6-Hydroxymethyl-7,8-dihydropterin pyrophosphokinase (HPPK) catalyzes the first reaction in the folate biosynthetic pathway. Comparison of its X-ray and nuclear magnetic resonance structures suggests that the enzyme undergoes significant conformational change upon binding to its substrates, especially in three catalytic loops. Experimental research has shown that, in its binary form, even bound by analogues of MgATP, loops 2 and 3 remain rather flexible; this raises questions about the putative large-scale induced-fit conformational change of the HPPK–MgATP binary complex. In this work, long-time all-atomic molecular dynamics simulations were conducted to investigate the loop dynamics in this complex. Our simulations show that, with loop 3 closed, multiple conformations of loop 2, including the open, semiopen, and closed forms, are all accessible to the binary complex. These results provide valuable structural insights into the details of conformational changes upon 6-hydroxymethyl-7,8-dihydropterin (HP) binding and biological activities of HPPK. Conformational network analysis and principal component analysis related to the loops are also discussed.

Small non-coding RNA (sRNA) plays very important role in the post transcriptional regulation in various organisms. In complex regulatory networks, highly significant relative fluctuations in RNAs copy numbers can not be neglected due to very small copy number of individual RNA molecules. Here we consider two simple regulation schemes, where one is single target gene regulated by a sRNA and the other is two target mRNAs (mRNAR and mRNAT) regulated by one sRNA. The Fano factor (a measure of the relative size of the internal fluctuations) formulae of RNA molecules in the post transcriptional regulation are theoretically derived by using of the Langevin theory. For single target gene regulated by a sRNA, it is shown that the intrinsic noise of both mRNA and sRNA approaches the bare Poissonian limit in the regimen of both target RNA silencing and surviving. However, the strong anti-correlation between the fluctuations of two components result in a large intrinsic fluctuations in the level of RNA molecules in the regimen of crossover. For two target mRNAs regulated by one sRNA, in the regimen of crossover, it is found that, with the increasing of transcription rate of target mRNAT, the maximal intrinsic fluctuation of RNA molecules is shifted from sRNA to target mRNAR, and then to target mRNAT. The intrinsic noise intensity of target mRNAR is determined by both the transcriptional rate of itself and that of sRNA, and independent of the transcriptional rate of the other target mRNAT.

Ryanodine receptor channel model is introduced to a dynamical model of pancreatic β-cells to discuss the effects of RyR channels and glucose concentration on membrane potential. The results show Ca2+ concentration changes responding to enhance of glucose concentration is more quickly than that of activating RyR channels, and both methods can induce bursting action potential and increase free cytosolic Ca2+ concentration. An interesting finding is that moderate stimulation to RyR channels will result in a kind of “complex bursting”, which is more effective in enhancing average Ca2+ concentration and insulin section.

Based on a model of intracellular calcium (Ca2+) oscillation with self-modulation of inositol 1,4,5-trisphosphate signal, the mesoscopic stochastic differential equations for the intracellular Ca2+ oscillations are theoretically derived by using the chemical Langevin equation method. The effects of the finite biochemical reaction molecule number on both simple and complex cytosolic Ca2+ oscillations are numerically studied. In the case of simple intracellular Ca2+ oscillation, it is found that, with the increase of molecule number, the coherence resonance or autonomous resonance phenomena can occur for some external stimulation parameter values. In the cases of complex cytosolic Ca2+ oscillations, each extremum of concentration of cytosolic Ca2+ oscillations corresponds to a peak in the histogram of Ca2+ concentration, and the most probability appeared during the bursting plateau level for bursting, but at the largest minimum of Ca2+ concentration for chaos. For quasi-periodicity, however, there are only two peaks in the histogram of Ca2+ concentration, and the most probability is located at low concentration state.

