32 research outputs found
Mathematical modeling reveals threshold mechanism in CD95-induced apoptosis
Mathematical modeling is required for understanding the complex behavior of large signal transduction networks. Previous attempts to model signal transduction pathways were often limited to small systems or based on qualitative data only. Here, we developed a mathematical modeling framework for understanding the complex signaling behavior of CD95(APO-1/Fas)-mediated apoptosis. Defects in the regulation of apoptosis result in serious diseases such as cancer, autoimmunity, and neurodegeneration. During the last decade many of the molecular mechanisms of apoptosis signaling have been examined and elucidated. A systemic understanding of apoptosis is, however, still missing. To address the complexity of apoptotic signaling we subdivided this system into subsystems of different information qualities. A new approach for sensitivity analysis within the mathematical model was key for the identification of critical system parameters and two essential system properties: modularity and robustness. Our model describes the regulation of apoptosis on a systems level and resolves the important question of a threshold mechanism for the regulation of apoptosis
The instability of Alexander-McTague crystals and its implication for nucleation
We show that the argument of Alexander and McTague, that the bcc crystalline
structure is favored in those crystallization processes where the first order
character is not too pronounced, is not correct. We find that any solution that
satisfies the Alexander-McTague condition is not stable. We investigate the
implication of this result for nucleation near the pseudo- spinodal in
near-meanfield systems.Comment: 20 pages, 0 figures, submitted to Physical Review
Zeros of the Partition Function and Pseudospinodals in Long-Range Ising Models
The relation between the zeros of the partition function and spinodal
critical points in Ising models with long-range interactions is investigated.
We find the spinodal is associated with the zeros of the partition function in
four-dimensional complex temperature/magnetic field space. The zeros approach
the real temperature/magnetic field plane as the range of interaction
increases.Comment: 20 pages, 9 figures, accepted to PR
Avalanches in the Weakly Driven Frenkel-Kontorova Model
A damped chain of particles with harmonic nearest-neighbor interactions in a
spatially periodic, piecewise harmonic potential (Frenkel-Kontorova model) is
studied numerically. One end of the chain is pulled slowly which acts as a weak
driving mechanism. The numerical study was performed in the limit of infinitely
weak driving. The model exhibits avalanches starting at the pulled end of the
chain. The dynamics of the avalanches and their size and strength distributions
are studied in detail. The behavior depends on the value of the damping
constant. For moderate values a erratic sequence of avalanches of all sizes
occurs. The avalanche distributions are power-laws which is a key feature of
self-organized criticality (SOC). It will be shown that the system selects a
state where perturbations are just able to propagate through the whole system.
For strong damping a regular behavior occurs where a sequence of states
reappears periodically but shifted by an integer multiple of the period of the
external potential. There is a broad transition regime between regular and
irregular behavior, which is characterized by multistability between regular
and irregular behavior. The avalanches are build up by sound waves and shock
waves. Shock waves can turn their direction of propagation, or they can split
into two pulses propagating in opposite directions leading to transient
spatio-temporal chaos. PACS numbers: 05.70.Ln,05.50.+q,46.10.+zComment: 33 pages (RevTex), 15 Figures (available on request), appears in
Phys. Rev.
Simulation of thermal conductivity and heat transport in solids
Using molecular dynamics (MD) with classical interaction potentials we
present calculations of thermal conductivity and heat transport in crystals and
glasses. Inducing shock waves and heat pulses into the systems we study the
spreading of energy and temperature over the configurations. Phonon decay is
investigated by exciting single modes in the structures and monitoring the time
evolution of the amplitude using MD in a microcanonical ensemble. As examples,
crystalline and amorphous modifications of Selenium and are
considered.Comment: Revtex, 8 pages, 11 postscript figures, accepted for publication in
PR
Random loop model for long polymers.
While the structure of chromatin has been studied in great detail on length
scales below 30 nm, amazingly little is known about the higher-order folding
motifs of chromatin in interphase. Recent experiments give evidence that the
folding may depend locally on gene density and transcriptional activity and
show a leveling-off at long distances where approximately . We
propose a new model that can explain this leveling-off by the formation of
random loops. We derive an analytical expression for the mean square
displacement between two beads where the average is taken over the thermal
ensemble with a fixed but random loop configuration, while quenched averaging
over the ensemble of different loop configurations -- which turns out to be
equivalent to averaging over an ensemble of random matrices -- is performed
numerically. A detailed investigation of this model shows that loops on all
scales are necessary to fit experimental data.Comment: 8 pages, 7 figures; major changes: added paragraph with calculation
of the annealed ensembl