Anna Ochab-Marcinek

• PhD
• Principal Investigator at Institute of Physical Chemistry, Polish Academy of Sciences

Since the seminal work of Powell, the relationships between the population growth rate, the probability distributions of generation time, and the distribution of cell age have been known for the bacterial population in a steady state of exponential growth. Here we generalize these relationships to include an unsteady (transient) state for both the...

New experimental methods allow for studying the dynamics of cell populations with increasing precision and time resolution, providing us with a large amount of high-quality data. These data, in turn, stimulate the mathematical modeling of such systems. Here, using a generalization of the McKendrick-von Foerster model proposed by Lebowitz and Rubino...

Kroniki pandemii to zbiór 27 stanowisk opublikowanych przez interdyscyplinarny Zespół doradczy ds. COVID-19 przy Prezesie Polskiej Akademii Nauk, działający od lipca 2020 roku. Jest to już drugie po Zrozumieć COVID-19 obszerniejsze opracowanie naszego zespołu porządkujące wiadomości dotyczące wirusa SARS-CoV-2 i powodowanej przez niego choroby COVI...

Opracowanie zespołu naukowców pracujących pod kierunkiem prezesa Polskiej Akademii Nauk prof. Jerzego Duszyńskiego w sposób przystępny przedstawia aktualny stan wiedzy na temat wirusa SARS-CoV-2, choroby COVID-19 oraz jej skutki medyczne, psychologiczne, gospodarcze i społeczne. W publikacji naukowcy prezentują prognozy epidemii w sezonie jesienno-...

We resolved to put together this present Report, as a compendium of knowledge about the SARS-CoV-2 virus and the disease it causes – COVID-19 – in view of the following considerations: 1. We wished to systematize the information on COVID-19 that has accumulated during the months since the new disease’s emergence in December 2019. Scientific publica...

Experiments with cells reveal the existence of a lower bound for protein noise, the noise floor, in highly expressed genes. Its origins are still debated. We propose a minimal model of gene expression in a proliferating bacterial cell population. The model predicts the existence of a noise floor and it semi-quantitatively reproduces the curved shap...

Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous deg...

Many of the existing stochastic models of gene expression contain the first-order decay reaction term that may describe active protein degradation or dilution. If the model variable is interpreted as the molecule number, and not concentration, the decay term may also approximate the loss of protein molecules due to cell division as a continuous deg...

An intuition based upon deterministic models of chemical kinetics is that population heterogeneity in the amount of transcription factors in cells is transmitted unchanged downstream to the target genes. We use a stochastic model of a two-gene cascade with a self-regulating upstream gene to show that, counter to intuition, there is no simple mappin...

The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants. Most of theories start from the Langevin equation to derive the dynamics, but there are few examples comparing it...

The dynamics of unimolecular photo-triggered reactions can be strongly affected by the surrounding medium. An accurate description of these reactions requires knowing the free energy surface (FES) and the friction felt by the reactants. Most of theories start from the Langevin equation to derive the dynamics, but there are few examples comparing it...

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability...

We study a stochastic model of gene expression, in which protein production has a form of random bursts whose size distribution is arbitrary, whereas protein decay is a first-order reaction. We find exact analytical expressions for the time evolution of the cumulant-generating function for the most general case when both the burst size probability...

Using an analytically solvable stochastic model, we study the properties of a simple genetic circuit consisting of multiple copies of an self-regulating gene. We analyse how the variation in gene copy number and the mutations changing the auto-regulation strength affect the steady-state distribution of protein concentration. We predict that one-rep...

Using an analytically solvable stochastic model, we study the properties of a simple genetic circuit consisting of multiple copies of an self-regulating gene. We analyse how the variation in gene copy number and the mutations changing the auto-regulation strength affect the steady-state distribution of protein concentration. We predict that one-rep...

This paper deals with the recent phenomenological model of the motion of nanoscopic objects (colloidal particles, proteins, nanoparticles, molecules) in complex liquids. We analysed motion in polymer, micellar, colloidal and protein solutions and the cytoplasm of living cells using the length-scale dependent viscosity model. Viscosity monotonically...

We study the response of an autoregulated gene to a range of concentrations of signal molecules. We show that transcriptional leakage and noise due to translational bursting have the opposite effects. In a positively autoregulated gene, increasing the noise converts the response from graded to binary, while increasing the leakage converts the respo...

We study the response of an autoregulated gene to a range of concentrations of signal molecules. We show that noise due to translational bursting and leakage have the opposite effects. In a positively autoregulated gene, increasing the noise converts the response from graded to binary, while increasing the leakage converts the response from binary...

The mobility of segments of the polymer mesh in a solution determines the dynamic response of the depletion layer (DL) to mechanical stimuli. This phenomenon can be used to vastly decrease the local viscosity experienced by any device performing periodic motion at the nano- and microscale in complex liquids. We refined the vibrating quartz tuning f...

