Multiscale approach to radiation damage induced by ion beams: complex DNA damage and effects of thermal spikes

We present the latest advances of the multiscale approach to radiation damage caused by irradiation of a tissue with energetic ions and report the most recent advances in the calculations of complex DNA damage and the effects of thermal spikes on biomolecules. The multiscale approach aims to quantify the most important physical, chemical, and biological phenomena taking place during and following irradiation with ions and provide a better means for clinically-necessary calculations with adequate accuracy. We suggest a way of quantifying the complex clustered damage, one of the most important features of the radiation damage caused by ions. This method can be used for the calculation of irreparable DNA damage. We include thermal spikes, predicted to occur in tissue for a short time after ion's passage in the vicinity of the ions' tracks in our previous work, into modeling of the thermal environment for molecular dynamics analysis of ubiquitin and discuss the first results of these simulations.Comment: 14 pages, 3 figures, submitted to EPJ

Alpha helix-coil phase transition: analysis of ab initio theory predictions

In the present paper we present results of calculations obtained with the use of the theoretical method described in our preceding paper [1] and perform detail analysis of alpha helix-random coil transition in alanine polypeptides of different length. We have calculated the potential energy surfaces of polypeptides with respect to their twisting degrees of freedom and construct a parameter-free partition function of the polypeptide using the suggested method [1]. From the build up partition function we derive various thermodynamical characteristics for alanine polypeptides of different length as a function of temperature. Thus, we analyze the temperature dependence of the heat capacity, latent heat and helicity for alanine polypeptides consisting of 21, 30, 40, 50 and 100 amino acids. Alternatively, we have obtained same thermodynamical characteristics from the use of molecular dynamics simulations and compared them with the results of the new statistical mechanics approach. The comparison proves the validity of the statistical mechanic approach and establishes its accuracy.Comment: 34 pages, 12 figure

On the variance of the number of occupied boxes

We consider the occupancy problem where balls are thrown independently at infinitely many boxes with fixed positive frequencies. It is well known that the random number of boxes occupied by the first n balls is asymptotically normal if its variance V_n tends to infinity. In this work, we mainly focus on the opposite case where V_n is bounded, and derive a simple necessary and sufficient condition for convergence of V_n to a finite limit, thus settling a long-standing question raised by Karlin in the seminal paper of 1967. One striking consequence of our result is that the possible limit may only be a positive integer number. Some new conditions for other types of behavior of the variance, like boundedness or convergence to infinity, are also obtained. The proofs are based on the poissonization techniques.Comment: 34 page

Ab initio theory of helix-coil phase transition

In this paper we suggest a theoretical method based on the statistical mechanics for treating the alpha-helix-random coil transition in alanine polypeptides. We consider this process as a first-order phase transition and develop a theory which is free of model parameters and is based solely on fundamental physical principles. It describes essential thermodynamical properties of the system such as heat capacity, the phase transition temperature and others from the analysis of the polypeptide potential energy surface calculated as a function of two dihedral angles, responsible for the polypeptide twisting. The suggested theory is general and with some modification can be applied for the description of phase transitions in other complex molecular systems (e.g. proteins, DNA, nanotubes, atomic clusters, fullerenes).Comment: 24 pages, 3 figure

Fluctuation of maximal particle energy of quantum ideal gas and random partitions

We investigate the limiting distribution of the fluctuations of the maximal summand in a random partition of a large integer with respect to a multiplicative statistics. We show that for a big family of Gibbs measures on partitions (so called generalized Bose--Einstein statistics) this distribution is the well-known Gumbel distribution which usually appears in the context of indepedent random variables. In particular, it means that the (properly rescaled) maximal energy of an individual particle in the grand canonical ensemble of the $d$-dimensional quantum ideal gas has the Gumbel distribution in the limit. We also apply our result to find the fluctuations of the height of a random 3D Young diagram (plane partition) and investigate the order statistics of random partitions under generalized Bose--Einstein statistics.Comment: 13 p., Ref. 1