Binding-rebinding dynamics of proteins interacting nonspecifically with a long DNA molecule

Facilitated Dissociation of Nucleoid Associated Proteins from DNA in the Bacterial Confinement

Transcription machinery depends on the temporal formation of protein-DNA complexes. Recent experiments demonstrated that not only the formation but also the lifetime of such complexes can affect the transcriptional machinery. In parallel, in vitro single-molecule studies showed that nucleoid-associated proteins (NAPs) leave the DNA rapidly as the bulk concentration of the protein increases via facilitated dissociation (FD). Nevertheless, whether such a concentration-dependent mechanism is functional in a bacterial cell, in which NAP levels and the 3d chromosomal structure are often coupled, is not clear a priori. Here, by using extensive coarse-grained molecular simulations, we model the unbinding of specific and nonspecific dimeric NAPs from a high-molecular-weight circular DNA molecule in a cylindrical structure mimicking the cellular confinement of a bacterial chromosome. Our simulations confirm that physiologically relevant peak protein levels (tens of micromolar) lead to highly compact chromosomal structures. This compaction results in rapid off rates (shorter DNA residence times) for specifically DNA-binding NAPs, such as the factor for inversion stimulation, which mostly dissociate via a segmental jump mechanism. Contrarily, for nonspecific NAPs, which are more prone to leave their binding sites via 1d sliding, the off rates decrease as the protein levels increase. The simulations with restrained chromosome models reveal that chromosome compaction is in favor of faster dissociation but only for specific proteins, and nonspecific proteins are not affected by the chromosome compaction. Overall, our results suggest that the cellular concentration level of a structural DNA-binding protein can be highly intermingled with its DNA residence time.

Development and Analysis of a Quantitative Mathematical Model of Bistability in the Cross Repression System Between APT and SLBO Within the JAK/STAT Signaling Pathway

Cell migration is a key component in development, homeostasis, immune function, and pathology. It is important to understand the molecular activity that allows some cells to migrate. Drosophila melanogaster is a useful model system because its genes are largely conserved with humans and it is straightforward to study biologically. The well-conserved transcriptional regulator Signal Transducer and Activator of Transcription (STAT) promotes cell migration, but its signaling is modulated by downstream targets Apontic (APT) and Slow Border Cells (SLBO). Inhibition of STAT activity by APT and cross-repression of APT and SLBO determines whether an epithelial cell in the Drosophila egg chamber becomes motile or remains stationary. Through mathematical modeling and analysis, we examine how the interaction of STAT, APT, and SLBO creates bistability in the Janus Kinase (JAK)/STAT signaling pathway. In this paper, we update and analyze earlier models to represent mechanistically the processes of the JAK/STAT pathway. We utilize parameter, bifurcation, and phase portrait analyses, and make reductions to the system to produce a minimal three-variable quantitative model. We analyze the manifold between migratory and stationary steady states in this minimal model and show that when the initial conditions of our model are near this manifold, cell migration can be delayed.

Diffusion of DNA-Binding Species in the Nucleus: A Transient Anomalous Subdiffusion Model

Single-particle tracking experiments have measured escape times of DNA-binding species diffusing in living cells: CRISPR-Cas9, TetR, and LacI. The observed distribution is a truncated power law. Working backward from the experimental results, the observed distribution appears inconsistent with a Gaussian distribution of binding energies. Working forward, the observed distribution 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 tcross, and the limits D(0) and D(∞) and to relate these quantities to the escape time distribution. The simplest interpretations identify the escape time as the actual binding time to DNA or the period of one-dimensional diffusion on DNA in the standard model combining one-dimensional and three-dimensional search, but a more complicated interpretation may be required. The model has several implications for cell biophysics. 1) The initial anomalous regime represents the search of the DNA-binding species for its target DNA sequence. 2) 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. 3) 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. 4) Overexpression of the DNA-binding species reduces anomalous subdiffusion because the deepest binding sites are occupied and unavailable. 5) 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.

DNA Mechanics and Topology

We review the current understanding of the mechanics of DNA and DNA-protein complexes, from scales of base pairs up to whole chromosomes. Mechanics of the double helix as revealed by single-molecule experiments will be described, with an emphasis on the role of polymer statistical mechanics. We will then discuss how topological constraints- entanglement and supercoiling-impact physical and mechanical responses. Models for protein-DNA interactions, including effects on polymer properties of DNA of DNA-bending proteins will be described, relevant to behavior of protein-DNA complexes in vivo. We also discuss control of DNA entanglement topology by DNA-lengthwise-compaction machinery acting in concert with topoisomerases. Finally, the chapter will conclude with a discussion of relevance of several aspects of physical properties of DNA and chromatin to oncology.

Receptor-Ligand Rebinding Kinetics in Confinement

Rebinding kinetics of molecular ligands plays a key role in the operation of biomachinery, from regulatory networks to protein transcription, and is also a key factor in design of drugs and high-precision biosensors. In this study, we investigate initial release and rebinding of ligands to their binding sites grafted on a planar surface, a situation commonly observed in single-molecule experiments and that occurs in vivo, e.g., during exocytosis. Via scaling arguments and molecular dynamic simulations, we analyze the dependence of nonequilibrium rebinding kinetics on two intrinsic length scales: the average separation distance between the binding sites and the total diffusible volume (i.e., height of the experimental reservoir in which diffusion takes place or average distance between receptor-bearing surfaces). We obtain time-dependent scaling laws for on rates and for the cumulative number of rebinding events. For diffusion-limited binding, the (rebinding) on rate decreases with time via multiple power-law regimes before the terminal steady-state (constant on-rate) regime. At intermediate times, when particle density has not yet become uniform throughout the diffusible volume, the cumulative number of rebindings exhibits a novel, to our knowledge, plateau behavior because of the three-dimensional escape process of ligands from binding sites. The duration of the plateau regime depends on the average separation distance between binding sites. After the three-dimensional diffusive escape process, a one-dimensional diffusive regime describes on rates. In the reaction-limited scenario, ligands with higher affinity to their binding sites (e.g., longer residence times) delay entry to the power-law regimes. Our results will be useful for extracting hidden timescales in experiments such as kinetic rate measurements for ligand-receptor interactions in microchannels, as well as for cell signaling via diffusing molecules.

