Recognition and binding of specific sites on DNA by proteins is central for many cellular functions such as transcription, replication, and recombination. In the process of recognition, a protein rapidly searches for its specific site on a long DNA molecule and then strongly binds this site. Here we aim to find a mechanism that can provide both a fast search (1-10 s) and high stability of the specific protein-DNA complex (Kd=10(-15)-10(-8) M). Earlier studies have suggested that rapid search involves sliding of the protein along the DNA. Here we consider sliding as a one-dimensional diffusion in a sequence-dependent rough energy landscape. We demonstrate that, despite the landscape's roughness, rapid search can be achieved if one-dimensional sliding is accompanied by three-dimensional diffusion. We estimate the range of the specific and nonspecific DNA-binding energy required for rapid search and suggest experiments that can test our mechanism. We show that optimal search requires a protein to spend half of its time sliding along the DNA and the other half diffusing in three dimensions. We also establish that, paradoxically, realistic energy functions cannot provide both rapid search and strong binding of a rigid protein. To reconcile these two fundamental requirements we propose a search-and-fold mechanism that involves the coupling of protein binding and partial protein folding. The proposed mechanism has several important biological implications for search in the presence of other proteins and nucleosomes, simultaneous search by several proteins, etc. The proposed mechanism also provides a new framework for interpretation of experimental and structural data on protein-DNA interactions.

A number of vital biological processes rely on fast and precise recognition of a specific DNA sequence (site) by a protein. How can a protein find its site on a long DNA molecule among 10 6 -10 9 decoy sites? Here, we present our recent studies of the protein-DNA search problem. Seminal biophysical works suggested that the protein-DNA search is facilitated by 1D diffusion of the protein along DNA (sliding). We present a simple framework to calculate the mean search time and focus on several new aspects of the process such as the roles of DNA sequence and protein conformational flexibility. We demonstrate that coupling of DNA recognition with conformational transition within the protein-DNA complex is essential for fast search. To approach the complexity of the in vivo environment, we examine how the search can proceed at realistic DNA concentrations and binding constants. We propose a new mechanism for local distance-dependent search that is likely essential in bacteria. Simulations of the search on tightly packed DNA and crowded DNA demonstrate that our theoretical framework can be extended to correctly predicts search time in such complicated environments. We relate our findings to a broad range of experiments and summarize the results of our recent singlemolecule studies of a eukaryotic protein (p53) sliding along DNA.

Neuronal circuits' ability to maintain the delicate balance between stability and flexibility in changing environments is critical for normal neuronal functioning. However, to what extent individual neurons and neuronal populations maintain internal firing properties remains largely unknown. In this study, we show that distributions of spontaneous population firing rates and synchrony are subject to accurate homeostatic control following increase of synaptic inhibition in cultured hippocampal networks. Reduction in firing rate triggered synaptic and intrinsic adaptive responses operating as global homeostatic mechanisms to maintain firing macro-stability, without achieving local homeostasis at the single-neuron level. Adaptive mechanisms, while stabilizing population firing properties, reduced short-term facilitation essential for synaptic discrimination of input patterns. Thus, invariant ongoing population dynamics emerge from intrinsically unstable activity patterns of individual neurons and synapses. The observed differences in the precision of homeostatic control at different spatial scales challenge cell-autonomous theory of network homeostasis and suggest the existence of network-wide regulation rules.DOI: http://dx.doi.org/10.7554/eLife.04378.001

Many biological processes involve one dimensional diffusion over a correlated inhomogeneous energy landscape with a correlation length ξc. Typical examples are specific protein target location on DNA, nucleosome repositioning, or DNA translocation through a nanopore, in all cases with ξc ≈ 10 nm. We investigate such transport processes by the mean first passage time (MFPT) formalism, and find diffusion times which exhibit strong sample to sample fluctuations. For a a displacement N , the average MFPT is diffusive, while its standard deviation over the ensemble of energy profiles scales as N 3/2 with a large prefactor. Fluctuations are thus dominant for displacements smaller than a characteristic Nc ≫ ξc: typical values are much less than the mean, and governed by an anomalous diffusion rule. Potential biological consequences of such random walks, composed of rapid scans in the vicinity of favorable energy valleys and occasional jumps to further valleys, is discussed.

The hopping probabilities defined in Eq. (6) should be modified to include factors of 1 / 2 in the exponent:In this form, the system exhibits detailed balance and equilibrates at the temperature T =1/␤ for asymptotic times. The definition assumes the existence of energetic barriers ͕E i,i±1 ͖ between each pair of neighboring sites; the barriers' energies are assumed to be distributed independently of the on-site energies ͕U i ͖. The full expression for hopping rates is [1,2]where is the attempt frequency. Redefinition (6) of hopping probabilities influences the results and the conclusions of the paper in the following way.(1) Factor ␤ should be replaced by ␤ / 2 throughout the paper.(2) Since the temperature enters into the final formulas only through the combination ␤, the results and the implications remain valid for values of twice as large as were discussed in the paper.[1] J.