Run and Tumble

An E. coli bacterium has no nervous system and cannot see where food is. It swims in straight runs, tumbles at random, and compares the nutrient signal it senses now with what it sensed over the last few seconds. When things are getting better, it tumbles less.

The green shading is the nutrient signal (attractant concentration). The simulation models chemical guidance only: the cells do not eat, grow, divide, or use up the nutrient.

Nutrient signal (attractant concentration) ▼ = focal cell

Focal bacterium

RUN
Attractant concentration here
Sensory signal now, s
Adapting reference, m
Tumble rate, λ

Last 20 simulated seconds. Green shading: signal above reference. Red shading: below. Lower lane: tumble rate on a log scale; dashed line is the baseline.

Statistics

How the algorithm works

Each bacterium runs the same short program, and it runs it whatever the environment. Every 0.01 simulated seconds it does four things:

  1. Sense. It reads the attractant concentration c at its own position, and nowhere else. It never sees the field, the slope, other cells, or where the food is.
  2. Compare. It converts c into a signal s, and keeps a slowly adapting reference m: a running average of the signal over the last few seconds. The difference s − m says whether things are better or worse than they were recently.
  3. Set the tumble rate. If things are improving, the tumble rate falls; if they are worsening, it rises. Even at its lowest the rate is above zero, so no run is guaranteed to continue, and even at its highest a tumble is only more likely, never certain.
  4. Move. While running it swims at constant speed with a little random wobble. When a tumble happens it nearly stops and turns by a random angle, chosen without any reference to the nutrient.

These words describe the computation, not an experience. “Improving” means only that s is greater than m.

The code that is running. The listings below are read from the live program, so they are exactly what the simulation executes.


      

      

      
This is a phenomenological teaching model, not a reconstruction of the molecular pathway. In a real cell, attractant binding to receptor clusters reduces the activity of the kinase CheA, which lowers phosphorylated CheY and so makes the flagellar motors less likely to switch into the clockwise rotation that causes a tumble. Slow methylation of the receptors by CheR and CheB plays the role of the adapting reference m.

    

  


  

    Advanced parameters
    

      
Changes take effect immediately and keep the cells where they are, except population size and seed, which apply when you restart.

      

      

        
        Freezes the reference m at the 2 µM background signal (τ = ∞), so the tumble rate depends on how rich the spot is rather than on whether it is getting richer. A counterfactual cell, for comparison.