Genome-wide organization of eukaryotic pre-initiation complex is influenced by nonconsensus protein-DNA binding

Genome-wide binding preferences of the key components of eukaryotic pre-initiation complex (PIC) have been recently measured with high resolution in Saccharomyces cerevisiae by Rhee and Pugh (Nature (2012) 483:295-301). Yet the rules determining the PIC binding specificity remain poorly understood. In this study we show that nonconsensus protein-DNA binding significantly influences PIC binding preferences. We estimate that such nonconsensus binding contribute statistically at least 2-3 kcal/mol (on average) of additional attractive free energy per protein, per core promoter region. The predicted attractive effect is particularly strong at repeated poly(dA:dT) and poly(dC:dG) tracts. Overall, the computed free energy landscape of nonconsensus protein-DNA binding shows strong correlation with the measured genome-wide PIC occupancy. Remarkably, statistical PIC binding preferences to both TFIID-dominated and SAGA-dominated genes correlate with the nonconsensus free energy landscape, yet these two groups of genes are distinguishable based on the average free energy profiles. We suggest that the predicted nonconsensus binding mechanism provides a genome-wide background for specific promoter elements, such as transcription factor binding sites, TATA-like elements, and specific binding of the PIC components to nucleosomes. We also show that nonconsensus binding influences transcriptional frequency genome-wide

Sequence correlations shape protein promiscuity

We predict analytically that diagonal correlations of amino acid positions within protein sequences statistically enhance protein propensity for nonspecific binding. We use the term 'promiscuity' to describe such nonspecific binding. Diagonal correlations represent statistically significant repeats of sequence patterns where amino acids of the same type are clustered together. The predicted effect is qualitatively robust with respect to the form of the microscopic interaction potentials and the average amino acid composition. Our analytical results provide an explanation for the enhanced diagonal correlations observed in hubs of eukaryotic organismal proteomes [J. Mol. Biol. 409, 439 (2011)]. We suggest experiments that will allow direct testing of the predicted effect

Universal reduction of pressure between charged surfaces by long-wavelength surface charge modulation

We predict theoretically that long-wavelength surface charge modulations universally reduce the pressure between the charged surfaces with counterions compared with the case of uniformly charged surfaces with the same average surface charge density. The physical origin of this effect is the fact that surface charge modulations always lead to enhanced counterion localization near the surfaces, and hence, fewer charges at the midplane. We confirm the last prediction with Monte Carlo simulations.Comment: 8 pages 1 figure, Europhys. Lett., in pres

Nonspecific Transcription-Factor-DNA Binding Influences Nucleosome Occupancy in Yeast

AbstractQuantitative understanding of the principles regulating nucleosome occupancy on a genome-wide level is a central issue in eukaryotic genomics. Here, we address this question using budding yeast, Saccharomyces cerevisiae, as a model organism. We perform a genome-wide computational analysis of the nonspecific transcription factor (TF)-DNA binding free-energy landscape and compare this landscape with experimentally determined nucleosome-binding preferences. We show that DNA regions with enhanced nonspecific TF-DNA binding are statistically significantly depleted of nucleosomes. We suggest therefore that the competition between TFs with histones for nonspecific binding to genomic sequences might be an important mechanism influencing nucleosome-binding preferences in vivo. We also predict that poly(dA:dT) and poly(dC:dG) tracts represent genomic elements with the strongest propensity for nonspecific TF-DNA binding, thus allowing TFs to outcompete nucleosomes at these elements. Our results suggest that nonspecific TF-DNA binding might provide a barrier for statistical positioning of nucleosomes throughout the yeast genome. We predict that the strength of this barrier increases with the concentration of DNA binding proteins in a cell. We discuss the connection of the proposed mechanism with the recently discovered pathway of active nucleosome reconstitution

Counterions at charge-modulated substrates

We consider counterions in the presence of a single planar surface with a spatially inhomogeneous charge distribution using Monte-Carlo simulations and strong-coupling theory. For high surface charges, multivalent counterions, or pronounced substrate charge modulation the counterions are laterally correlated with the surface charges and their density profile deviates strongly from the limit of a smeared-out substrate charge distribution, in particular exhibiting a much increased laterally averaged density at the surface.Comment: 7 page

Multi-scale sequence correlations increase proteome structural disorder and promiscuity

Numerous experiments demonstrate a high level of promiscuity and structural disorder in organismal proteomes. Here we ask the question what makes a protein promiscuous, i.e., prone to non-specific interactions, and structurally disordered. We predict that multi-scale correlations of amino acid positions within protein sequences statistically enhance the propensity for promiscuous intra- and inter-protein binding. We show that sequence correlations between amino acids of the same type are statistically enhanced in structurally disordered proteins and in hubs of organismal proteomes. We also show that structurally disordered proteins possess a significantly higher degree of sequence order than structurally ordered proteins. We develop an analytical theory for this effect and predict the robustness of our conclusions with respect to the amino acid composition and the form of the microscopic potential between the interacting sequences. Our findings have implications for understanding molecular mechanisms of protein aggregation diseases induced by the extension of sequence repeats

Statistically enhanced self-attraction of random patterns

In this work we develop a theory of interaction of randomly patterned surfaces as a generic prototype model of protein-protein interactions. The theory predicts that pairs of randomly superimposed identical (homodimeric) random patterns have always twice as large magnitude of the energy fluctuations with respect to their mutual orientation, as compared with pairs of different (heterodimeric) random patterns. The amplitude of the energy fluctuations is proportional to the square of the average pattern density, to the square of the amplitude of the potential and its characteristic length, and scales linearly with the area of surfaces. The greater dispersion of interaction energies in the ensemble of homodimers implies that strongly attractive complexes of random surfaces are much more likely to be homodimers, rather than heterodimers. Our findings suggest a plausible physical reason for the anomalously high fraction of homodimers observed in real protein interaction networks.Comment: Submitted to PR

