Ideas regarding the digital bacellaria

Collective Pattern Generators: behavioral signatures of environmental interactions

Main Idea:

Central Pattern Generators (CPGs) generate oscillations from a small neural circuit (pacemaker neurons). In neuronal systems, CPGs generate oscillations from a small neural circuit (pacemaker neurons).

In Bacillaria, we observe collective pattern generators (CoPGs), which are generated from collective and coordinated behavior. No central nervous system or brain is involved.

Aneural Architecture

Bacillaria behavior-generation system looks like the following:

• no spatial representation (free-moving), but does exhibit limited goal-directed behavior. Behaviors are explicitly spatial in that multicellular chains move in certain directions (not simply via Brownian motion).

• movement as the seat of intelligence, as suggested in particular Michael Graziano's "Intelligent Movement Machine".

• produces a set of sine waves, one for each pair of filaments. More complicated movements can result in other types of waveforms, but there is a basic oscillatory rhythm due to anatomical constrints.

• the entire chain produces an oscillator with harmonics (delayed by n degrees out-of-phase).

• potentially we may see spindles at the extremes of each cycle (pauses in oscillation or changes in orientation).

How to model:

• model sine waves, sinusoidals, and hybrid sinusoidal-tangent functions.

• how do these map measurements in the previous Bacillaria paper?

Each pair of filamentous cells act as an oscillatory unit in a CoPG. Oscillatory units overlap, so that a colony of 7 filaments consist of 6 oscillatory units. While they generally produce a sine wave, they can also stretch to a maximal value and stay there for long periods of time.

• introduce chains of x interconnected filaments.

• modeling modes of movement behavior from microscopy data.

CPGs in a stick insect: synergistic CPGs

Paper: Daun et.al (2019). Unravelling intra- and intersegmental neuronal connectivity between central pattern generating networks in a multi-legged locomotor system. PLoS One, 14(8), e0220767.

Dataset: Figshare

Figure showing integration of multiple legs.

Simulation:

Sine wave with tangent at quarter-phase

Sine wave with tangent at three-quarter phase

Two adjacent and overlapping pairs of oscillatory cell movements (sine waves, quarter-phase)

Two adjacent and overlapping pairs of oscillatory cell movements (sine waves, three-quarter phase)

Attractor map (based on sine waves, quarter-phase)

Sine wave with random (white) noise

Analysis

Using methods derived to analyze CPGs, we can use at least three types of technique: bifurcation analysis, a simple return map, and a Poincare maps. A recurrence map can be used in lieu of a Poincare map.

In terms of a state transition from oscillator to stretched out, do we observe halting behavior? Can this be controlled by the colony, or is this a random behavior?

We can use algorithmic information theory (Chaitin's constant) to approximate the random nature of this behavior. If this is random, then the CoPG can be relaxed due to exogenous forces (aging, hydrodynamics). If it is not random, then there is some endogenous control.

• simulate a range of stopping times (colony oscillates for n cycles, then halts). Use noise inputs to model physical contraints (reach a noise threshold, CoPG "relaxes" and thus halts.

Discussion.

Does a simple oscillator provide a means for intelligent behavior? An oscillator provides a deterministic signal that entrains behavior, but does not allow for computation nor information content.

• in terms of computation, stretching resembles a Turing machine, where stretching can resemble "halting" behaviors. Discuss CoPG relaxing conditions -- due to decoupling of neighbors, self-reinforcing dampening.

• in terms of information content, stopping and stretching allows for symmetry breaking, and thus information.

• more complex behaviors are not currently known.

References Arshavsky, Cellular and network properties in the functioning of the nervous system: from central pattern generators to cognition. Brain Research Reviews, 41(2–3), 229-267 (2003).

Graziano, The Intelligent Movement Machine. An Ethological Perspective on the Primate Motor System. Oxford University Press Oxford, UK (2009).

Hanczyc and Ikegami, Chemical Basis for Minimal Cognition, Artificial Life, 16: 233–243 (2010).

Marder and Bucher, Central pattern generators and the control of rhythmic movements. Current Biology, 11(23), R986-R996 (2011).