Antagonism between granulocytic maturation and deacetylase inhibitor-induced apoptosis in acute promyelocytic leukaemia cells.

BACKGROUND: Transcriptional repression is a key mechanism driving leukaemogenesis. In acute promyelocytic leukaemia (APL), the fusion protein promyelocytic leukaemia-retinoic acid receptor-α fusion (PML-RARα) recruits transcriptional repressors to myeloid differentiation genes. All-trans-retinoic acid (ATRA) induces the proteasomal degradation of PML-RARα and granulocytic differentiation. Histone deacetylases (HDACs) fall into four classes (I-IV) and contribute to the transcription block caused by PML-RARα. METHODS: Immunoblot, flow cytometry, and May-Grünwald-Giemsa staining were used to analyze differentiation and induction of apoptosis. RESULTS: A PML-RARα- and ATRA-dependent differentiation programme induces granulocytic maturation associated with an accumulation of the myeloid transcription factor CCAAT/enhancer binding protein (C/EBP)ɛ and of the surface protein CD11b. While this process protects APL cells from inhibitors of class I HDAC activity, inhibition of all Zinc-dependent HDACs (classes I, II, and IV) with the pan-HDACi (histone deacetylase inhibitor(s)) LBH589 induces apoptosis of immature and differentiated APL cells. LBH589 can eliminate C/EBPɛ and the mitochondrial apoptosis regulator B-cell lymphoma (BCL)-xL in immature and differentiated NB4 cells. Thus, BCL-xL and C/EBPɛ are newly identified molecular markers for the efficacy of HDACi against APL cells. CONCLUSIONS: Our results could explain the therapeutic limitations occurring with ATRA and class I HDACi combinations. Pro-apoptotic effects caused by pan-HDAC inhibition are not blunted by ATRA-induced differentiation and may provide a clinically interesting alternative.

Nonlinear response of a linear chain to weak driving.

We study the escape of a chain of coupled units over the barrier of a metastable potential. It is demonstrated that a very weak external driving field with a suitably chosen frequency suffices to accomplish speedy escape. The latter requires passage through a transition state, the formation of which is triggered by permanent feeding of energy from a phonon background into humps of localized energy and elastic interaction of the arising breather solutions. In fact, cooperativity between the units of the chain entailing coordinated energy transfer is shown to be crucial for enhancing the rate of escape in an extremely effective and low-energy cost way where the effects of entropic localization and breather coalescence conspire.

Current reversals of coupled driven and damped particles evolving in a tilted potential landscape.

We explore the driven and damped dynamics of two coupled particles evolving in a symmetric and periodic substrate potential that is subjected to a static bias force. In addition, each particle is time-periodically driven with the same magnitude as, but out of phase to, its counterpart. It is shown that, for a certain parameter regime, the coupled particles can become self-organized and go against the direction of the bias force. This self-organization involves the particles becoming frequency locked with the driving force, and thus periodic motion ensues. We employ numerical arguments to show that running periodic states provide solutions of the system. Further, heuristic evidence is provided explaining how the two particles can travel against the bias force. In an effort to unearth coupling phenomena within the system, a detailed analysis of how the coupling strength affects the nonlinear dynamics is carried out. We show that within a range of coupling strengths the existence of periodic running solutions associated with negative mobility. To examine the robustness of our results we compare the deterministic system with the corresponding Langevin system. It is shown that, below a critical temperature, the qualitative behavior of the system remains the same.

From collective periodic running states to completely chaotic synchronised states in coupled particle dynamics.