ОБ АСИМПТОТИЧЕСКОЙ ФОРМЕ УРАВНЕНИЯ ЛАНДАУ – ЛИФШИЦА НА ТРЕХМЕРНОМ ТОРЕ

We consider the Landau-Lifshitz equation on a three-dimensional torus. The equation is reduced to the form of the Euler equation for the geodesic left-invariant metric on the infinite-dimensional Lie algebra of the current group. The group of currents is given by a pointwise mapping of the three-dimensional torus into a three-dimensional orthogonal group. In Lie algebra we use the non-standard commutator introduced earlier. The solutions of the Landau-Lifshitz equation can be expanded in terms of the orthonormal basis of the left-invariant metric in the currents algebra. For the expansion coefficients of the solution of the Landau-Lifshitz equation, the explicit form of the evolution equations is deduced in the framework of the constructed model. To do this, we use the expressions obtained earlier for the sums of the adjoint and coadjoint action operators in an infinite-dimensional Lie algebra of currents with nonstandard commutator. The compactness property of the indicated sum operators makes it possible to obtain the asymptotic form of the Landau-Lifshitz equation on a threedimensional torus. Evolution equations are found on the subspace of flows consisting of vector fields whose Fourier expansions contain only simple harmonics of the form cos (kØ) Such vector fields form a subalgebra of the currents algebra which is also closed under the action of coadjoint operators. In this case, an arbitrary Landau-Lifshitz equation for which the vector of initial conditions lies in this subalgebra remains in it for all t for which this solution is defined. We note that to study the Landau-Lifshitz equation the currents algebra with the standard commutator turned out to be ineffective: in particular, the Landau-Lifshitz equation is not an Euler equation on the current algebra with a standard commutator. Thus, for the Landau-Lifshitz equation on the three-dimensional torus, the explicit form of the evolution equations for the coefficients of the Fourier expansion of its solutions by means of operators representing the sum of the operators of the adjoint and co-adjoint action of the current algebra on a three-dimensional torus with nonstandard commutator is obtained. Moreover, it is the property of compactness of the indicated sum operators (while, separately, their components, the operator of the adjoint action operator as well as the coadjoint one are not even continuous) made it possible to obtain the indicated asymptotic form. Рассматривается уравнение Ландау – Лифшица на трехмерном торе. Уравнение приводится к форме уравнения Эйлера на геодезические левоинвариантной метрики в бесконечномерной алгебре Ли группы токов. Группа токов задается поточечным отображением трехмерного тора в трехмерную ортогональную группу. В алгебре Ли используется введенный ранее нестандартный коммутатор. Решения уравнения Ландау – Лифшица разлагаются по ортонормированному базису левоинвариантной метрики в алгебре токов. Для коэффициентов разложения решения уравнения Ландау – Лифшица в рамках построенной модели вычисляется явный вид эволюционных уравнений. Для этого используются полученные ранее выражения для сумм операторов присоединенного и коприсоединенного действия в бесконечномерной алгебре Ли токов с нестандартным коммутатором. Свойство компактности указанных операторов суммы позволяет получить асимптотическую форму уравнения Ландау – Лифшица на трехмерном торе. Найдены эволюционные уравнения на подпространство потоков, состоящее из векторных полей, чьи Фурье-разложения содержат только простые гармоники вида cos . kf Такие векторные поля составляют подалгебру алгебры токов, которая является также замкнутой относительно действия коприсоединенных операторов. В таком случае произвольное уравнение Ландау – Лифшица, для которого вектор начальных условий лежит в этой подалгебре, останется в ней для всех t, для которых это решение определено. Отметим, что для изучения уравнения Ландау – Лифшица алгебра токов со стандартным коммутатором оказалась неэффективной: в частности, уравнение Ландау – Лифшица не является уравнением Эйлера на алгебре токов со стандартным коммутатором. Таким образом, для уравнения Ландау – Лифшица на трехмерном торе вычислен явный вид эволюционных уравнений на коэффициенты Фурье-разложений его решений при помощи операторов, представляющих собой сумму операторов присоединенного и коприсоединенного действия алгебры токов на трехмерном торе с нестандартным коммутатором. При этом именно свойство компактности указанных операторов суммы (в то время как по отдельности их составляющие оператор присоединенного и оператор коприсоединенного действий не являются даже непрерывными) позволило получить указанную асимптотическую форму.

О конструкции продолжения локальных бездивергентных векторных полей на Rn

The problem of a prolongation of non-divergent vector field, defined in a vicinity of zero in Rn t, to a finite non-divergent vector field on Rn is considered. Explicit formulas for the elements of the simple Lie algebra of non-divergent vector from the well-known Cartan series are obtained. This construction allows to move from the Euler equations for the ideal incompressible fluid to the Euler equations on finite-dimensional Lie groups.Рассматривается задача продолжения бездивергентных векторных полей, определенных в окрестности начала координат в Rn, до бездивергентных финитных наRn . Получены явные формулы продолжений для элементов простой алгебры Ли бездивергентных векторных полей известной серии Э. Картана. Конструкция позволяет перейти от уравнений Эйлера идеальной несжимаемой жидкости к уравнениям Эйлера на конечномерных группах Ли