Understanding non-linear effects from Hill-type dynamics with application to decoding of p53 signaling

Synthesis of N-isopropyl acrylamide copolymerized acrylic acid caped with Dibenzo-18-crown-6 composite for selective separation of Co-60 radioisotope from radioactive liquid waste containing Cs-137

A new selective polymeric composite capped with crown ether was successfully synthesized using N-isopropyl acrylamide copolymerized acrylic acid paired with Dibenzo-18-crown-6, P(NIPAm-Co-AA-DB 18C-6), by Gamma irradiation and ultrasonic homogenizer polymerization. Scanner electron microscopy (SEM), Fourier transform infrared spectroscopy (FTIR), and dynamic light scattering were used to characterize the selected polymeric composite's chemical and physical constitution. SEM shows a rough irregular surface, and FTIR spectra confirmed the function groups of P(NIPAm-Co-AA-DB 18C-6). Moreover, a systematic study of monomer and crown ether concentration was investigated to enhance the composite's performance. The behavior of the synthetic composite toward the selective separation of Co-60 from Cs-137 in a binary system was evaluated. Effects of pH, contact time, and initial ion concentration were investigated in a batch mode and the maximum capacity reached 108.0 mg/g for Co-60 and 82.0 mg/g for Cs-137. Four Kinetic models were investigated (pseudo-first-order, pseudo-second-order, Elovich, and Intra-particle diffusion). Regarding the calculated parameters, pseudo-second-order and Elovich models are the most describing the sorption process, indicating the chemisorptions process. Six adsorption isotherms were examined, two-parameter models (Langmuir, and Freundlich) and three-parameter models (Redlich-Peterson, Khan, Sips, and Hills). The best-fitted isotherm was identified using three error methodological approaches: the correlation coefficient (R2), the chi-square test (χ2), and the root-mean-square error. Isotherm models fit the experimental values in the following sequence: Khan > Rdlish-Peterson > Hills > Sips. Finally, an application for column separation was conducted, and Co-60 was completely separated from Cs-137 by 0.1 M HNO3. These findings indicate promising applications in the successive separation of Co-60 from radioactive liquid waste containing Cs-137 from Egyptian reactors.

Graphical abstract

A Hill type equation can predict target gene expression driven by p53 pulsing

Many factors determine target gene expression dynamics under p53 pulsing. In this study, I sought to determine the mechanism by which duration, frequency, binding affinity and maximal transcription rate affect the expression dynamics of target genes. Using an analytical method to solve a simple model, I found that the fold change of target gene expression increases relative to the number of p53 pulses, and the optimal frequency, 0.18 h-1 , from two real p53 pulses drives the maximal fold change with a decay rate of 0.18 h-1 . Moreover, p53 pulses may also lead to a higher fold change than sustained p53. Finally, I discovered that a Hill-type equation, including these effect factors, can characterise target gene expression. The average error between the theoretical predictions and experiments was 23%. Collectively, this equation advances the understanding of transcription factor dynamics, where duration and frequency play a significant role in the fine regulation of target gene expression with higher binding affinity.