Telomeres constitute the nucleoprotein ends of eukaryotic chromosomes which are essential for their proper function. Telomere end binding protein (TEBP) from Oxytricha nova was among the first telomeric proteins, which were well characterized biologically. TEBP consists of two protein subunits (alpha, beta) and forms a ternary complex with single stranded telomeric DNA containing tandem repeats TTTTGGGG. This work presents the characterization of the thermodynamic and electrostatic properties of this complex by computational chemistry methods (continuum Poisson-Boltzmann and solvent accessible surface calculations). Our calculations give a new insight into molecular properties of studied system. Based on the thermodynamic analysis we provide a rationale for the experimental observation that alpha and ssDNA forms a binary complex and the beta subunit joins alpha:ssDNA complex only after the latter is formed. Calculations of distribution of the molecular electrostatic potential for protein subunits alone and for all possible binary complexes revealed the important role of the "guiding funnel" potential generated by alpha:ssDNA complex. This potential may help the beta subunit to dock to the already formed alpha:DNA intermediate in highly steric and electrostatic favorable manner. Our pK(a) calculations of TEBP are able to explain the experimental mobility shifts of the complex in electrophoretic non-denaturating gels.