Estimates for the Prebiotic Reaction Volume Necessary for the Origin of Life

The prebiotic chemistry necessary for the development of life requires a low-probability combination of steps to reach the complexity of a living cell. An unanswered question is how big the reaction space must be to favor this process, if it is driven by stochastic forces. The space must be large enough and diverse enough to provide reaction centers as well as storage reservoirs to hold chemical intermediates. Using the carbon footprint of various lifeforms on Earth and their average cell masses, the number of cells alive today in various taxa can be calculated. It is shown that as cells increase in mass and complexity, they occupy progressively smaller shares of the biosphere and exist in smaller numbers. Conversely, the basic units of life increase in number as complexity decreases. Following this trajectory to the starting atomic elements of life yields a count of the CHNOPS needed to enable prebiotic chemistry to begin. Estimates of the starting volume of water necessary to contain this number of elements approaches the volume of Earth's oceans. Furthermore, assigning the cell counts of various taxa to their times of first appearance on Earth yields a linear regression that can be extrapolated back in time to a point when only CHNOPS existed. This occurs at ~9.0 Gyr before the present. The implications of these findings are discussed, with a particular focus on a world existing 9 Gyr ago, with characteristics similar to Europa, with a large, protected water environment that can store chemical intermediates over a long time and thereby support combinatoric prebiotic chemistry.