The Tumble

A bacterium two microns long is swimming in a drop of water toward a grain of sugar dissolving somewhere off in the murk. It has no eyes. It has no map. It does not know where the sugar is, and it does not know where it is; it has never known either, and it will reach the sugar anyway — will end up, reliably, in the richest patch of the drop. And it does this without being able to tell which way the sugar lies. It is far too small to compare the concentration at its front against its back; across two microns the difference is lost in molecular noise. And the ceaseless battering of water molecules turns it to a new heading within seconds, so a bearing, even if it had one, would not keep. It cannot point itself at anything. It arrives regardless.

The cell's machinery offers one pair of moves. Its several whip-like flagella, when their motors turn counterclockwise, wind together into a single corkscrew and drive it forward in a fairly straight line — a run. When one or more motors reverse, the bundle flies apart, the cell lurches and reorients, the filaments regather, and it swims off along a roughly new bearing; a tumble. A run of about a second, a tumble of a tenth of one, another run somewhere else: left alone, the alternation is a random walk, and it carries the cell nowhere in particular. Nothing in the machinery points toward food; there is no rudder, and nothing that could read one. When Howard Berg, in the early 1970s, built a microscope that could chase a single cell and clock it, this aimless stagger is what he saw.

What it can do instead is compare. As it swims a run it tastes the sugar where it happens to be, and holds that against what it was tasting a second or two before — a short rolling comparison, always of the present against the just-past, of whether things are getting better right now. It cannot read the gradient laid out in space, so it reads it in time, by moving through it. And it makes one use of the answer. If the sugar is thickening as it goes — if this run happens to be carrying it up the slope — it postpones its next tumble, and the run runs on. If nothing is improving, it tumbles on schedule and heads off elsewhere. It never turns toward the sugar; it cannot. It only lets the runs that happen to be going the right way last longer than the ones that are not.

And what it tastes is not the sugar but the change in it. The receptors doing the tasting are continually retuned, reset to treat whatever level they now sit in as a fresh zero, so that only a departure from it registers. The cell is not measuring the concentration, which it lets go of almost at once, but the trend. This is what lets a single plain rule work in a trace of sugar and in a near-drowning excess alike: a cell that clung to the actual levels would be swamped in the rich part of the drop and lost in the lean, while this one, keeping only the direction of change, reads a faint gradient and a steep one by the same light. The absolute level it discards; only the change survives to reach the motor.

It is tempting to call this feedback and be done — the cell reading its world and correcting its course, the way a thermostat reads the room and nudges it back toward seventy-two. But the thermostat has two things this cell lacks and cannot acquire. It has a setpoint, a fixed number it holds the room to; the bacterium, forever resetting its own zero, holds nothing to anything, has no level it is trying to reach. And the thermostat can act on its error — it registers that the room is three degrees cold and drives it warmer; the bacterium cannot sense direction at all, so it has no error to cancel, no colder or warmer to correct toward. With neither a target nor any way to steer at one, it is left with the single move available to a thing that cannot aim: it goes at random, and leans the randomness — a drunkard's walk given the faintest tilt uphill. The rise toward the sugar is not a course being corrected. It is a stagger that, run by run, goes up a little oftener than down, and the cell that seems to seek the sugar is only leaning, again and again, toward a second's worth of better.