Paweł Żuk, Ph.D.

Department of Biosystems and Soft Matter (ZBiMM)
Division of Complex Fluids (PFPZ)
position: programmer
telephone: (+48) 22 826 12 81 ext.: 421
room: 322
e-mail: pzuk

Doctoral thesis
2016-09-19Dynamika płynów złożonych w przepływach i polach zewnętrznych 
supervisor -- Piotr Szymczak, Ph.D., Dr. Habil., UW
1319
 
Recent publications
1.Żuk P.J., Wajnryb E., Mizerski K.A., Szymczak P., Rotne–Prager–Yamakawa approximation for different-sized particles in application to macromolecular bead models, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2013.668, Vol.741, pp.R5-1-13, 2014
Abstract:

The Rotne–Prager–Yamakawa (RPY) approximation is a commonly used approach to model the hydrodynamic interactions between small spherical particles suspended in a viscous fluid at a low Reynolds number. However, when the particles overlap, the RPY tensors lose their positive definiteness, which leads to numerical problems in the Brownian dynamics simulations as well as errors in calculations of the hydrodynamic properties of rigid macromolecules using bead modelling. These problems can be avoided by using regularizing corrections to the RPY tensors; so far, however, these corrections have only been derived for equal-sized particles. Here we show how to generalize the RPY approach to the case of overlapping spherical particles of different radii and present the complete set of mobility matrices for such a system. In contrast to previous ad hoc approaches, our method relies on the direct integration of force densities over the sphere surfaces and thus automatically provides the correct limiting behaviour of the mobilities for the touching spheres and for a complete overlap, with one sphere immersed in the other one. This approach can then be used to calculate hydrodynamic properties of complex macromolecules using bead models with overlapping, different-sized beads, which we illustrate with an example.

Keywords:

complex fluids, computational methods, low-Reynolds-number flows, mathematical foundations, suspensions

Affiliations:
Żuk P.J.-other affiliation
Wajnryb E.-IPPT PAN
Mizerski K.A.-other affiliation
Szymczak P.-University of Warsaw (PL)
2.Mizerski K.A., Wajnryb E., Żuk P.J., Szymczak P., The Rotne-Prager-Yamakawa approximation for periodic systems in a shear flow, JOURNAL OF CHEMICAL PHYSICS, ISSN: 0021-9606, DOI: 10.1063/1.4871113, Vol.140, pp.184103-1-9, 2014
Abstract:

Rotne-Prager-Yamakawa approximation is a commonly used approach to model hydrodynamic interactions between particles suspended in fluid. It takes into account all the long-range contributions to the hydrodynamic tensors, with the corrections decaying at least as fast as the inverse fourth power of the interparticle distances, and results in a positive definite mobility matrix, which is fundamental in Brownian dynamics simulations. In this communication, we show how to construct the Rotne-Prager-Yamakawa approximation for the bulk system under shear flow, which is modeled using the Lees-Edwards boundary conditions.

Keywords:

Tensor methods, Hydrodynamics, Shear flows, Brownian dynamics, Boundary value problems

Affiliations:
Mizerski K.A.-other affiliation
Wajnryb E.-IPPT PAN
Żuk P.J.-other affiliation
Szymczak P.-University of Warsaw (PL)
3.Pękalski J., Żuk P.J., Kochańczyk M., Junkin M., Kellogg R., Tay S., Lipniacki T., Spontaneous NF-κB Activation by Autocrine TNFα Signaling: A Computational Analysis, PLOS ONE, ISSN: 1932-6203, DOI: 10.1371/journal.pone.0078887, Vol.8, No.11, pp.e78887-1-14, 2013
Abstract:

