Cooperativity Dominates the Genomic Organization of p53-Response Elements: A Mechanistic View

p53-response elements (p53-REs) are organized as two repeats of a palindromic DNA segment spaced by 0 to 20 base pairs (bp). Several experiments indicate that in the vast majority of the human p53-REs there are no spacers between the two repeats; those with spacers, particularly with sizes beyond two nucleotides, are rare. This raises the question of what it indicates about the factors determining the p53-RE genomic organization. Clearly, given the double helical DNA conformation, the orientation of two p53 core domain dimers with respect to each other will vary depending on the spacer size: a small spacer of 0 to 2 bps will lead to the closest p53 dimer-dimer orientation; a 10-bp spacer will locate the p53 dimers on the same DNA face but necessitate DNA looping; while a 5-bp spacer will position the p53 dimers on opposite DNA faces. Here, via conformational analysis we show that when there are 0–2 bp spacers, p53-DNA binding is cooperative; however, cooperativity is greatly diminished when there are spacers with sizes beyond 2 bp. Cooperative binding is broadly recognized to be crucial for biological processes, including transcriptional regulation. Our results clearly indicate that cooperativity of the p53-DNA association dominates the genomic organization of the p53-REs, raising questions of the structural organization and functional roles of p53-REs with larger spacers. We further propose that a dynamic landscape scenario of p53 and p53-REs can better explain the selectivity of the degenerate p53-REs. Our conclusions bear on the evolutionary preference of the p53-RE organization and as such, are expected to have broad implications to other multimeric transcription factor response element organization

Boundary Value Problem with Integral Condition for the Mixed Type Equation with a Singular Coefficient

© 2020, Springer Nature Switzerland AG. We study the boundary value problem for the mixed type equation with a singular coefficient and nonlocal integral first-kind condition. We establish the uniqueness criterion and prove the solution existence and stability theorems. The solution of the problem is constructed explicitly and the proof of convergence of the series in the class of regular solutions is derived