We consider the damped and driven dynamics of two interacting particles evolving in a symmetric and spatially periodic potential. The latter is exerted to a time-periodic modulation of its inclination. Our interest is twofold: First, we deal with the issue of chaotic motion in the higher-dimensional phase space. To this end, a homoclinic Melnikov analysis is utilised assuring the presence of transverse homoclinic orbits and homoclinic bifurcations for weak coupling allowing also for the emergence of hyperchaos. In contrast, we also prove that the time evolution of the two coupled particles attains a completely synchronised (chaotic) state for strong enough coupling between them. The resulting "freezing of dimensionality" rules out the occurrence of hyperchaos. Second, we address coherent collective particle transport provided by regular periodic motion. A subharmonic Melnikov analysis is utilised to investigate persistence of periodic orbits. For directed particle transport mediated by rotating periodic motion, we present exact results regarding the collective character of the running solutions entailing the emergence of a current. We show that coordinated energy exchange between the particles takes place in such a manner that they are enabled to overcome--one particle followed by the other--consecutive barriers of the periodic potential resulting in collective directed motion.

Current reversals and current suppression in an open two-degree-of-freedom system.

We explore the scattering of particles evolving in a two-degree-of-freedom Hamiltonian system, in which both degrees of freedom are open. Particles, initially having all kinetic energy, are sent into a so-called "interaction region," where there will be an exchange of energy with particles that are initially at rest. The open nature of both components of this system eliminates any restrictions on which particles can escape from the interaction region. Notably, it is shown that two particles can cooperate in a mutual exchange of energy allowing both particles to escape and travel large distances. It is also shown that this level of cooperation is highly sensitive to the coupling strength between both components of the system. Indeed, large fluctuations of the magnitude and direction of the current are observed for small changes of this coupling parameter. Further, it is seen that current reversals are a prominent feature of this model. Another interesting observation is that even with the presence of chaotic scattering, it is possible that the system, for certain parameter regimes, will express a vanishing current, suggesting that there is a restoration of symmetry which, due to the initial setup, is broken. For an explanation of the different features of particle motion, we relate the phase-space dynamics to the various regimes of particle current.

Directed current in the Holstein system.

We propose a mechanism to rectify charge transport in the semiclassical Holstein model. It is shown that localized initial conditions associated with a polaron solution, in conjunction with static electron on-site potential not having inversion symmetry, constitute minimal prerequisites for the emergence of a directed current in the underlying periodic lattice system. In particular, we demonstrate that for unbiased spatially localized initial conditions (constituted by kicked static polaron states), violation of parity prevents the existence of pairs of counterpropagating trajectories, thus allowing for a directed current despite the time reversibility of the equations of motion. Nevertheless, propagating polaron solutions associated with sets of unbiased localized initial conditions which eventually leave the region of localized initial conditions do not exhibit time reversibility. Since the initial conditions belonging to the corresponding counterpropagating, current-compensating polaron solutions are not contained in the set, this gives rise to the emergence of a current. Occurrence of long-range coherent charge transport is demonstrated.

Emergence of continual directed flow in hamiltonian systems.

We propose a minimal model for the emergence of a directed flow in autonomous hamiltonian systems. It is shown that internal breaking of the spatiotemporal symmetries, via localized initial conditions, which are unbiased with respect to the transporting degree of freedom, and transient chaos conspire to form the physical mechanism for the occurrence of a current. Most importantly, after passage through the transient chaos, trajectories perform solely regular transporting motion so that the resulting current is of continual ballistic nature. This has to be distinguished from the features of transport reported previously for driven hamiltonian systems with mixed phase space where transport is determined by intermittent behavior exhibiting power-law decay statistics of the duration of regular ballistic periods.

Current control in a tilted washboard potential via time-delayed feedback.

We consider the motion of an overdamped Brownian particle in a washboard potential exerted to a static tilting force. The bias yields directed net particle motion, i.e., a current. It is demonstrated that with an additional time-delayed feedback term, the particle current can be reversed against the direction of the bias. The control function induces a ratchetlike effect that hinders further current reversals and thus the particle moves against the direction of the static bias. Furthermore, varying the delay time allows also to continuously depreciate and even stop the transport in the washboard potential. We identify and characterize the underlying mechanism which applies to the current control in a wide temperature range.

Directed transport of an inertial particle in a washboard potential induced by delayed feedback.