NF-κB is a key transcription factor that regulates innate immune response. Its activity is tightly controlled by numerous feedback loops, including two negative loops mediated by NF-κB inducible inhibitors, IκBα and A20, which assure oscillatory responses, and by positive feedback loops arising due to the paracrine and autocrine regulation via TNFα, IL-1 and other cytokines. We study the NF-κB system of interlinked negative and positive feedback loops, combining bifurcation analysis of the deterministic approximation with stochastic numerical modeling. Positive feedback assures the existence of limit cycle oscillations in unstimulated wild-type cells and introduces bistability in A20-deficient cells. We demonstrated that cells of significant autocrine potential, i.e., cells characterized by high secretion of TNFα and its receptor TNFR1, may exhibit sustained cytoplasmic–nuclear NF-κB oscillations which start spontaneously due to stochastic fluctuations. In A20-deficient cells even a small TNFα expression rate qualitatively influences system kinetics, leading to long-lasting NF-κB activation in response to a short-pulsed TNFα stimulation. As a consequence, cells with impaired A20 expression or increased TNFα secretion rate are expected to have elevated NF-κB activity even in the absence of stimulation. This may lead to chronic inflammation and promote cancer due to the persistent activation of antiapoptotic genes induced by NF-κB. There is growing evidence that A20 mutations correlate with several types of lymphomas and elevated TNFα secretion is characteristic of many cancers. Interestingly, A20 loss or dysfunction also leaves the organism vulnerable to septic shock and massive apoptosis triggered by the uncontrolled TNFα secretion, which at high levels overcomes the antiapoptotic action of NF-κB. It is thus tempting to speculate that some cancers of deregulated NF-κB signaling may be prone to the pathogen-induced apoptosis.

Affiliations:
Pękalski J.-Institute of Physical Chemistry, Polish Academy of Sciences (PL)
Żuk P.J.-other affiliation
Kochańczyk M.-IPPT PAN
Junkin M.-Eidgenössische Technische Hochschule Zürich (CH)
Kellogg R.-Eidgenössische Technische Hochschule Zürich (CH)
Tay S.-Eidgenössische Technische Hochschule Zürich (CH)
Lipniacki T.-IPPT PAN
4.Wajnryb E., Mizerski K.A., Żuk P.J., Szymczak P., Generalization of the Rotne-Prager-Yamakawa mobility and shear disturbance tensors, JOURNAL OF FLUID MECHANICS, ISSN: 0022-1120, DOI: 10.1017/jfm.2013.402, Vol.731, pp.R3-1-12, 2013
Abstract:

The Rotne–Prager–Yamakawa approximation is one of the most commonly used methods of including hydrodynamic interactions in modelling of colloidal suspensions and polymer solutions. The two main merits of this approximation are that it includes all long-range terms (i.e. decaying as R−3 or slower in interparticle distances) and that the diffusion matrix is positive definite, which is essential for Brownian dynamics modelling. Here, we extend the Rotne–Prager–Yamakawa approach to include both translational and rotational degrees of freedom, and derive the regularizing corrections to account for overlapping particles. Additionally, we show how the Rotne–Prager–Yamakawa approximation can be generalized for other geometries and boundary conditions.

Keywords:

computational methods, low-Reynolds-number flows, suspensions

Affiliations:
Wajnryb E.-IPPT PAN
Mizerski K.A.-other affiliation
Żuk P.J.-other affiliation
Szymczak P.-University of Warsaw (PL)
5.Jaruszewicz J., Żuk P.J., Lipniacki T., Type of noise defines global attractors in bistable molecular regulatory systems, JOURNAL OF THEORETICAL BIOLOGY, ISSN: 0022-5193, DOI: 10.1016/j.jtbi.2012.10.004, Vol.317, pp.140-151, 2013
Abstract:

The aim of this study is to demonstrate that in molecular dynamical systems with the underlying bi- or multistability, the type of noise determines the most strongly attracting steady state or stochastic attractor. As an example we consider a simple stochastic model of autoregulatory gene with a nonlinear positive feedback, which in the deterministic approximation has two stable steady state solutions. Three types of noise are considered: transcriptional and translational – due to the small number of gene product molecules and the gene switching noise – due to gene activation and inactivation transitions. We demonstrate that the type of noise in addition to the noise magnitude dictates the allocation of probability mass between the two stable steady states. In particular, we found that when the gene switching noise dominates over the transcriptional and translational noise (which is characteristic of eukaryotes), the gene preferentially activates, while in the opposite case, when the transcriptional noise dominates (which is characteristic of prokaryotes) the gene preferentially remains inactive. Moreover, even in the zero-noise limit, when the probability mass generically concentrates in the vicinity of one of two steady states, the choice of the most strongly attracting steady state is noise type-dependent. Although the epigenetic attractors are defined with the aid of the deterministic approximation of the stochastic regulatory process, their relative attractivity is controlled by the type of noise, in addition to noise magnitude. Since noise characteristics vary during the cell cycle and development, such mode of regulation can be potentially employed by cells to switch between alternative epigenetic attractors.

