Competitive ligand binding kinetics to linear polymers.

Different types of ligands compete in binding to polymers with different consequences for the physical and chemical properties of the resulting complex. Here, we derive a general kinetic model for the competitive binding kinetics of different types of ligands to a linear polymer, using the McGhee and von Hippel detailed binding-site counting procedure. The derived model allows the description of the competitive binding process in terms of the size of the ligand, binding, and release rates, and cooperativity parameters. We illustrate the implications of the general theory showing the equations for the competitive binding of two ligands. The size of the ligand, given by the number of monomers occluded, is shown to have a great impact on competitive binding. Ligands requiring a large available gap for binding are strongly inhibited by smaller ligands. Ligand size then has a leading role compared to binding affinity or cooperativity. For ligands that can bind in different modes (i.e., different number of monomers), this implies that they are more effective in covering or passivating the polymer in lower modes, if the different modes have similar binding energies.

Cooperative kinetics of ligand binding to linear polymers.

Ligands change the chemical and mechanical properties of polymers. In particular, single strand binding protein (SSB) non-specifically bounds to single-stranded DNA (ssDNA), modifying the ssDNA stiffness and the DNA replication rate, as recently measured with single-molecule techniques. SSB is a large ligand presenting cooperativity in some of its binding modes. We aim to develop an accurate kinetic model for the cooperative binding kinetics of large ligands. Cooperativity accounts for the changes in the affinity of a ligand to the polymer due to the presence of another bound ligand. Large ligands, attaching to several binding sites, require a detailed counting of the available binding possibilities. This counting has been done by McGhee and von Hippel to obtain the equilibrium state of the ligands-polymer complex. The same procedure allows to obtain the kinetic equations for the cooperative binding of ligands to long polymers, for all ligand sizes. Here, we also derive approximate cooperative kinetic equations in the large ligand limit, at the leading and next-to-leading orders. We found cooperativity is negligible at the leading-order, and appears at the next-to-leading order. Positive cooperativity (increased affinity) can be originated by increased binding affinity or by decreased release affinity, implying different kinetics. Nevertheless, the equilibrium state is independent of the origin of cooperativity and only depends on the overall increase in affinity. Next-to-leading approximation is found to be accurate, particularly for small cooperativity. These results allow to understand and characterize relevant ligand binding processes, as the binding kinetics of SSB to ssDNA, which has been reported to affect the DNA replication rate for several SSB-polymerase pairs.

DNA replication: In vitro single-molecule manipulation data analysis and models.

DNA replication is a key biochemical process of the cell cycle. In the last years, analysis of in vitro single-molecule DNA replication events has provided new information that cannot be obtained with ensembles studies. Here, we introduce crucial techniques for the proper analysis and modelling of DNA replication in vitro single-molecule manipulation data. Specifically, we review some of the main methods to analyze and model the real-time kinetics of the two main molecular motors of the replisome: DNA polymerase and DNA helicase. Our goal is to facilitate access to and understanding of these techniques to promotetheir use in the study of DNA replication at the single-molecule level. A proper analysis of single-molecule data is crucial to obtain a detailed picture of, among others, the kinetics rates, equilibrium contants and conformational changes of the system under study. The techniques presented here have been used or can be adapted to study the operation of other proteins involved in nucleic acids metabolism.

Noncooperative thermodynamics and kinetic models of ligand binding to polymers: Connecting McGhee-von Hippel model with the Tonks gas model.

Ligand binding to polymers modifies the physical and chemical properties of the polymers, leading to physical, chemical, and biological implications. McGhee and von Hippel obtained the equilibrium coverage as a function of the ligand affinity, through the computation of the possible binding sites for the ligand. Here, we complete this theory deriving the kinetic model for the ligand-binding dynamics and the associated equilibrium chemical potential, which turns out to be of the Tonks gas model type. At low coverage, the Tonks chemical potential becomes the Fermi chemical potential and even the ideal gas chemical potential. We also discuss kinetic models associated with these chemical potentials. These results clarify the kinetic models of ligand binding, their relations with the chemical potentials, and their range of validity. Our results highlight the inaccuracy of ideal and simplified kinetic approaches for medium and high coverages.

Spatial Scales of Population Synchrony in Predator-Prey Systems.

Many species show synchronous fluctuations in population size over large geographical areas, which are likely to increase their regional extinction risk. Here we examine how the degree of spatial synchrony in population dynamics is affected by trophic interactions using a two-species predator-prey model with spatially correlated environmental noise. We show that the predator has a larger spatial scale of population synchrony than the prey if the population fluctuations of both species are mainly determined by the direct effect of stochastic environmental variations in the prey. This result implies that in ecosystems regulated from the bottom up, the spatial scale of synchrony of the predator population increases beyond the scale of the spatial autocorrelation in the environmental noise and in the prey fluctuations. Harvesting the prey increases the spatial scale of population synchrony of the predator, while harvesting the predator reduces the spatial scale of the population fluctuations of its prey. Hence, the development of sustainable harvesting strategies should also consider the impact on unharvested species at other trophic levels as well as human perturbations of ecosystems, whether the result of exploitation or an effect on dispersal processes, as they can affect food web structures and trophic interactions over large geographical areas.