]  S. Lockery,et al.  The awake behaving worm: simultaneous imaging of neuronal activity and behavior in intact animals at millimeter scale. , 2006, Journal of neurophysiology.

[22]  S. Lockery,et al.  Step Response Analysis of Thermotaxis in Caenorhabditis elegans , 2003, The Journal of Neuroscience.

[23]  Gürol M. Süel,et al.  An excitable gene regulatory circuit induces transient cellular differentiation , 2006, Nature.

[24]  R. Shingai,et al.  Computer-driven automatic identification of locomotion states in Caenorhabditis elegans , 2006, Journal of Neuroscience Methods.

[25]  S. Lehman.  The Neural and Behavioural Organization of Goal‐Directed Movements , 1990, Neurology.

[26]  P. Cosman,et al.  Quantitative classification and natural clustering of Caenorhabditis elegans behavioral phenotypes. , 2003, Genetics.

[27]  S. Lockery,et al.  Step-Response Analysis of Chemotaxis in Caenorhabditis elegans , 2003, The Journal of Neuroscience.

[28]  Nicolas Roussel,et al.  A Computational Model for C. elegans Locomotory Behavior: Application to Multiworm Tracking , 2007, IEEE Transactions on Biomedical Engineering.

[29]  S. Ward.  Chemotaxis by the nematode Caenorhabditis elegans: identification of attractants and analysis of the response by use of mutants. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[30]  W. Bialek,et al.  A sensory source for motor variation , 2005, Nature.

[31]  Andrew Smith.  Genome sequence of the nematode C-elegans: A platform for investigating biology , 1998 .

[32]  M. de Bono,et al.  Neuronal substrates of complex behaviors in C. elegans. , 2005, Annual review of neuroscience.

[33]  Cori Bargmann.  Genetic and cellular analysis of behavior in C. elegans. , 1993, Annual review of neuroscience.

[34]  J. Berg.  Genome sequence of the nematode C. elegans: a platform for investigating biology. , 1998, Science.

[35]  W. Bialek,et al.  Physical limits to sensation and perception. , 1987, Annual review of biophysics and biophysical chemistry.

[36]  A. Porporato,et al.  Langevin equations from time series. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  H. Berg,et al.  Physics of chemoreception. , 1977, Biophysical journal.

[38]  P. Cosman,et al.  Machine vision based detection of omega bends and reversals in C. elegans , 2006, Journal of Neuroscience Methods.

[39]  N. A. Croll.  Components and patterns in the behaviour of the nematode Caenorhabditis elegans , 2009 .

[40]  Aravinthan D. T. Samuel,et al.  Thermotaxis in Caenorhabditis elegans Analyzed by Measuring Responses to Defined Thermal Stimuli , 2002, The Journal of Neuroscience.

[41]  Christopher J. Taylor,et al.  Kernel Principal Component Analysis and the construction of non-linear Active Shape Models , 2001, BMVC.

[42]  Cori Bargmann,et al.  A circuit for navigation in Caenorhabditis elegans , 2005 .

[43]  D. Struik.  Lectures on classical differential geometry , 1951 .

[44]  Thomas M. Morse,et al.  The Fundamental Role of Pirouettes in Caenorhabditis elegans Chemotaxis , 1999, The Journal of Neuroscience.