Now showing 1 - 6 of 6
  • Placeholder Image
    Publication
    A lattice model on the rate of in vivo site-specific DNA-protein interactions
    (01-01-2021)
    We develop a lattice model of site-specific DNA-protein interactions under in vivo conditions where DNA is modelled as a self-avoiding random walk that is embedded in a cubic lattice box resembling the living cell. The protein molecule searches for its cognate site on DNA via a combination of three dimensional (3D) and one dimensional (1D) random walks. Hopping and intersegmental transfers occur depending on the conformational state of DNA. Results show that the search acceleration ratio (= search time in pure 3D route/search time in 3D and 1D routes) asymptotically increases towards a limiting value as the dilution factor of DNA (= volume of the cell/the volume of DNA) tends towards infinity. When the dilution ratio is low, then hopping and intersegmental transfers significantly enhance the search efficiency over pure sliding. At high dilution ratio, hopping does not enhance the search efficiency much since under such situation DNA will be in a relaxed conformation that favors only sliding. In the absence of hopping and intersegmental transfers, there exists an optimum sliding time at which the search acceleration ratio attains a maximum in line with the current theoretical results. However, existence of such optimum sliding length disappears in the presence of hopping. When the DNA is confined in a small volume inside the cell resembling a natural cell system, then there exists an optimum dilution and compression ratios (= total cell volume/volume in which DNA is confined) at which the search acceleration factor attains a maximum especially in the presence of hopping and intersegmental transfers. These optimum values are consistent with the values observed in the Escherichia coli cell system. In the absence of confinement of DNA, position of the specific binding site on the genomic DNA significantly influences the search acceleration. However, such position dependent changes in the search acceleration ratio will be nullified in the presence of hopping and intersegmental transfers especially when the DNA is confined in a small volume that is embedded in an outer cell.
  • Placeholder Image
    Publication
    Approximate solutions to the response time problems of transcription autoregulatory gene networks
    (01-03-2022)
    The response time is the time required by a gene expression machinery to generate half of its steady state protein level. Response time decides how fast a gene regulatory motif can response to an external adverse signal. The differential kinetic rate equations associated with the response time of the autoregulatory gene networks are generally nonlinear and they are not solvable analytically. We derive analytical approximations for the response time of unregulated, positive and negative autoregulated gene expression systems. We further show that our approximations are accurately in line with the numerical simulations over wide range of parameter values. Results suggest a linear increase in the response times with respect to changes in the ratio of the lifetimes of protein-product and mRNA in all the unregulated, positive and negative autoregulated gene expression systems. There exists of an optimum affinity condition for the promoter-protein product interactions of the positive autoregulatory motif at which the response time attains a maximum. We argue that such maximum response-time originates mainly from the unbinding dynamics of the protein-product from the respective promoter.
  • Placeholder Image
    Publication
    Multiple transcription auto regulatory loops can act as robust oscillators and decision-making motifs
    (01-01-2022) ;
    Kreiman, Gabriel
    Response time decides how fast a gene can react against an external signal at the transcription level in a signalling cascade. The steady state protein levels of the responding genes decide the coupling between two consecutive members of a signalling cascade. A negative autoregulatory loop (NARL) present in a transcription factor network can speed up the response time of the regulated gene at the cost of reduced steady state protein level. We present here a multi NARL motif which can be tuned for both the steady state protein level as well as response time in the required direction. Remarkably, there exists an optimum Hill coefficient nopt ≅4 at which the response time of the NARL motif is at minimum. When the Hill coefficient is n < nopt, then under strong binding conditions, one can raise the steady state protein level by increasing the gene copy number with almost no change in the response time of the multi NARL motif. Using detailed computational analysis, we show that the coupled multi NARL and positive auto regulatory loop (PARL) motifs can act as an oscillator as well as decision making component which are robust against extrinsic fluctuations in the control parameters. We further demonstrate that the period of oscillation of the coupled multi NARL-PARL dual feedback oscillator can also be fine-tuned by the gene copy number apart from the inducer concentration. We finally demonstrate robustness of bistable dual feedback decision making motifs with multi autoregulatory loop component.
  • Placeholder Image
    Publication
    Theory on the looping mediated directional-dependent propulsion of transcription factors along DNA
    We show that the looping mediated transcription activation by the combinatorial transcription factors (TFs) can be achieved via directional-dependent propulsion, tethered sliding and tethered binding-sliding-unbinding modes. In the propulsion mode, the first arrived TF at the cis-regulatory motifs (CRMs) further recruits other TFs via protein-protein interactions. Such TFs complex has two different types of DNA binding domains (DBDs) viz. DBD1 which forms tight site-specific complex with CRMs via hydrogen bonding network and the promoter specific DBD2s which form nonspecific interactions around CRMs. When the sum of these specific and cumulative nonspecific interactions is sufficient, then the flanking DNA of CRMs will be bent into a circle over the TFs complex. The number of TFs involved in the combinatorial regulation plays critical role here. When the site-specific interactions and the cumulative nonspecific interactions are strong enough to resist the dissociation, then the sliding of DBD2s well within the Onsager radius associated with the DBD2s-DNA interface towards the promoter is the only possible way to release the elastic stress of the bent DNA. The DBD2s form tight synaptosome complex upon finding the promoter via sliding. When the number of TFs is not enough to bend the DNA in to a circle, then tethered sliding or tethered binding-sliding-unbinding modes are the possibilities. In tethered sliding, the CRMs-TFs complex forms nonspecific contacts with DNA via dynamic loops and then slide along DNA towards promoter without dissociation. In tethered binding-sliding-unbinding, the CRMs-TFs performs several cycles of nonspecific binding-sliding-unbinding before finding the promoter. Elastic and entropic energy barriers associated with the looping of DNA shape up the distribution of distances between CRMs and promoters. The combinatorial regulation of TFs in eukaryotes has evolved to overcome the looping energy barrier.
