Simulation of proliferation and differentiation of cells in a stem-cell niche

Stem-cell niches represent microscopic compartments formed of environmental cells that nurture stem cells and enable them to maintain tissue homeostasis. The spatio-temporal kinetics of proliferation and differentiation of cells in such niches depend on the specifics of the niche structure and on adhesion and communication between cells and may also be influenced by spatial constraints on cell division. We propose a generic lattice model, taking all these factors into account, and systematically illustrate their role. The model is motivated by the experimental data available for the niches located in the subventricular zone of adult mammalian brain. The general conclusions drawn from our Monte Carlo simulations are applicable to other niches as well. One of our main findings is that the kinetics under consideration are highly stochastic due to a relatively small number of cells proliferating and differentiating in a niche and the autocatalytic character of the symmetric cell division. In particular, the kinetics exhibit huge stochastic bursts especially if the adhesion between cells is taken into account. In addition, the results obtained show that despite the small number of cells present in stem-cell niches, their arrangement can be predetermined to appreciable extent provided that the adhesion of different cells is different so that they tend to segregate.     

Modeling polymerization of microtubules: A semi-classical nonlinear field theory approach

In this paper, for the first time, a three-dimensional treatment of microtubules’ polymerization is presented. Starting from fundamental biochemical reactions during microtubule’s assembly and disassembly processes, we systematically derive a nonlinear system of equations that determines the dynamics of microtubules in three dimensions. We found that the dynamics of a microtubule is mathematically expressed via a cubic-quintic nonlinear Schrödinger (NLS) equation. We show that in 3D a vortex filament, a generic solution of the NLS equation, exhibits linear growth/shrinkage in time as well as temporal fluctuations about some mean value which is qualitatively similar to the dynamic instability of microtubules. By solving equations numerically, we have found spatio-temporal patterns consistent with experimental observations.     

Matching allele dynamics and coevolution in a minimal predator-prey replicator model

A minimal Lotka-Volterra type predator-prey model describing coevolutionary traits among entities with a strength of interaction influenced by a pair of haploid diallelic loci is studied with a deterministic time continuous model. We show a Hopf bifurcation governing the transition from evolutionary stasis to periodic Red Queen dynamics. If predator genotypes differ in their predation efficiency the more efficient genotype asymptotically achieves lower stationary concentrations.     

Characterisation under static and dynamic conditions of commercial activated carbons for their use in wastewater plants

The use of activated carbon for removing organic contaminants in fixed beds is increasing. This is a dynamic process in which the kinetics plays an important role. The aim of this paper is to get more insight into adsorption of p-nitrophenol (PNP) in activated carbon under equilibrium and dynamic conditions. Five commercial activated carbons were studied. The analysis carried out were PNP adsorption isotherms in aqueous solution at 20 °C, N₂ at 77 K isotherms, FT-IR and PNP adsorption under dynamic conditions. The results indicate that the external porous affinity toward the organic contaminants determines in large extent the adsorbents behaviour under dynamic conditions.     

Inter-basin dynamics on multidimensional potential surfaces

A statistically based characterization of the topography of a standard potential surface (PS) may allow its reconstruction in basins containing monotonic sequences of local minima and saddles. Starting with this partition of the PS, one can explore kinetic properties of those basins and provide a reliable dynamical diagnosis. We found that certain topographical patterns of the standard PS underly kinetic properties which may lead the probability density to concentrate in basins of high energy, in which wrong structures are kinetically favored, rather than in the basin of the global minimum. We examined also considerations that link properties of the contact between the reaction coordinate and thermal bath with the efficiency of relaxation on the PS.     

