Theory on the Dynamics of Oscillatory Loops in the Transcription Factor Networks

We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-buffering) whereas in case of -AND- type coupling the overall period of the system moves towards the perturbed oscillator. Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type. Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes. Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes.Comment: 37 pages, 13 figures, 2 table

Theory on the mechanism of DNA renaturation: Stochastic nucleation and zipping

Renaturation of complementary single strands of DNA is one of the important processes that requires better understanding in the view of molecular biology and biological physics. Here we develop a stochastic dynamical model on the DNA renaturation. According to our model there are at least three steps in the renaturation process viz. incorrect-contact formation, correct-contact formation and nucleation, and zipping. Most of the earlier two-state models combined nucleation with incorrect-contact formation step. In our model we suggest that it is considerably meaningful when we combine the nucleation with the zipping since nucleation is the initial step of zipping and the nucleated and zipping molecules are indistinguishable. Incorrect-contact formation step is a pure three-dimensional diffusion controlled collision process. Whereas nucleation involves several rounds of one-dimensional slithering dynamics of one single strand of DNA on the other complementary strand in the process of searching for the correct-contact and then initiate nucleation. Upon nucleation, the stochastic zipping follows to generate a fully renatured double stranded DNA. It seems that the square-root dependency of the overall renaturation rate constant on the length of reacting single strands originates mainly from the geometric constraints in the diffusion controlled incorrect-contact formation step. Further the inverse scaling of the renaturation rate on the viscosity of the reaction medium also originates from the incorrect-contact formation step. On the other hand the inverse scaling of the renaturation rate with the sequence complexity originates from the stochastic zipping which involves several rounds of crossing over the free-energy barrier at microscopic levels.Comment: 17 pages, 2 figure

Theory on the Coupled Stochastic Dynamics of Transcription and Splice-Site Recognition

Eukaryotic genes are typically split into exons that need to be spliced together to form the mature mRNA. The splicing process depends on the dynamics and interactions among transcription by the RNA polymerase II complex (RNAPII) and the spliceosomal complex consisting of multiple small nuclear ribonucleo proteins (snRNPs). Here we propose a biophysically plausible initial theory of splicing that aims to explain the effects of the stochastic dynamics of snRNPs on the splicing patterns of eukaryotic genes. We consider two different ways to model the dynamics of snRNPs: pure three-dimensional diffusion and a combination of three- and one-dimensional diffusion along the emerging pre-mRNA. Our theoretical analysis shows that there exists an optimum position of the splice sites on the growing pre-mRNA at which the time required for snRNPs to find the 5′ donor site is minimized. The minimization of the overall search time is achieved mainly via the increase in non-specific interactions between the snRNPs and the growing pre-mRNA. The theory further predicts that there exists an optimum transcript length that maximizes the probabilities for exons to interact with the snRNPs. We evaluate these theoretical predictions by considering human and mouse exon microarray data as well as RNAseq data from multiple different tissues. We observe that there is a broad optimum position of splice sites on the growing pre-mRNA and an optimum transcript length, which are roughly consistent with the theoretical predictions. The theoretical and experimental analyses suggest that there is a strong interaction between the dynamics of RNAPII and the stochastic nature of snRNP search for 5′ donor splicing sites

A review of compensation topologies and control techniques of bidirectional wireless power transfer systems for electric vehicle applications

Owing to the constantly rising energy demand, Internal Combustion Engine (ICE)-equipped vehicles are being replaced by Electric Vehicles (EVs). The other advantage of using EVs is that the batteries can be utilised as an energy storage device to increase the penetration of renewable energy sources. Integrating EVs with the grid is one of the recent advancements in EVs using Vehicle-to-Grid (V2G) technology. A bidirectional technique enables power transfer between the grid and the EV batteries. Moreover, the Bidirectional Wireless Power Transfer (BWPT) method can support consumers in automating the power transfer process without human intervention. However, an effective BWPT requires a proper vehicle and grid coordination with reasonable control and compensation networks. Various compensation techniques have been proposed in the literature, both on the transmitter and receiver sides. Selecting suitable compensation techniques is a critical task affecting the various design parameters. In this study, the basic compensation topologies of the Series-Series (SS), Series-Parallel (SP), Parallel-Parallel (PP), Parallel-Series (SP), and hybrid compensation topology design requirements are investigated. In addition, the typical control techniques for bidirectional converters, such as Proportional-Integral-Derivative (PID), sliding mode, fuzzy logic control, model predictive, and digital control, are discussed. In addition, different switching modulation schemes, including Pulse-Width Modulation (PWM) control, PWM + Phase Shift control, Single-Phase Shift, Dual-Phase Shift, and Triple-Phase Shift methods, are discussed. The characteristics and control strategies of each are presented, concerning the typical applications. Based on the review analysis, the low-power (Level 1/Level 2) charging applications demand a simple SS compensation topology with a PID controller and a Single-Phase Shift switching method. However, for the medium- or high-power applications (Level 3/Level 4), the dual-side LCC compensation with an advanced controller and a Dual-Side Phase-Shift switching pattern is recommended.Web of Science1520art. no. 781

Theory on the dynamics of feedforward loops in the transcription factor networks.

