171 research outputs found
Slow-Fast Analysis of a Multi-Group Asset Flow Model with Implications for the Dynamics of Wealth
The multi-group asset flow model is a nonlinear dynamical system originally developed as a tool for understanding the behavioral foundations of market phenomena such as flash crashes and price bubbles. In this paper we use a modification of this model to analyze the dynamics of a single-asset market in situations when the trading rates of investors (i.e., their desire to exchange stock for cash) are prescribed ahead of time and independent of the state of the market. Under the assumption of fast trading compared to the time-rate of change in the prescribed trading rates we decompose the dynamics of the system to fast and slow components. We use the model to derive a variety of observations regarding the dynamics of price and investorsâ wealth, and the dependence of these quantities on the prescribed trading rates. In particular, we show that strategies with constant trading rates, which represent the well-known constant-rebalanced portfolio (CRP) strategies, are optimal in the sense that they minimize investment risks. In contrast, we show that investors pursuing non-CRP strategies are at risk of loss of wealth, as a result of the slow system not being integrable in the sense that cyclic trading rates do not always result in periodic price variations
Nonlinear Dynamics and Stability In a Multigroup Asset Flow Model
The multigroup asset flow model for asset price dynamics incorporates distinct motivations, e. g., trend and fundamentals (value) and assessments of value by different groups of investors. The stability and bifurcation properties are established for the curve of equilibria. We prove that if all trader groups focus on fundamentals, then all equilibria are stable. For systems in which there is one fundamental and one momentum (trend) group, we establish conditions for stability. In particular, an equilibrium that is stable becomes unstable as the time scale on which momentum investors focus diminishes. The computations examine the excursions, which we define as the maximum deviation in price of the trajectory from its initial price located near the curve of equilibria
Using a continuum model to predict closure time of gaps in intestinal epithelial cell layers
A two-dimensional continuum model of collective cell migration is used to predict the closure of gaps in intestinal epithelial cell layers. The model assumes that cell migration is governed by lamellipodia formation, cell-cell adhesion, and cell-substrate adhesion. Model predictions of the gap edge position and complete gap closure time are compared with experimental measures from cell layer scratch assays (also called scratch wound assays). The goal of the study is to combine experimental observations with mathematical descriptions of cell motion to identify effects of gap shape and area on closure time and to propose a method that uses a simple measure (e.g., area) to predict overall gap closure time early in the closure process. Gap closure time is shown to increase linearly with increasing gap area; however, gaps of equal areas but different aspect ratios differ greatly in healing time. Previous methods that calculate overall healing time according to the absolute or percent change in gap area assume that the gap area changes at a constant rate and typically underestimate gap closure time. In this study, data from scratch assays suggest that the rate of change of area is proportional to the first power or square root power of area
A three-tiered study of differences in murine intrahost immune response to multiple pneumococcal strains
We apply a previously developed 4-variable ordinary differential equation model of in-host immune response to pneumococcal pneumonia to study the variability of the immune response of MF1 mice and to explore bacteria-driven differences in disease progression and outcome. In particular, we study the immune response to D39 strain of bacteria missing portions of the pneumolysin protein controlling either the hemolytic activity or complement-activating activity, the response to D39 bacteria deficient in either neuraminidase A or B, and the differences in the response to D39 (serotype 2), 0100993 (serotype 3), and TIGR4 (serotype 4) bacteria. The model accurately reproduces infection kinetics in all cases and provides information about which mechanisms in the immune response have the greatest effect in each case. Results suggest that differences in the ability of bacteria to defeat immune response are primarily due to the ability of the bacteria to elude nonspecific clearance in the lung tissue as well as the ability to create damage to the lung epithelium
DNA cyclization and looping in the wormlike limit: normal modes and the validity of the harmonic approximation
For much of the last three decades Monte Carlo-simulation methods have been
the standard approach for accurately calculating the cyclization probability,
, or J factor, for DNA models having sequence-dependent bends or
inhomogeneous bending flexibility. Within the last ten years, however,
approaches based on harmonic analysis of semi-flexible polymer models have been
introduced, which offer much greater computational efficiency than Monte Carlo
techniques. These methods consider the ensemble of molecular conformations in
terms of harmonic fluctuations about a well-defined elastic-energy minimum.