Secondary structure prediction of beta-hairpin peptide tryptophan zipper-I

We have investigated the folding properties of tryptophan zipper-I molecule which folds into a stable β-hairpin motif in aqueous solution as suggested by nuclear magnetic resonance (NMR) experiments. An all-atom presentation, including hydrogen, was used with an implicit solvent. As a simulation technique, simulated tempering algorithm was used to obtain equilibrium conformations of the molecule at ten distinct temperatures. Our minimum energy configuration obtained from simulated tempering algorithm is a β-hairpin motif with 1.30 Å backbone root-mean-square deviation from the reference PDB structure (1le0.pdb). Several quantities and exhaustive folding free energy landscapes were determined and discussed in order to clarify the folding behavior.     

Three-species reaction-diffusion processes on scale-free networks

We study the novel three-species reaction-diffusion processes of scale-free networks that are significantly different from numerical calculations manipulated on regular and small-world lattices. The inverse particle density for the three-species process scales according to the power-law with a scaling exponent α=1.5 for γ>3. It is, however, found from numerical results that the inverse particle density scales in a different way depending on time t when γ<3. In the early time regime, α?1.5, but the inverse particle density increases exponentially over time. We also discuss the possible relationship with the dynamical properties of random walks. In particular, we measure the ratio between the number of inactive and active bonds which shows the segregation of the particles.     

Monomer Adsorption-Desorption Processes

We propose an adsorption-desorption model for a deposit growth system, in which the adsorption and desorption of particles coexist. By means of the generalized rate equation we investigate the cluster （island） size distribution in the dynamic equilibrium state. The results show that the evolution behaviour of the system depends crucially on the details of the rate kernels. The cluster size distribution can take the scale-free power-law form in some cases, while it grows exponentially with size in other cases.     

Entropy of electromyography time series

A nonlinear analysis based on Renyi entropy is applied to electromyography (EMG) time series from back muscles. The time dependence of the entropy of the EMG signal exhibits a crossover from a subdiffusive regime at short times to a plateau at longer times. We argue that this behavior characterizes complex biological systems. The plateau value of the entropy can be used to differentiate between healthy and low back pain individuals.     

Quantum ergodicity and energy flow in molecules

We review a theory for coupled many-nonlinear oscillator systems that describes quantum ergodicity and energy flow in molecules. The theory exploits the isomorphism between quantum energy flow in Fock space, that is, vibrational state space, and single-particle quantum transport in disordered solid-state systems. The quantum ergodicity transition in molecules is thereby analogous to the Anderson transition in disordered solids. The theory reviewed here, local random matrix theory (LRMT), describes the nature of the quantum ergodicity transition, statistical properties of vibrational eigenstates, and quantum energy flow through the vibrational states of molecules. Predictions of LRMT have been observed in computational studies of coupled nonlinear oscillator systems, which are summarized here. We also review applications of LRMT to molecular spectroscopy and chemical reaction rate theory, including adoption of LRMT in theories that predict rates of conformational change of molecules taking place at energies corresponding to those below and above the quantum ergodicity transition. A number of specific examples are reviewed, including the application of LRMT to predict (1) dilution factors of IR spectra of organic molecules, (2) rates of conformational change in chemical and photochemical reactions, (3) conformational dynamics of biological molecules in molecular beams, (4) rates of hydrogen bond breaking and rearrangement in clusters of biological molecules and water, and (5) excited state proton transfer reactions in proteins.     

Protein conformational fluctuations and free-energy transduction

Non-equilibrium fluctuations, whether imposed externally or driven by an energy-releasing chemical reaction, can cause a protein to cycle through several conformations. This cycling can drive a process thermodynamically uphill even though any one conformation considered independently catalyzes the process in the downhill direction. This is because the different conformations have different rate constants (energy barriers) between the states in the catalytic cycle. Even though each conformation individually obeys detailed balance, the flashing between different energy profiles gives rise to a ratchet effect. Further, by exploiting protein conformational dynamics, a single stochastic input can be converted into two phase-shifted internal parameters (e.g. a kinetic barrier height and a binding well energy). This allows the output process to be driven nearly adiabatically, explaining in part the very high efficiencies observed for some biological energy-transduction processes. The results apply equally to driving a biochemical reaction away from equilibrium by an enzyme, to formation of an osmotic gradient across a membrane by a molecular pump, or to motion and generation of force by a molecular motor. Received: 8 February 2002 / Accepted: 4 March 2002 / Published online: 22 April 2002     

