Of bees and extracellular matrices

Six feet apart. Une distance d’un mètre. Eineinhalb Meter Abstand. Two metres away. The new metric comes in chunks the size of nation states. This is where its elasticity already ends.

The new metric is usually invisible, yet constantly conceived and observed by its inhabitants, therefore virtualised and enacted. However, it is suspended in a fragile state. When it is threatened to contract or collapse, it needs to be materialised. Meticulously drawn fields of squares, circles and crosses help imagine this quantisation of space into distinctive and discrete cellulae of life, for commuters, homeless, park dwellers and protesters to inhabit.

These grids are spanned along two perpendicular axes, organised in rows and columns, rank and files, allowing easy access and addressing. They adapt to the physical space, are confined to it and are sometimes left to expand in any direction if necessary. Even if it has not fully materialised, the new metric seeks to spread out in space. Potentially, it is omnipresent.

The grid is also porous. It always reserves a public space bounding all these monadic safe spaces, a room for traffic, international waters of non-interference. But just as in living bodies, this extracellular space does more than is visible to the eye. It provides scaffolding and structure for cells to settle within, defines their direction of spread as well as boundaries to their size. It dictates which types of cells are allowed to settle and stimulates them to adopt behaviour suitable for the context it specifies.

In contrast, the new metric lacks in flexibility and adaptability what the extracellular matrix of human and other tissues easily achieves. It is stiff and inert, unable to adapt to local perturbations and overall inefficient. Its biological counterpart, on the other hand, will naturally fill up space with close to the highest possible density. Biological tissue seeks to fill in gaps, lets cells shrink and grow, move and settle if needed, but allows each to maintain a locally defined distance to each other.

From a mathematical description, biological tissues achieve close to optimal packing densities in a three-dimensional non-uniformly sized sphere packing problem. Packing density is defined as the ratio of space filled with bodies to the total of space they are allowed to settle in. The optimal packing density η of uniformly sized spheres in a three-dimensional space is 0.7406. For spheres of varying size – much like in most biological and physical systems – its value is unknown, yet they spontaneously arrange in lattices and irregular patterns that represent an equilibrium of the forces enacted on them.

A Cartesian system – that is, a lattice where each object is aligned along straight rows and columns, is far from being optimal. For equally sized spheres, its density is only 0.524. Such a Cartesian system is exemplified by the new metric. When drawn with chalk on the pavement, it is always a rectilinear grid of squares, circles or crosses, in other words: a waste of space.

Yet another biological system can teach us how to cram more people into a protest and how to cover more of our parks’ grass with blankets. Think of the honey bee and its hive. It is a crowded space, but it is a wonder of efficiency and order. The insects, of course, store their honey in combs, the best way to make use of limited space. Its hexagonal pattern is proven to be optimal for circle packing in a plane – more than 90 per cent of coverage achieved. Let’s learn from the honey bee and design a new new metric.