Biological processes as exploratory dynamics.

Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure, or function is achieved. A classic example is the way in which microtubules attach to kinetochores as a prerequisite for chromosome segregation and cell division. In this example, the dynamics is characterized by apparently futile time histories in which microtubules repeatedly grow and shrink without chromosomal attachment. We hypothesize that for biological processes for which it is not the initial conditions that matter, but rather the final state, this kind of exploratory dynamics is biology's unique and necessary solution to achieving these functions with high fidelity. This kind of cause-and-effect relationship can be contrasted to examples from physics and chemistry where the initial conditions determine the outcome. In this paper, we examine the similarities of many biological processes that depend upon random trajectories starting from the initial state and the selection of subsets of these trajectories to achieve some desired functional final state. We begin by reviewing the long history of the principles of dynamics, first in the context of physics, and then in the context of the study of life. These ideas are then stacked up against the broad categories of biological phenomenology that exhibit exploratory dynamics. We then build on earlier work by making a quantitative examination of a succession of increasingly sophisticated models for exploratory dynamics, all of which share the common feature of being a series of repeated trials that ultimately end in a "winning" trajectory. We also explore the ways in which microscopic parameters can be tuned to alter exploratory dynamics as well as the energetic burden of performing such processes. It is a great privilege to take part in this special volume dedicated to the life and work of Prof. Erich Sackmann (1934-2024). For one of us (R.P.), at the time of making a switch from traditional condensed matter physics to a life engaged in the study of life, he went to a meeting near Munich that completely opened his eyes to the ways in which the approach of physics could be brought to bear on the study of the living. Sackmann's work was an inspiring presence at that meeting. One of the hallmarks of his work was a principled approach to dissecting biological processes over a range of scales and phenomena. One common thread to much of his work was that it acknowledged the dynamical character of living organisms. The present paper attempts to follow in the tradition of Sackmann's studies of dynamics by suggesting a new way of looking at many biological processes all through the unifying perspective of what we will call exploratory dynamics.