Fluorescence correlation spectroscopy (FCS) is frequently used to study the processes of restricted diffusion. The most important quantity to determine is the size of the structures that hinder the Brownian motion of the molecules. We study three qualitatively different models of restricted diffusion, widely applied in biophysics and material scien...

Taylor Dispersion Analysis (TDA) has been performed for analytes moving at high flow rates in long, coiled capillaries. A thin injection zone of the analyte is stretched by the flow and final distribution of concentration of the analyte at the end of the capillary has the Gaussian shape. The high flow rates in coiled capillary generate vortices. Th...

We introduce a model of diffusion of nanoparticles in solutions of flexible, polydisperse polymers. The model takes into account the effect of depletion layer with soft boundaries. The presence of depletion layer leads to nonlinear dependence of the mean square displacement (MSD) on time. Our model may be an alternative choice for the study of thos...

We present a theoretical description of diffusion of a sphere in polymer solution. The depletion layer around the sphere affects its motion and leads to scale-dependent diffusion. We propose the model of walking confined diffusion. Although it is different from anomalous diffusion, we show that the experimental data generated by this process may ha...

Bimodality of gene expression, as a mechanism contributing to phenotypic diversity, enhances the survival of cells in a fluctuating environment. To date, the bimodal response of a gene regulatory system has been attributed to the cooperativity of transcription factor binding or to feedback loops. It has remained unclear whether noncooperative bindi...

The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering...

Ionizing radiation is known to delay the cell cycle progression. In particular after particle exposure significant delays have been observed and it has been shown that the extent of delay affects the expression of damage, such as chromosome aberrations. Thus, to predict how cells respond to ionizing radiation and to derive reliable estimates of rad...

The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering...

In the framework of the Michaelis-Menten (MM) reaction kinetics, we analyze the cancer growth dynamics in the presence of the immune response. We found the coexistence of noise enhanced stability (NES) and resonant activation (RA) phenomena which act in an opposite way with respect to the extinction of the tumor. The role of the stochastic resonanc...

We consider noise-assisted spike propagation in myelinated axons within a multicompartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal electric coupling, we show that (i) intrinsic noise removes the sharply defined threshold for spike propagation...

We consider noise-assisted spike propagation in myelinated axons within a multi-compartment stochastic Hodgkin-Huxley model. The noise originates from a finite number of ion channels in each node of Ranvier. For the subthreshold internodal electric coupling, we show that (i) intrinsic noise removes the sharply defined threshold for spike propagatio...

Transient properties of different physical systems with metastable states perturbed by external white noise have been investigated. Two noise-induced phenomena, namely the noise enhanced stability and the resonant activation, are theoretically predicted in a piece-wise linear fluctuating potential with a metastable state. The enhancement of the lif...

We investigate a mathematical model describing the growth of tumor in the presence of immune response of a host organism. The dynamics of tumor and immune cells populations is based on the generic Michaelis-Menten kinetics depicting interaction and competition between the tumor and the immune system. The appropriate phenomenological equation modeli...

We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a genetic switch with the concentration of one substrate fluctuating around a constant mean. The proposed method...

We present a simple analytical tool which gives an approximate insight into the stationary behavior of nonlinear systems undergoing the influence of a weak and rapid noise from one dominating source, e.g. the kinetic equations describing a genetic switch with the concentration of one substrate fluctuating around a constant mean. The proposed method...

We investigate a stochastic version of a simple enzymatic reaction which follows the generic Michaelis-Menten kinetics. At sufficiently high concentrations of reacting species, that represent here populations of cells involved in cancerous proliferation and cytotoxic response of the immune system, the overall kinetics can be approximated by a one-d...

We study a Langevin equation derived from the Michaelis-Menten (MM) phenomenological scheme for catalysis accompanying a spontaneous replication of molecules, which may serve as a simple model of cell-mediated immune surveillance against cancer. We examine how two different and statistically independent sources of noise - dichotomous multiplicative...

We study a spatially inhomogeneous model of cancer growth based on Michaelis--Menten kinetics, subjected to additive Gaussian noise and multiplicative dichotomous noise. In presence of the latter, we can observe a transition between two stationary states of the system. The transient behaviour generates a spatial pattern of two phases, where cancer...

We investigate noise-induced pattern formation in a model of cancer growth based on Michaelis-Menten kinetics, subject to additive and multiplicative noises. We analyse stability properties of the system and discuss the role of diffusion and noises in the system's dynamics. We find that random dichotomous fluctuations in the immune response intensi...

We study the joint effect of thermal bath fluctuations and an external noise tuning activity of cytotoxic cells on the triggered immune response in a growing cancerous tissue. The immune response is assumed to be primarily mediated by effector cells that develop a cytotoxic activity against the abnormal tissue. The kinetics of such a reaction is re...