A Simple Kinetic Model with Explicit Predictions for Nuclear Transport

Abstract

Molecular exchange between the cell nucleus and cytoplasm is one of the most fundamental features of eukaryotic cell biology. The nuclear pores act as a conduit of this transport, both for cargo that crosses the pore autonomously as well as that whose translocation requires an intermediary receptor. The major class of such receptors is regulated by the small GTPase Ran, via whose interaction the nucleo-cytoplasmic transport system functions as a selective molecular pump. We propose a simple analytical model for transport that includes both translocation and receptor binding kinetics. The model is suitable for steady-state kinetics such as fluorescence recovery after photobleaching. Time constants appear as a combination of parameters whose effects on measured kinetics are not separable. Competitive cargo binding to receptors and large cytoplasmic volume buffer the transport properties of any particular cargo. Specific limits to the solutions provide a qualitative insight and interpretation of nuclear transport in the cellular context. Most significantly, we find that under realistic conditions receptor binding, rather than permeability of the nuclear pores, may be rate-limiting for nucleo-cytoplasmic exchange.

Thermodynamic Paradigm for Solution Demixing Inspired by Nuclear Transport in Living Cells

“…This competition leads to a partitioning according to equilibrium binding affinities and may lead to vastly different kinetics. However the steady-state NL ratio (in solution) is independent of the affinity, reflecting thermodynamic control and equilibration of the chemical potentials [24,25,34]. Consistent with this paradigm, in which a net accumulation occurs together with a balanced bidirectional flux, the simulations show that the nuclear and cytoplasmic concentrations of the importincargo complex (X 4 and X 11 , respectively) equilibrate in steady-state.…”

“…Consistent with this paradigm, in which a net accumulation occurs together with a balanced bidirectional flux, the simulations show that the nuclear and cytoplasmic concentrations of the importincargo complex (X 4 and X 11 , respectively) equilibrate in steady-state. It is also interesting to note that RanGTP loading onto importin (reaction 4) was identified in the earlier analysis as the primary rate-limiting step in accumulation kinetics [34].…”

“…In addition, we also include the reverse conversion of RanGDP to RanGTP through the action of guanine Exchange Factor RCC1 (known as RanGEF). In addition to the standard model of nuclear transport whose biochemistry is summarized below, we also incorporates the backward reactions to account for the reversibile nature of this transport process [34]. Schematics of the reactions involved in nuclear transport.…”

“…Demixing is powered by transducing free energy from GTP hydrolysis through the interactions of transport re- ceptor with Ran. The transport machinery has been formulated in terms of coupled chemical kinetics [23,33,34] but the energetics have not yet been addressed. In particular, we ask: How does the rate of dissipation (energy consumption) relate to the achieved concentration gradient?…”

Competition between histone and transcription factor binding regulates the onset of transcription in zebrafish embryos

“…We suggest that this may limit the capacity of the nucleus to concentrate histones. The process of nuclear transport has been investigated in great detail (Kim and Elbaum, 2013a;2013b;Kopito and Elbaum, 2007; 2009) and we can assume that the nuclear envelope can create a certain fold difference in concentrations between the nucleus and cytoplasm. During the initial stages of zebrafish development, the nucleus occupies only a very small fraction of the cell volume (1.1% at 128-cell stage, Figure 4-figure supplement 1A).…”