Effects of electrostatic interactions on ligand dissociation kinetics

We study unbinding of multivalent cationic ligands from oppositely charged polymeric binding sites sparsely grafted on a flat neutral substrate. Our molecular dynamics simulations are suggested by single-molecule studies of protein-DNA interactions. We consider univalent salt concentrations spanning roughly a 1000-fold range, together with various concentrations of excess ligands in solution. To reveal the ionic effects on unbinding kinetics of spontaneous and facilitated dissociation mechanisms, we treat electrostatic interactions both at a Debye-Hückel (DH) (or implicit ions, i.e., use of an electrostatic potential with a prescribed decay length) level and by the more precise approach of considering all ionic species explicitly in the simulations. We find that the DH approach systematically overestimates unbinding rates, relative to the calculations where all ion pairs are present explicitly in solution, although many aspects of the two types of calculation are qualitatively similar. For facilitated dissociation (FD) (acceleration of unbinding by free ligands in solution) explicit-ion simulations lead to unbinding at lower free-ligand concentrations. Our simulations predict a variety of FD regimes as a function of free-ligand and ion concentrations; a particularly interesting regime is at intermediate concentrations of ligands where nonelectrostatic binding strength controls FD. We conclude that explicit-ion electrostatic modeling is an essential component to quantitatively tackle problems in molecular ligand dissociation, including nucleic-acid-binding proteins.

Facilitated Dissociation Kinetics of Dimeric Nucleoid-Associated Proteins Follow a Universal Curve

Recent experimental work has demonstrated facilitated dissociation of certain nucleoid-associated proteins that exhibit an unbinding rate that depends on the concentration of freely diffusing proteins or DNA in solution. This concentration dependence arises due to binding competition with these other proteins or DNA. The identity of the binding competitor leads to different qualitative trends, motivating an investigation to understand observed differences in facilitated dissociation. We use a coarse-grained simulation that takes into account the dimeric nature of many nucleoid-associated proteins by allowing an intermediate binding state. The addition of this partially bound state allows the protein to be unbound, partially bound, or fully bound to a DNA strand, leaving opportunities for other molecules in solution to participate in the unbinding mechanism. Previous models postulated symmetric binding energies for each state of the coarse-grained protein corresponding to the symmetry of the dimeric protein; this model relaxes this assumption by assigning different energies for the different steps in the unbinding process. Allowing different unbinding energies not only has equilibrium effects on the system, but kinetic effects as well. We were able to reproduce the unbinding trends seen experimentally for both DNA and protein competitors. All trends collapse to a universal curve regardless of the unbinding energies used or the identity of the dissociation facilitator, suggesting that facilitated dissociation can be described with a single set of scaling parameters that are related to the energy landscape and geometric nature of the competitors.

How nonspecifically DNA-binding proteins search for the target in crowded environments

We investigate how a tracer particle searches a target located in DNA modeled by a stiff chain in crowded environments using theoretical analysis and Langevin dynamics simulations. First, we show that the three-dimensional (3D) diffusion coefficient of the tracer only depends on the density of crowders ϕ, while its one-dimensional (1D) diffusion coefficient is affected by not only ϕ but also the nonspecific binding energy ε. With increasing ϕ and ε, no obvious change in the average 3D diffusion time is observed, while the average 1D sliding time apparently increases. We propose theoretically that the 1D sliding of the tracer along the chain could be well captured by the Kramers' law of escaping rather than the Arrhenius law, which is verified directly by the simulations. Finally, the average search time increases monotonously with an increase in ϕ while it has a minimum as a function of ε, which could be understood from the different behaviors of the average number of search rounds with the increasing ϕ or ε. These results provide a deeper understanding of the role of facilitated diffusion in target search of proteins on DNA in vivo.

Method for the analysis of contribution of sliding and hopping to a facilitated diffusion of DNA-binding protein: Application to in vivo data

DNA-binding protein searches for its target, a specific site on DNA, by means of diffusion. The search process consists of many recurrent steps of one-dimensional diffusion (sliding) along the DNA chain and three-dimensional diffusion (hopping) after dissociation of a protein from the DNA chain. Here we propose a computational method that allows extracting the contribution of sliding and hopping to the search process in vivo from the measurements of the kinetics of the target search by the lac repressor in Escherichia coli [P. Hammar et al., Science 336, 1595 (2012)]. The method combines lattice Monte Carlo simulations with the Brownian excursion theory and includes explicitly steric constraints for hopping due to the helical structure of DNA. The simulation results including all experimental data reveal that the in vivo target search is dominated by sliding. The short-range hopping to the same base pair interrupts one-dimensional sliding while long-range hopping does not contribute significantly to the kinetics of the search of the target in vivo.

Biophysics of protein-DNA interactions and chromosome organization

The function of DNA in cells depends on its interactions with protein molecules, which recognize and act on base sequence patterns along the double helix. These notes aim to introduce basic polymer physics of DNA molecules, biophysics of protein-DNA interactions and their study in single-DNA experiments, and some aspects of large-scale chromosome structure. Mechanisms for control of chromosome topology will also be discussed.