Partner: Paweł Nałęcz-Jawecki

University of Warsaw (PL)

Recent publications
1.Białecki S., Nałęcz-Jawecki P., Kaźmierczak B., Lipniacki T., Traveling and standing fronts on curved surfaces, PHYSICA D-NONLINEAR PHENOMENA, ISSN: 0167-2789, DOI: 10.1016/j.physd.2019.132215, Vol.401, pp.132215-1-8, 2020
Abstract:

We analyze heteroclinic traveling waves propagating on two dimensional manifolds to show that the geometric modification of the front velocity is proportional to the geodesic curvature of the frontline. As a result, on surfaces of concave domains, stable standing fronts can be formed on lines of constant geodesic curvature. These lines minimize the geometric functional describing the system’s energy, consisting of terms proportional to the front line-length and to the inclosed surface area. Front stabilization at portions of surface with negative Gaussian curvature, provides a mechanismof pattern formation. In contrast to the mechanism associated with the Turing instability, the proposed mechanism requires only a single scalar bistable reaction–diffusion equation and connects the intrinsic surface geometry with the arising pattern. By considering a system of equations modeling boundary-volume interactions, we show that polarization of the boundary may induce a corresponding polarization in the volume.

Keywords:

Heteroclinic traveling waves, Standing fronts, Geodesic curvature, Negative Gaussian curvature, Domain polarization, Pattern formation

Affiliations:
Białecki S.-IPPT PAN
Nałęcz-Jawecki P.-IPPT PAN
Kaźmierczak B.-IPPT PAN
Lipniacki T.-IPPT PAN
2.Korwek Z., Tudelska K., Nałęcz-Jawecki P., Czerkies M., Prus W., Markiewicz J., Kochańczyk M., Lipniacki T., Importins promote high-frequency NF-κB oscillations increasing information channel capacity, Biology Direct, ISSN: 1745-6150, DOI: 10.1186/s13062-016-0164-z, Vol.11, No.61, pp.1-21, 2016
Abstract:

BACKGROUND:
Importins and exportins influence gene expression by enabling nucleocytoplasmic shuttling of transcription factors. A key transcription factor of innate immunity, NF-κB, is sequestered in the cytoplasm by its inhibitor, IκBα, which masks nuclear localization sequence of NF-κB. In response to TNFα or LPS, IκBα is degraded, which allows importins to bind NF-κB and shepherd it across nuclear pores. NF-κB nuclear activity is terminated when newly synthesized IκBα enters the nucleus, binds NF-κB and exportin which directs the complex to the cytoplasm. Although importins/exportins are known to regulate spatiotemporal kinetics of NF-κB and other transcription factors governing innate immunity, the mechanistic details of these interactions have not been elucidated and mathematically modelled.
RESULTS:
Based on our quantitative experimental data, we pursue NF-κB system modelling by explicitly including NF-κB-importin and IκBα-exportin binding to show that the competition between importins and IκBα enables NF-κB nuclear translocation despite high levels of IκBα. These interactions reduce the effective relaxation time and allow the NF-κB regulatory pathway to respond to recurrent TNFα pulses of 45-min period, which is about twice shorter than the characteristic period of NF-κB oscillations. By stochastic simulations of model dynamics we demonstrate that randomly appearing, short TNFα pulses can be converted to essentially digital pulses of NF-κB activity, provided that intervals between input pulses are not shorter than 1 h.
CONCLUSIONS:
By including interactions involving importin-α and exportin we bring the modelling of spatiotemporal kinetics of transcription factors to a more mechanistic level. Basing on the analysis of the pursued model we estimated the information transmission rate of the NF-κB pathway as 1 bit per hour.

Keywords:

Karyopherins, Nucleocytoplasmic transport, Negative feedback, Channel information capacity, Mathematical modelling

Affiliations:
Korwek Z.-IPPT PAN
Tudelska K.-other affiliation
Nałęcz-Jawecki P.-University of Warsaw (PL)
Czerkies M.-IPPT PAN
Prus W.-IPPT PAN
Markiewicz J.-IPPT PAN
Kochańczyk M.-IPPT PAN
Lipniacki T.-IPPT PAN
3.Nałęcz-Jawecki P., Szymańska P., Kochańczyk M., Miękisz J., Lipniacki T., Effective reaction rates for diffusion-limited reaction cycles, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.4936131, Vol.143, No.21, pp.215102-1-12, 2015
Abstract:

Biological signals in cells are transmitted with the use of reaction cycles, such as the phosphorylation-dephosphorylation cycle, in which substrate is modified by antagonistic enzymes. An appreciable share of such reactions takes place in crowded environments of two-dimensional structures, such as plasma membrane or intracellular membranes, and is expected to be diffusion-controlled. In this work, starting from the microscopic bimolecular reaction rate constants and using estimates of the mean first-passage time for an enzyme–substrate encounter, we derive diffusion-dependent effective macroscopic reaction rate coefficients (EMRRC) for a generic reaction cycle. Each EMRRC was found to be half of the harmonic average of the microscopic rate constant (phosphorylation c or dephosphorylation d), and the effective (crowding-dependent) motility divided by a slowly decreasing logarithmic function of the sum of the enzyme concentrations. This implies that when c and d differ, the two EMRRCs scale differently with the motility, rendering the steady-state fraction of phosphorylated substrate molecules diffusion-dependent. Analytical predictions are verified using kinetic Monte Carlo simulations on the two-dimensional triangular lattice at the single-molecule resolution. It is demonstrated that the proposed formulas estimate the steady-state concentrations and effective reaction rates for different sets of microscopic reaction rates and concentrations of reactants, including a non-trivial example where with increasing diffusivity the fraction of phosphorylated substrate molecules changes from 10% to 90%.

Keywords:

Enzymes, Enzyme kinetics, Diffusion, Reaction rate constants, Membrane biochemistry

Affiliations:
Nałęcz-Jawecki P.-University of Warsaw (PL)
Szymańska P.-University of Warsaw (PL)
Kochańczyk M.-IPPT PAN
Miękisz J.-University of Warsaw (PL)
Lipniacki T.-IPPT PAN