Two Problems In Biophysics: Brownian Motors And The Detection Of Microbial Community

Biophysics is a rapidly developing interdiscipline in recent years,which applies many principles and approaches in physics to biology,explaining the phenomena of life at di?erent levels from single molecules to systems.And the technical advances in physics are also beneficial for the reveal of molecular structure and function in biology.Therefore,there is a wealth of content in biophysics,in which our research includes two frontier problems based on di?erent computational methods: one problem is the directed motion of Brownian motors related closely to the directed transport and the generation of forces in biological systems,and another problem is the detection of microbial community concerning how to analyze the data from high-throughput sequencers.In the directed motion of Brownian motors,we study one kind of Brownian motors simplified from the Feynman Ratchet systematically.After going over its calculation,we find that one special Brownian motor named the Triangula would drift anomalously under some initial temperatures if the mass of particles in the two baths are not equal to each other,which is also supported by the stochastic simulation.By considering the physical realization in reality,we particularly discuss the motion of Brownian motors in one single bath with temperature gradient.Then,we extend the translational Brownian motors to the rotational ones,proposing a two-headed rotational Brownian motor with directed rotation driven by temperature gradient.The steady angular velocity of the rotational Brownian motor is also calculated analytically and confirmed by particles' dynamics simulation at the same time.In order to obtain more stable average rotation,we further extend the two-headed Brownian motor to four-headed and even manyheaded Brownian motors.Finally,we discuss the freely moving Brownian motors with multiple degrees of freedom,which are found to have similar dynamic behaviors with the constrained ones,and we also figure out one application for them in biology??the separation of enantiomers.The detection of microbial community composition is an important and challenging task in microbiology.A few statistical methods based on convex optimization have been proposed to partially replace the accurate but time-consuming approaches through clustering plus alignment to speedup the detection algorithms.We investigate the k-mer statistics usually used as the representation of RNA/DNA sequences in these statistical methods,and construct a new feature vector that consists of Legendre expansion coe cients of sequences aimed at its defects such as the slow generation,the sequence order information loss and the exponentially increase with parameter k of dimensionality.This new feature vector is generated much faster than k-mer statistics and proven as an e?ective representation of sequences.We carry out experiments on two datasets of bacterial 16 S rRNA sequences,and it turns out that the detection algorithm used the new feature vector can perform with higher speed and without much loss of accuracy under proper expansion order,compared with existing methods.