Spatial gradients in kinase cascade regulation.

The spatiotemporal kinetics of proteins and other substrates regulate cell fate and signaling. In this study, we consider a reaction-diffusion model of interaction of membrane receptors with a two-step kinase cascade. The receptors activate the 'up-stream' kinase, which may diffuse over cell volume and activate the 'down-stream' kinase, which is also diffusing. Both kinase species and receptors are inactivated by uniformly distributed phosphatases. The positive feedback, key to the considered dynamics, arises since the up-stream kinase activates the receptors. Such a mutual interaction is characteristic for immune cell receptors. Based on the proposed model, we demonstrated that cell sensitivity (measured as a critical value of phosphatase activity at which cell maybe activated) increases with decreasing motility of receptor-interacting kinases and with increasing polarity of receptors distribution. These two effects are cooperating, the effect of receptors localisation close to one pole of the cell grows with the decreasing kinase diffusion and vanishes in the infinite diffusion limit. As the cell sensitivity increases with decreasing diffusion of receptor-interacting kinase, the overall activity of the down-stream kinase increases with its diffusion. In conclusion, the analysis of the proposed model shows that, for the fixed substrate interaction rates, spatial distribution of the surface receptors together with the motility of intracellular kinases control cell signalling and sensitivity to extracellular signals. The increase of the cell sensitivity can be achieved by (i) localisation of receptors in a small subdomain of the cell membrane, (ii) lowering the motility of receptor-interacting kinase, (iii) increasing the motility of down-stream kinases which distribute the signal over the whole cell.

Exploring mechanisms of oscillations in p53 and nuclear factor-B systems.

A number of regulatory networks have the potential to generate sustained oscillations of irregular amplitude, but well conserved period. Single-cell experiments revealed that in p53 and nuclear factor (NF)-B systems the oscillation period is homogenous in cell populations, insensitive to the strength of the stimulation, and is not influenced by the overexpression of p53 or NF-B transcription factors. We propose a novel computational method of validation of molecular pathways models, based on the analysis of sensitivity of the oscillation period to the particular gene(s) copy number and the level of stimulation. Using this method, the authors demonstrate that existing p53 models, in which oscillations are borne at a saddle-node-on-invariant-circle or subcritical Hopf bifurcations (characteristic for systems with interlinked positive and negative feedbacks), are highly sensitive to gene copy number. Hence, these models cannot explain existing experiments. Analysing NF-B system, the authors show the importance of saturation in transcription of the NF-B inhibitor IB. Models without saturation predict that the oscillation period is a rapidly growing function of total NF-B level, which is in disagreement with experiments. The study supports the hypothesis that oscillations of robust period are based on supercritical Hopf bifurcation, characteristic for dynamical systems involving negative feedback and time delay. We hypothesise that in the p53 system, the role of positive feedback is not sustaining oscillations, but terminating them in severely damaged cells in which the apoptotic programme should be initiated.

Crosstalk between p53 and nuclear factor-B systems: pro- and anti-apoptotic functions of NF-B.

Nuclear factors p53 and NF-B control many physiological processes including cell cycle arrest, DNA repair, apoptosis, death, innate and adaptive immune responses, and inflammation. There are numerous pathways linking these systems and there is a bulk of evidence for cooperation as well as for antagonisms between p53 and NF-B. In this theoretical study, the authors use earlier models of p53 and NF-B systems and construct a crosstalk model of p53-NF-B network in order to explore the consequences of the two-way coupling, in which NF-B upregulates the transcription of p53, whereas in turn p53 attenuates transcription of NF-B inhibitors IB and A20. We consider a number of protocols in which cells are stimulated by tumour necrosis factor- (TNF) (that activates NF-B pathway) and/or gamma irradiation (that activates p53 pathway). The authors demonstrate that NF-B may have both anti- and pro-apoptotic roles. TNF stimulation, preceding DNA damaging irradiation, makes cells more resistant to irradiation-induced apoptosis, whereas the same TNF stimulation, when preceded by irradiation, increases the apoptotic cell fraction. The finding suggests that diverse roles of NF-B in apoptosis and cancer could be related to the dynamical context of activation of p53 and NF-B pathways. [Includes supplementary material].

Homoclinic solutions in mechanical systems with small dissipation. Application to DNA dynamics.

This paper analyzes the problem of persistence of homoclinic solutions to perturbed systems of second order ODE's. These systems arise from PDE's, when considering solutions in the form of travelling waves. It is shown that homoclinic solutions persist in the presence of dissipation. Dissipation can be balanced by nonautonomous terms of compact support, which are controlled by a single parameter. This result is applied to prove the existence of torsional pulse-like travelling waves propagating along a nonelastic DNA molecule. In this case the energy is added to system by advancing the RNA polymerase.

Thermodynamics of local DNA openings.

A mechanism connecting the local untwisting and opening of DNA double helix is proposed. The presented thermodynamical approach is based on two models: the Peyrard-Bishop model that describes the denaturation of DNA due to thermal fluctuations and the model developed by the author describing solitary torsional waves, which propagate along the DNA molecule forced by advancing RNA polymerase. The torsional wave implies that the DNA untwists locally causing a local decrease in the stacking interaction between adjacent base pairs. Molecular dynamics simulations have shown that thermal fluctuations (which are too small at physiological temperatures to denaturate the twisted DNA) may lead to the formation of a denaturation bubble placed in the untwisted region.

Chemically driven traveling waves in DNA.

The nonlinear mechanical model constructed in a previous paper [Nuovo Cimento D 20, 833 (1998)] is developed in order to study the dynamics of the DNA double helix. It is assumed that the hydrophobic interaction between subsequent base pairs may be influenced by a RNA polymerase. The Lagrangian, constructed on the basis of "geometrical" properties of the DNA molecule, depends on time and contains first and second derivatives of the twist angle. The energy dissipation term is added to the dynamical equations resulting from the Lagrange formalism. It is proved that the system has pulse-like solitary wave solutions for which the dissipated energy is balanced by the energy pumped by the advancing RNA polymerase. The physical interpretation of our solution is the local untwisting of the DNA molecule during transcription of messenger RNA.