Statistical characteristics of photon distributions in a semi-infinite turbid medium: Analytical expressions and their application to optical tomography

The paper focuses on the determination of statistical characteristics of photon distributions in a semi-infinite turbid medium, specifically the photon average trajectory and the root-mean-square deviation of photons from the average trajectory, with an approach based on the diffusion approximation to the radiative transfer equation. We show that the Dirichlet and Robin boundary conditions used for this purpose give close results. We derive exact analytical expressions for the case of the Dirichlet boundary condition. To demonstrate the practical value of our results we consider approximate solution of the inverse problem of time-domain diffuse optical tomography with the flat layer transmission geometry. The problem is solved with the method of photon average trajectories which are constructed with analytical expressions derived for a semi-infinite medium.     

Folding kinetics of two-state proteins based on the model of general random walk in native contact number space

We investigated the folding kinetics of a series of two-state proteins by using the model of general random walk in native contact number space, and derive the observed linear relationship between the logarithms of the folding rate constants and the numbers of native contacts from “kinetic viewpoint”. The protein folding speed limit and stability in this model are consistent with experimental observations.     

Coupled oscillator models with no scale separation

We consider a class of spatially discrete wave equations that describe the motion of a system of linearly coupled oscillators perturbed by a nonlinear potential. We show that the dynamical behavior of this system cannot be understood by considering the slowest modes only: there is an “inverse cascade” in which the effects of changes in small scales are felt by the largest scales and the mean-field closure does not work. Despite this, a one and a half degree of freedom model is derived that includes the influence of the small-scale dynamics and predicts global conformational changes accurately. Thus, we provide a reduced model for a system in which there is no separation of scales. We analyze a specific coupled-oscillator system that models global conformation change in biomolecules, introduced in [I. Mezi?, On the dynamics of molecular conformation, Proc. Natl. Acad. Sci. 103 (20) (2006) 7542-7547]. In this model, the conformational states are stable to random perturbations, yet global conformation change can be quickly and robustly induced by the action of a targeted control. We study the efficiency of small-scale perturbations on conformational change and show that “zipper” traveling wave perturbations provide an efficient means for inducing such change. A visualization method for the transport barriers in the reduced model yields insight into the mechanism by which the conformation change occurs.     

Active Control of Cellular Orientation through In-Situ Stress in the Substrate

We investigate the orientation of cells on substrates to find possible methods for controlling the cellular orientation. The force dipole model is employed in our modelling and simulation. The elastic interaction between cells as well as the elastic interaction between the cell and in-situ stress field in the substrate are found to be the two main physical mechanisms to control the cellular orientation. The former interaction dominates the cellular orientation when the in-situ stress is small, while the later dominates when the in-situ stress is large enough. Two cells tend to align perpendicularly on a free substrate, but the cellular orientation varies with the increasing in-situ stress. Two cells tendto align in parallel when the normal stress is large enough. Their direction is perpendicular to the extension stress direction or parallel to the compression stress direction. When the positive in-situ shear stress is large enough, the two cells tend to align at -45°. Based on this theoretical simulation, it is believed that the cellular orientation on substrates can be controlled by thein-situ stresses.     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

Parameter selection in a Peyrard-Bishop-Dauxois model for DNA dynamics

In this Letter we study possible intervals for some parameters existing in the Peyrard-Bishop-Dauxois (PBD) model for the DNA dynamics. These parameters describe longitudinal and helicoidal interactions between nucleotides and a Morse potential approximating transverse interactions. We also estimate a possible interval for a wave number of a carrier component of a modulated solitonic wave. Finally, we compare our statements with experimental value of solitonic velocity in DNA.