We consider motion of an underdamped Brownian particle in a washboard potential that is subjected to an unbiased time-periodic external field. While in the limiting deterministic system in dependence of the strength and phase of the external field directed net motion can exist; for a finite temperature the net motion averages to zero. Strikingly, with the application of an additional time-delayed feedback term directed particle motion can be accomplished persisting up to fairly high levels of the thermal noise. In detail, there exist values of the feedback strength and delay time for which the feedback term performs oscillations that are phase locked to the time-periodic external field. This yields an effective biasing rocking force promoting periods of forward and backward motion of distinct duration, and thus directed motion. In terms of phase space dynamics we demonstrate that with applied feedback desymmetrization of coexisting attractors takes place leaving the ones supporting either positive or negative velocities as the only surviving ones. Moreover, we found parameter ranges for which in the presence of thermal noise the directed transport is enhanced compared to the noiseless case.

Escape dynamics of coupled particles in nonlinear, disordered lattices.

We consider the deterministic escape dynamics of a lattice chain of harmonically coupled particles from a metastable state over a one-dimensional potential barrier. While the case of periodic lattices has already been elaborated, the aim of the present work is to explore the extension to nonperiodic, i.e., disordered, lattices. Each particle evolves in an individual local potential, which is characterized by a harmonic term and a nonlinear term. Two kinds of parametric disorder are considered. "Disorder in nonlinearity" is only caused by different nonlinear terms--"disorder in harmonicity" only by different harmonic terms. We assure that the two kinds of disorder, with their individual potential barriers uniformly distributed around a globally equal mean barrier height, exhibit a comparable strength of disorder. Starting with an initial completely delocalized state, we observe localization of energy and formation of breathers ensues. It is shown that increasing disorder in nonlinearity decreases the mean escape time opposite to increasing mean escape times resulting from increased disorder in harmonicity. Comparison with the mean escape time obtained for a third kind of parametric disorder characterized by overall equal barrier heights leads to the conclusion that indeed inhomogeneous barriers facilitate the speedy escape.

Resonancelike phenomena in the mobility of a chain of nonlinear coupled oscillators in a two-dimensional periodic potential.

We study the Langevin dynamics of a two-dimensional discrete oscillator chain absorbed on a periodic substrate and subjected to an external localized point force. Going beyond the commonly used harmonic bead-spring model, we consider a nonlinear Morse interaction between the next-nearest neighbors. We focus interest on the activation of directed motion instigated by thermal fluctuations and the localized point force. In this context the local transition states are identified and the corresponding activation energies are calculated. It is found that the transport of the chain in point force direction is determined by stepwise escapes of a single unit or segments of the chain due to the existence of multiple locally stable attractors. The nonvanishing net current of the chain is quantitatively assessed by the value of the mobility of the center of mass. It turns out that the latter as a function of the ratio of the competing length scales of the system, that is the period of the substrate potential and the equilibrium distance between two chain units, shows a resonance behavior. More precisely there exists a set of optimal parameter values maximizing the mobility. Interestingly, the phenomenon of negative resistance is found, i.e., the mobility possesses a minimum at a finite value of the strength of the thermal fluctuations for a given overcritical external driving force.

Transition between locked and running states for dimer motion induced by periodic external driving.

We study the motion of a dimer in a one-dimensional spatially periodic washboard potential. The tilt of the latter is time-periodically modulated by an ac field. We focus interest on the detrapping of the (static) ground state solution of the dimer caused by the ac field. Moreover, we demonstrate that slow tilt modulations not only induce a trapping-detrapping transition but drive the dimer dynamics into a regime of transient long-range running states. Most strikingly, the motion proceeds then unidirectionally, so that the dimer covers huge distances regardless of the fact that the bias force in the driven system vanishes on the average. We elucidate the underlying dynamics in phase space and associate long-lasting running states with the motion in ballistic channels occurring due to stickiness to invariant tori.

Deterministic escape dynamics of two-dimensional coupled nonlinear oscillator chains.