Keywords:

Gene expression, Bistability, Stochastic processes, Epigenetic attractors

Affiliations:
Jaruszewicz J.-IPPT PAN
Żuk P.J.-other affiliation
Lipniacki T.-IPPT PAN
6.Żuk P.J., Kochańczyk M., Jaruszewicz J., Bednorz W., Lipniacki T., Dynamics of a stochastic spatially extended system predicted by comparing deterministic and stochastic attractors of the corresponding birth–death process, PHYSICAL BIOLOGY, ISSN: 1478-3967, DOI: 10.1088/1478-3975/9/5/055002, Vol.9, pp.055002-1-12, 2012
Abstract:

Living cells may be considered as biochemical reactors of multiple steady states. Transitions between these states are enabled by noise, or, in spatially extended systems, may occur due to the traveling wave propagation. We analyze a one-dimensional bistable stochastic birth–death process by means of potential and temperature fields. The potential is defined by the deterministic limit of the process, while the temperature field is governed by noise. The stable steady state in which the potential has its global minimum defines the global deterministic attractor. For the stochastic system, in the low noise limit, the stationary probability distribution becomes unimodal, concentrated in one of two stable steady states, defined in this study as the global stochastic attractor. Interestingly, these two attractors may be located in different steady states. This observation suggests that the asymptotic behavior of spatially extended stochastic systems depends on the substrate diffusivity and size of the reactor. We confirmed this hypothesis within kinetic Monte Carlo simulations of a bistable reaction–diffusion model on the hexagonal lattice. In particular, we found that although the kinase–phosphatase system remains inactive in a small domain, the activatory traveling wave may propagate when a larger domain is considered.

Keywords:

multi-stability, Markov process, spatially extended system, kinetic Monte Carlo on the lattice, cell signalling

Affiliations:
Żuk P.J.-other affiliation
Kochańczyk M.-IPPT PAN
Jaruszewicz J.-IPPT PAN
Bednorz W.-University of Warsaw (PL)
Lipniacki T.-IPPT PAN

Conference papers
1.Jaruszewicz J., Żuk P.J., Lipniacki T., Probability density functions in bistable gene activation Model with two types of noise, 16th National Conference on Applications of Mathematics in Biology and Medicine, 2010-09-14/09-18, Krynica (PL), pp.47-52, 2010
Abstract:

The aim of this study is to demonstrate that in dynamical systems with underlying bistability the type of noise qualitatively influences the stationary probability distribution (SPD). Specifically, we consider a simplified model of gene expression with the nonlinear positive feedback, which in the deterministic approximation has two stable steady state solutions. Two types of noise are considered; transcriptional - due to the limited number of protein molecules, and gene switching noise - due to gene activation and inactivation. In the limit of zero noise, the SPD generically concentrates in the decreasing vicinity of one of the two stable steady states. We demonstrated that for a range of parameters the SPD corresponding to the system with transcriptional noise only concentrates around a different steady state than SPD corresponding to the system with gene switching noise only.

Keywords:

Gene expression, Bistability, Stochastic processes, Epigenetic attractors

Affiliations:
Jaruszewicz J.-IPPT PAN
Żuk P.J.-other affiliation
Lipniacki T.-IPPT PAN
2.Żuk P.J., Lipniacki T., Probability density functions in bistable kinase activation model, 16th National Conference on Applications of Mathematics in Biology and Medicine, 2010-09-14/09-18, Krynica (PL), pp.121-126, 2010
Abstract:

We consider a kinase auto-activation model in which the number of activated kinases follows the timecontinuous Markov process. In the deterministic approximation the process is described by the single nonlinear ordinary differential equation, which may have two stable steady states. We found that for sufficiently large number of kinases, the stationary probability distribution given by the Markov process concentrates in the vicinity of the two stable steady states of the deterministic approximation. However, if the number of kinases diverges to the infinity (zero noise limit), the stationary probability distribution concentrates (generically) in only one of the two steady states.

Affiliations:
Żuk P.J.-other affiliation
Lipniacki T.-IPPT PAN