This work presents both deterministic and stochastic models of genetic expression modulated by intracellular calcium (Ca2+) oscillations, based on macroscopic differential equations and chemical Langevin equations, respectively. In deterministic case, the oscillations of intracellular Ca2+ decrease the effective Ca2+ threshold for the activation of transcriptional activator (TF-A). The average activation of TF-A increases with the increase of the average amplitude of intracellular Ca2+ oscillations, but decreases with the increase of the period of intracellular Ca2+ oscillations, which are qualitatively consistent with the experimental results on the gene expression in lymphocytes. In stochastic case, it is found that a large internal fluctuation of the biochemical reaction can enhance gene expression efficiency specifically at a low level of external stimulations or at a small rate of TF-A dimer phosphorylation activated by Ca2+, which reduces the threshold of the average intracellular Ca2+ concentration for gene expression.

Considering the ATP-driven (SERCA) pump flux as function of glucose concentration and the calcium flux from the endoplasmic reticulum (ER) through the IP3R channel, the calcium-based phantom bursting model (PBM) of β-cells (Bertram and Sherman in Bull Math Biol 66:1313, 2004) is theoretically extended to discuss the effects of glucose and inositol 1,4,5-trisphosphate (IP3) concentration on the membrane potential activities. When IP3 concentration is fixed, it is found that there is a critical glucose concentration at which electrical bursting oscillations transfer into spiking, and the critical concentration of glucose is increased with the increasing of IP3 concentration. To get the bursting oscillations in β-cells, our theoretical results show that the stimulatory glucose concentration should be more than 10 mM, which is consistent with the normal physiological IP3 level. When the stochastic opening and closing of IP3R channels are considered, it is shown that the membrane potential oscillation transfers from spiking to bursting with the channel number decreasing, and the average cytosolic free Ca2+ concentration is increased with the increase of glucose concentration.

In various cell types cytosolic calcium (Ca2+) is an important regulator. The possible role of Ca2+ release from the inositol 1,4,5-trisphosphate (IP3) receptor channel in the regulation of the phosphorylation–dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase have theoretically investigated by using the Li–Rinzel model for cytosolic Ca2+ oscillations. For the case of deterministic cytosolic Ca2+ oscillations, there exists an optimal frequency of cytosolic Ca2+ oscillations at which the average fraction of active glycogen phosphorylase reaches a maximum value, and a mutation for the average fraction of active glycogen phosphorylase occurs at the higher bifurcation point of Ca2+ oscillations. For the case of stochastic cytosolic Ca2+ oscillations, the fraction of active phosphorylase is strongly affected by the number of IP3 receptor channels and the level of IP3 concentration. Small number of IP3 receptor channels can potentiate the sensitivity of the activity of glycogen phosphorylase. The average frequency and amplitude of active phosphorylase stochastic oscillations are increased with the level of increasing IP3 stimuli. The various distributions for the amplitude of active glycogen phosphorylase oscillations in parameters plane are discussed.

Taking into account the Ca2+-stimulated degradation of inositol 1,4,5-trisphosphate (IP3) by a 3-kinase, we have theoretically explored the effects of both simple and complex Ca2+ oscillations on the regulation of a phosphorylation–dephosphorylation cycle process involved in glycogen degradation by glycogen phosphorylase a-form, respectively. For the case of simple Ca2+ oscillations, the roles of cytosolic Ca2+ oscillations in the regulation of active phosphorylase depend upon the maximum rate of IP3 degradation by the 3-kinase, VM5. In particular, the smaller the values of VM5 are, the lower the effective Ca2+ threshold for the activation of glycogen phosphorylase will be. For the case of complex Ca2+ oscillations, the average level of fraction of active phosphorylase is nearly independent from the level of stimulation increasing in the bursting oscillatory domain. Both simple and complex Ca2+ oscillations can contribute to increase the efficiency and specificity of cellular signalling, and some theoretical results of activation of glycogen phosphorylase regulated by Ca2+ oscillations are close to the experimental results for gene expression in lymphocytes.