We consider the deterministic escape dynamics of a chain of coupled oscillators under microcanonical conditions from a metastable state over a cubic potential barrier. The underlying dynamics is conservative and noise free. We introduce a two-dimensional chain model and assume that neighboring units are coupled by Morse springs. It is found that, starting from a homogeneous lattice state, due to the nonlinearity of the external potential the system self-promotes an instability of its initial preparation and initiates complex lattice dynamics leading to the formation of localized large amplitude breathers, evolving in the direction of barrier crossing, accompanied by global oscillations of the chain transverse to the barrier. A few chain units accumulate locally sufficient energy to cross the barrier. Eventually the metastable state is left and either these particles dissociate or pull the remaining chain over the barrier. We show this escape for both linear rodlike and coil-like configurations of the chain in two dimensions.

Compounds of paired electrons and lattice solitons moving with supersonic velocity.

We study the time evolution of two correlated electrons of opposite spin in an anharmonic lattice chain. The electrons are described quantum mechanically by the Hubbard model while the lattice is treated classically. The lattice units are coupled via Morse-Toda potentials. Interaction between the lattice and the electrons arises due to the dependence of the electron transfer-matrix element on the distance between neighboring lattice units. Localized configurations comprising a paired electron and a pair of lattice deformation solitons are constructed such that an associated energy functional is minimized. We investigate long-lived, stable pairing features. It is demonstrated that traveling pairs of lattice solitons serve as carriers for the paired electrons realizing coherent transport of the two correlated electrons. We also observe dynamical narrowing of the states, that is, starting from an initial double-peak profile of the electron probability distribution, a single-peak profile is adopted going along with enhancement of localization of the paired electrons. Interestingly, a parameter regime is identified for which supersonic transport of paired electrons is achieved.

Self-organized escape of oscillator chains in nonlinear potentials.

We present the noise-free escape of a chain of linearly interacting units from a metastable state over a cubic on-site potential barrier. The underlying dynamics is conservative and purely deterministic. The mutual interplay between nonlinearity and harmonic interactions causes an initially uniform lattice state to become unstable, leading to an energy redistribution with strong localization. As a result, a spontaneously emerging localized mode grows into a critical nucleus. By surpassing this transition state, the nonlinear chain manages a self-organized, deterministic barrier crossing. Most strikingly, these noise-free, collective nonlinear escape events proceed generally by far faster than transitions assisted by thermal noise when the ratio between the average energy supplied per unit in the chain and the potential barrier energy assumes small values.

Electron capture and transport mediated by lattice solitons.

We study electron transport in a one-dimensional molecular lattice chain. The molecules are linked by Morse interaction potentials. The electronic degree of freedom, expressed in terms of a tight binding system, is coupled to the longitudinal displacements of the molecules from their equilibrium positions along the axis of the lattice. More specifically, the distance between two sites influences in an exponential fashion the corresponding electronic transfer matrix element. We demonstrate that when an electron is injected in the undistorted lattice it causes a local deformation such that a compression results leading to a lowering of the electron's energy below the lower edge of the band of linear states. This corresponds to self-localization of the electron due to a polaronlike effect. Then, if a traveling soliton lattice deformation is launched a distance apart from the electron's position, upon encountering the polaronlike state it captures the latter dragging it afterwards along its path. Strikingly, even when the electron is initially uniformly distributed over the lattice sites a traveling soliton lattice deformation gathers the electronic amplitudes during its traversing of the lattice. Eventually, the electron state is strongly localized and moves coherently in unison with the soliton lattice deformation. This shows that for the achievement of coherent electron transport we need not start with the polaronic effect.

Synchronization and firing death in the dynamics of two interacting excitable units with heterogeneous signals.

