Biology subjects

Kilic, Z.

Publications and source records attributed to Kilic, Z..

3 recordsLinked to original sources

bioRxiv2020

A Continuous Time Representation of smFRET for the Extraction of Rapid Kinetics

Our goal is to learn kinetic rates from single molecule FRET (smFRET) data even if these exceed the data acquisition rate. To achieve this, we develop a variant of our recently proposed hidden Markov jump process (HMJP) with which we learn transition kinetics from parallel measurements in donor and acceptor channels. Our HMJP generalizes the hidden Markov model (HMM) paradigm in two critical ways: (1) it deals with physical smFRET systems as they switch between conformational states in continuous time; (2) it estimates the transition rates between conformational states directly without having recourse to transition probabilities or assuming slow dynamics (as is necessary of the HMM). Our continuous time treatment learns transition kinetics and photon emission rates for dynamical regimes inaccessible to the HMM which treats system kinetics in discrete time. We validate the robustness of our framework on simulated data and demonstrate its performance on experimental data from FRET labeled Holliday junctions.

biophysics↗

bioRxiv2020

Residence Time Analysis of RNA Polymerase Transcription Dynamics: A Bayesian Sticky HMM Approach

The time spent by a single RNA polymerase (RNAP) at specific locations along the DNA, termed "residence time", reports on the initiation, elongation and termination stages of transcription. At the single molecule level, this information can be obtained from dual ultra-stable optical trapping experiments, revealing a transcriptional elongation of RNAP interspersed with residence times of variable duration. Successfully discriminating between long and short residence times was used by previous approaches to learn about RNAPs transcription elongation dynamics. Here, we propose an approach based on the Bayesian sticky hidden Markov models that treats all residence times, for an E. Coli RNAP, on an equal footing without a priori discriminating between long and short residence times. In addition, our method has two additional advantages, we provide: full distributions around key point statistics; and directly treat the sequence-dependence of RNAPs elongation rate. By applying our approach to experimental data, we find: no emergent separation between long and short residence times warranted by the data; force dependent average residence time transcription elongation dynamics; limited effects of GreB on average backtracking durations and counts; and a slight drop in the average residence time as a function of applied force in RNaseAs presence. STATEMENT OF SIGNIFICANCEMuch of what we know about RNA Polymerase, and its associated transcription factors, relies on successfully discriminating between what are believed to be short and long residence times in the data. This is achieved by applying pause-detection algorithms to trace analysis. Here we propose a new method relying on Bayesian sticky hidden Markov models to interpret time traces provided by dual optical trapping experiments associated with transcription elongation of RNAP. Our method does not discriminate between short and long residence times from the offset in the analysis. It allows for DNA site-dependent transition probabilities of RNAP to neighboring sites (thereby accounting for chemical variability in site to site transitions) and does not demand any time trace pre-processing (such as denoising).

biophysics↗

bioRxiv2020

Generalizing HMMs to Continuous Time for Fast Kinetics: Hidden Markov Jump Processes

The hidden Markov model (HMM) is a framework for time series analysis widely applied to single molecule experiments. It has traditionally been used to interpret signals generated by systems, such as single molecules, evolving in a discrete state space observed at discrete time levels dictated by the data acquisition rate. Within the HMM framework, originally developed for applications outside the Natural Sciences, such as speech recognition, transitions between states, such as molecular conformational states, are modeled as occurring at the end of each data acquisition period and are described using transition probabilities. Yet, while measurements are often performed at discrete time levels in the Natural Sciences, physical systems evolve in continuous time according to transition rates. It then follows that the modeling assumptions underlying the HMM are justified if the transition rates of a physical process from state to state are small as compared to the data acquisition rate. In other words, HMMs apply to slow kinetics. The problem is, as the transition rates are unknown in principle, it is unclear, a priori, whether the HMM applies to a particular system. For this reason, we must generalize HMMs for physical systems, such as single molecules, as these switch between discrete states in continuous time. We do so by exploiting recent mathematical tools developed in the context of inferring Markov jump processes and propose the hidden Markov jump process (HMJP). We explicitly show in what limit the HMJP reduces to the HMM. Resolving the discrete time discrepancy of the HMM has clear implications: we no longer need to assume that processes, such as molecular events, must occur on timescales slower than data acquisition and can learn transition rates even if these are on the same timescale or otherwise exceed data acquisition rates.

biophysics↗