  • Placeholder Image
    Publication
    Theory of transcription bursting: stochasticity in the transcription rates
    Transcription bursting creates variation among the individuals of a given population. Bursting emerges as the consequence of turning on and off the transcription process randomly. There are at least three sub-processes involved in the bursting phenomenon with different timescale regimes viz. flipping across the on–off state channels, microscopic transcription elongation events and the mesoscopic transcription dynamics along with the mRNA recycling. We demonstrate that when the flipping dynamics is coupled with the microscopic elongation events, then the distribution of the resultant transcription rates will be over-dispersed. This in turn reflects as the transcription bursting with over-dispersed non-Poisson type distribution of mRNA numbers. We further show that there exist optimum flipping rates (αC, βC) at which the stationary state Fano factor and variance associated with the mRNA numbers attain maxima. These optimum points are connected via αC=βC(βC+γr). Here α is the rate of flipping from the on-state to the off-state, β is the rate of flipping from the off-state to the on-state and γr is the decay rate of mRNA. When α = β = χ with zero rate in the off-state channel, then there exist optimum flipping rates at which the non-stationary Fano factor and variance attain maxima. Here χC,v≃3kr+/2(1+kr+t) (here kr+ is the rate of transcription purely through the on-state elongation channel) is the optimum flipping rate at which the variance of mRNA attains a maximum and χC,κ≃ 1.72 / t is the optimum flipping rate at which the Fano factor attains a maximum. Close observation of the transcription mechanism reveals that the RNA polymerase performs several rounds of stall-continue type dynamics before generating a complete mRNA. Based on this observation, we model the transcription event as a stochastic trajectory of the transcription machinery across these on–off state elongation channels. Each mRNA transcript follows different trajectory. The total time taken by a given trajectory is the first passage time (FPT). Inverse of this FPT is the resultant transcription rate associated with the particular mRNA. Therefore, the time required to generate a given mRNA transcript will be a random variable. For a stall-continue type dynamics of RNA polymerase, we show that the overall average transcription rate can be expressed as kr≃h∞+kr+ where kr+≃λr+/L, λr+ is the microscopic transcription elongation rate in the on-state channel and L is the length of a complete mRNA transcript and h∞+ = [β/(α + β)] is the stationary state probability of finding the transcription machinery in the on-state channel.
  • Placeholder Image
    Publication
    Lattice model on the rate of DNA hybridization
    (01-06-2022)
    We develop a lattice model on the rate of hybridization of the complementary single-stranded DNAs (c-ssDNAs). Upon translational diffusion mediated collisions, c-ssDNAs interpenetrate each other to form correct (cc), incorrect (icc), and trap correct contacts (tcc) inside the reaction volume. Correct contacts are those with exact registry matches, which leads to nucleation and zipping. Incorrect contacts are the mismatch contacts which are less stable compared to tcc, which can occur in the repetitive c-ssDNAs. Although tcc possess registry match within the repeating sequences, they are incorrect contacts in the view of the whole c-ssDNAs. The nucleation rate (kN) is directly proportional to the collision rate and the average number of correct contacts ((ncc)) formed when both c-ssDNAs interpenetrate each other. Detailed lattice model simulations suggest that (ncc)?L/V where L is the length of c-ssDNAs and V is the reaction volume. Further numerical analysis revealed the scaling for the average radius of gyration of c-ssDNAs (Rg) with their length as Rg?L. Since the reaction space will be approximately a sphere with radius equals to 2Rg and V?L3/2, one obtains kN?1L. When c-ssDNAs are nonrepetitive, the overall renaturation rate becomes as kR?kNL, and one finally obtains kR?L in line with the experimental observations. When c-ssDNAs are repetitive with a complexity of c, earlier models suggested the scaling kR?Lc, which breaks down at c=L. This clearly suggests the existence of at least two different pathways of renaturation in the case of repetitive c-ssDNAs, viz., via incorrect contacts and trap correct contacts. The trap correct contacts can lead to the formation of partial duplexes which can keep the complementary strands in the close proximity for a prolonged timescale. This is essential for the extended 1D slithering, inchworm movements, and internal displacement mechanisms which can accelerate the searching for the correct contacts. Clearly, the extent of slithering dynamics will be inversely proportional to the complexity. When the complexity is close to the length of c-ssDNAs, the pathway via incorrect contacts will dominate. When the complexity is much less than the length of c-ssDNA, pathway via trap correct contacts would be the dominating one.