We study the response of two coupled FitzHugh-Nagumo systems to heterogeneous external inputs. The latter, modeled by periodic parametric stimuli, force the uncoupled excitable systems into a regime of chaotic firing. Due to parameter dispersion involved in randomly distributed amplitudes and/or phases of the external forces the units are nonidentical and their firing events will be asynchronous. Interest is focused on mutually synchronized spikings arising through the coupling. It is demonstrated that the phase difference of the two external forces crucially affects the onset of spike synchronization as well as the resulting degree of synchrony. For large phase differences the degree of spike synchrony is constricted to a maximal possible value and cannot be enhanced upon increasing the coupling strength. We even found that overcritically strong couplings lead to suppression of firing so that the units perform synchronous subthreshold oscillations. This effect, which we call "firing death," is due to a coupling-induced modification of the excitation threshold impeding spiking of the units. In clear contrast, when only the amplitudes of the forces are distributed perfect spike synchrony is achieved for sufficiently strong coupling.

Regular patterns in dichotomically driven activator-inhibitor dynamics.

We investigate Turing pattern formation in the presence of additive dichotomous fluctuations in the context of an extended system with diffusive coupling and FitzHugh-Nagumo kinetics. The fluctuations vary in space and/or time. Depending on the realization of the dichotomous switching the system is, at a given time (for spatial disorder at a given position) in one of two possible excitable dynamical regimes. Each of the two excitable dynamics for itself does not support pattern formation. With proper dichotomous fluctuations, however, the homogeneous steady state is destabilized via a Turing instability. We investigate the influence of different switching rates (different correlation length of the spatial disorder) on pattern formation. We find three distinct mechanisms: For slow switching existing boundaries become unstable, for high rates the system exhibits "effective bistability" which allows for a Turing instability. For medium rates the fluctuations create spatial structures via a new mechanism where the influence of the fluctuations is twofold. First they produce local inhomogeneities, which then grow (again caused by fluctuations) until the whole space is covered. Utilizing a nonlinear map approach we show bistability of a period-one and a period-two orbit being associated with the steady homogeneous and the Turing pattern state, respectively. Finally, for purely static dichotomous disorder we find destabilization of homogeneous steady states for finite nonzero correlation length of the disorder resulting again in Turing patterns.

Localization properties of electronic states in a polaron model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers.

We numerically investigate localization properties of electronic states in a static model of poly(dG)-poly(dC) and poly(dA)-poly(dT) DNA polymers with realistic parameters obtained by quantum-chemical calculation. The randomness in the on-site energies caused by the electron-phonon coupling is completely correlated to the off-diagonal parts. In the single electron model, the effect of the hydrogen-bond stretchings, the twist angles between the base pairs and the finite system size effects on the energy dependence of the localization length and on the Lyapunov exponent are given. The localization length is reduced by the influence of the fluctuations in the hydrogen bond stretchings. It is also shown that the helical twist angle affects the localization length in the poly(dG)-poly(dC) DNA polymer more strongly than in the poly(dA)-poly(dT) one. Furthermore, we show resonance structures in the energy dependence of the localization length when the system size is relatively small.

Modelling the thermal evolution of enzyme-created bubbles in DNA.

The formation of bubbles in nucleic acids (NAs) is fundamental in many biological processes such as DNA replication, recombination, telomere formation and nucleotide excision repair, as well as RNA transcription and splicing. These processes are carried out by assembled complexes with enzymes that separate selected regions of NAs. Within the frame of a nonlinear dynamics approach, we model the structure of the DNA duplex by a nonlinear network of coupled oscillators. We show that, in fact, from certain local structural distortions, there originate oscillating localized patterns, that is, radial and torsional breathers, which are associated with localized H-bond deformations, reminiscent of the replication bubble. We further study the temperature dependence of these oscillating bubbles. To this aim, the underlying nonlinear oscillator network of the DNA duplex is brought into contact with a heat bath using the Nosé-Hoover method. Special attention is paid to the stability of the oscillating bubbles under the imposed thermal perturbations. It is demonstrated that the radial and torsional breathers sustain the impact of thermal perturbations even at temperatures as high as room temperature. Generally, for non-zero temperature, the H-bond breathers move coherently along the double chain, whereas at T=0 standing radial and torsional breathers result.