Feedforward loops (FFLs) consist of three genes which code for three different transcription factors A, B and C where B regulates C and A regulates both B and C. We develop a detailed model to describe the dynamical behavior of various types of coherent and incoherent FFLs in the transcription factor networks. We consider the deterministic and stochastic dynamics of both promoter-states and synthesis and degradation of mRNAs of various genes associated with FFL motifs. Detailed analysis shows that the response times of FFLs strongly dependent on the ratios (w(h) = γ(pc)/γ(ph) where h = a, b, c corresponding to genes A, B and C) between the lifetimes of mRNAs (1/γ(mh)) of genes A, B and C and the protein of C (1/γ(pc)). Under strong binding conditions we can categorize all the possible types of FFLs into groups I, II and III based on the dependence of the response times of FFLs on w(h). Group I that includes C1 and I1 type FFLs seem to be less sensitive to the changes in w(h). The coherent C1 type seems to be more robust against changes in other system parameters. We argue that this could be one of the reasons for the abundant nature of C1 type coherent FFLs

Precise Measurement of Tellurium Isotope Ratios in Terrestrial Standards Using a Multiple Collector Inductively Coupled Plasma Mass Spectrometry

Precise tellurium (Te) isotope ratio measurement using mass spectrometry is a challenging task for many decades. In this paper, Te isotope ratio measurements using multi-collector inductively coupled plasma mass spectrometry (MC–ICP–MS) in terrestrial Te standards have been reported. Newly developed Faraday cup with 1012 Ω resistor is used to measure low abundance 120Te, whereas the 1011 Ω resistor is used to measure other Te isotopes. The relative standard deviation obtained for Te isotope ratio measurement by Faraday cups of 120Te/128Te [0.002907(05)], 122Te/128Te [0.079646(10)], 123Te/128Te [0.027850(07)], 125Te/128Te [0.221988(09)], 126Te/128Te [0.592202(20)], and 130Te/128Te [1.076277(30)] were 0.140%, 0.014%, 0.026%, 0.005%, 0.004%, and 0.004%, respectively. The measured isotope ratio results are compared with previous results obtained by thermal ionization mass spectrometry (TIMS), negative thermal ionization mass spectrometry (N–TIMS), and MC–ICP–MS, showing an improvement in the precision about one order of magnitude for 120Te/128Te ratio. The present study shows better precision for Te isotope ratios compared to earlier studies

Dependency of filtering efficiency of P-P type (C1 type with AND-logic) FFL on the set of binding parameters

<p><b>.</b> Here the general settings are:  = 0.12,  = 0.0003,  = 4, <i>T</i> = 25 generation times, and was varied as (0.1, 0.2, 0.3, 0.4, 0.5, 1, 3 and 5). A. Input signal at the promoter of TF gene A. This has one short rectangular pulse with a width of <i>θ = </i>0.3 and a large one with <i>θ = </i>8 all are measured in terms of number of generation times. B. TF gene A responds similarly for all values of to both the signals irrespective of the binding strengths. The response seems to be proportional to the pulse width <i>θ</i> without any delay. C. As binding strength increase, the response of B also increases proportionately. D. There exists a cutoff value of above which the expression level of TF gene C is practically zero. With the current settings, this cutoff seems to occur at  = 1. Arrow shows the increasing direction of .</p

Parameters used to describe the interactions between various components of FFLs.

<p><b>Note</b>: This table describes various parameters associated with the different types of regulatory interactions in FFLs. The value <i>K_hk</i> is the dissociation constant connected with binding of protein of gene ‘<i>h</i>’ with promoter of gene ‘<i>k</i>’. The column AB denotes the regulation of the promoter of gene B by the protein product of A and so on.</p

Coefficient of variation (CV) associated with the fluctuations in the response times of various types of FFLs under strong binding conditions (

<p><b> = 0.001).</b> CV was calculated over 10⁵ numbers of stochastic trajectories. The coherent C1 type FFL possesses lower CV of response times than other FFLs whereas I1 type possesses highest CV of response times. A. Here the settings are that is applicable to both prokaryotes and eukaryotes such as yeast, was iterated from 0.001 to 10, and  = 4, <i>T</i> = 25 generation times. B. Here the settings are that is applicable to higher eukaryotes such as human, was iterated from 0.001 to 10, and  = 4, <i>T</i> = 25 generation times.</p