Diffusion of DNA-binding species in the nucleus: A transient anomalous subdiffusion model

Abstract

ABSTRACTSingle-particle tracking experiments have measured the distribution of escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. One important property of this distribution is that it is inconsistent with a Gaussian distribution of binding energies. Another is that it leads to transient anomalous subdiffusion, in which diffusion is anomalous at short times and normal at long times, here only mildly anomalous. Monte Carlo simulations are used to characterize the time-dependent diffusion coefficient D(t) in terms of the anomalous exponent α, the crossover time t(cross), and the limits D(0) and D(∞), and to relate these quantities to the escape time distribution. The simplest interpretations identifSubdiffusion of DNA-binding speciesy the escape time as the actual binding time to DNA, or the period of 1D diffusion on DNA in the standard model combining 1D and 3D search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. (a), The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. (b), Non-target DNA sites have a significant effect on search kinetics. False positives in bioinformatic searches of the genome are potentially rate-determining in vivo. For simple binding, the search would be speeded if false-positive sequences were eliminated from the genome. (c), Both binding and obstruction affect diffusion. Obstruction ought to be measured directly, using as the primary probe the DNA-binding species with the binding site inactivated, and eGFP as a calibration standard among laboratories and cell types. (d), Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. (e), The model provides a coarse-grained phenomenological description of diffusion of a DNA-binding species, useful in larger-scale modeling of kinetics, FCS, and FRAP.SIGNIFICANCEDNA-binding proteins such as transcription factors diffuse in the nucleus until they find their biological target and bind to it. A protein may bind to many false-positive sites before it reaches its target, and the search process is a research topic of considerable interest. Experimental results from the Dahan lab show a truncated power law distribution of escape times at these sites. We show by Monte Carlo simulations that this escape time distribution implies that the protein shows transient anomalous subdiffusion, defined as anomalous subdiffusion at short times and normal diffusion at long times. Implications of the model for experiments, controls, and interpretation of experiments are discussed.