Nucleosomes, transcription, and probability

Abstract

Speaking of current measurements on single ion channel molecules, David Colquhoun wrote in 2006, “Individual molecules behave randomly, so suddenly we had to learn how to deal with stochastic processes.” Here I describe theoretical efforts to understand recent experimental observations on the chromatin structure of single gene molecules, a molecular biologist's path toward probabilistic theories.

From Structural Variation of Gene Molecules to Chromatin Dynamics and Transcriptional Bursting

“…However, such an assumption neither explains variation, nor does it seem physiologically reasonable. This leaves the following alternative explanation: single gene molecules visit each promoter nucleosome configuration over time, in some sequence (see below), with statistically distributed sojourn times in between transitions [ 12 ]; in other words, the variation across a population of molecules arises from the stochastic dynamical behavior of each single molecule. We shall refer to this conjecture as “ergodic hypothesis”.…”

“…The nucleosome configurations of the promoter are represented as nodes with directed edges (arrows) between them to indicate allowed transitions between configurations ( Figure 1 ). We call the set of nodes and directed edges a “transition graph” [ 12 ]. A stochastic process may be viewed as probability mass flowing between the nodes along the edges of the graph.…”

“…The refutability of mathematical models, e.g., a stochastic process, decreases with the number of freely adjustable model parameters (degrees of freedom). Therefore, explanations with fewer degrees of freedom must be preferred over those with more [ 12 ].…”

“…The following assumption of a “simple process” dramatically limits the degrees of freedom. The assumption is this: the kinetic parameter for the transition between two nucleosome configurations only depends on the “kind of transition” [ 4 , 12 ]. We may distinguish between three different kinds of transitions: assembly, disassembly, and sliding.…”

“…Dynamical conjectures, i.e. , transition graphs, may thus be refuted given an alternative conjecture of greater likelihood [ 4 , 12 ]. Graphs that are not strongly connected may be excluded without calculation, because for such graphs only a subset of the experimentally observed configurations would have a probability larger than zero at steady state.…”