However, the harmonic approximation is only applicable for small systems,
because the accessible conformation space of larger systems is increasingly
dominated by anharmonic contributions. In the case of computed values of the J
factor, deviations of the harmonic approximation from the exact value of as
a function of DNA length have not been characterized. Using a recent,
numerically exact method that accounts for both anharmonic and harmonic
contributions to for wormlike chains of arbitrary size, we report here the
apparent error that results from neglecting anharmonic behavior. For wormlike
chains having contour lengths less than four times the persistence length the
error in arising from the harmonic approximation is generally small,
amounting to free energies less than the thermal energy, . For larger
systems, however, the deviations between harmonic and exact values increase
approximately linearly with size.Comment: 23 pages, 6 figures. Typos corrected. Manuscript improve
Nucleosome repositioning via loop formation
Active (catalysed) and passive (intrinsic) nucleosome repositioning is known
to be a crucial event during the transcriptional activation of certain
eucaryotic genes. Here we consider theoretically the intrinsic mechanism and
study in detail the energetics and dynamics of DNA-loop-mediated nucleosome
repositioning, as previously proposed by Schiessel et al. (H. Schiessel, J.
Widom, R. F. Bruinsma, and W. M. Gelbart. 2001. {\it Phys. Rev. Lett.}
86:4414-4417). The surprising outcome of the present study is the inherent
nonlocality of nucleosome motion within this model -- being a direct physical
consequence of the loop mechanism. On long enough DNA templates the longer
jumps dominate over the previously predicted local motion, a fact that
contrasts simple diffusive mechanisms considered before. The possible
experimental outcome resulting from the considered mechanism is predicted,
discussed and compared to existing experimental findings
Lac repressor mediated DNA looping: Monte Carlo simulation of constrained DNA molecules complemented with current experimental results
Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor. © 2014 Biton et al
Tops and Writhing DNA
The torsional elasticity of semiflexible polymers like DNA is of biological
significance. A mathematical treatment of this problem was begun by Fuller
using the relation between link, twist and writhe, but progress has been
hindered by the non-local nature of the writhe. This stands in the way of an
analytic statistical mechanical treatment, which takes into account thermal
fluctuations, in computing the partition function. In this paper we use the
well known analogy with the dynamics of tops to show that when subjected to
stretch and twist, the polymer configurations which dominate the partition
function admit a local writhe formulation in the spirit of Fuller and thus
provide an underlying justification for the use of Fuller's "local writhe
expression" which leads to considerable mathematical simplification in solving
theoretical models of DNA and elucidating their predictions. Our result
facilitates comparison of the theoretical models with single molecule
micromanipulation experiments and computer simulations.Comment: 17 pages two figure
Sequence Dependence of Transcription Factor-Mediated DNA Looping
DNA is subject to large deformations in a wide range of biological processes.
Two key examples illustrate how such deformations influence the readout of the
genetic information: the sequestering of eukaryotic genes by nucleosomes, and
DNA looping in transcriptional regulation in both prokaryotes and eukaryotes.
These kinds of regulatory problems are now becoming amenable to systematic
quantitative dissection with a powerful dialogue between theory and experiment.
Here we use a single-molecule experiment in conjunction with a statistical
mechanical model to test quantitative predictions for the behavior of DNA
looping at short length scales, and to determine how DNA sequence affects
looping at these lengths. We calculate and measure how such looping depends
upon four key biological parameters: the strength of the transcription factor
binding sites, the concentration of the transcription factor, and the length
and sequence of the DNA loop. Our studies lead to the surprising insight that
sequences that are thought to be especially favorable for nucleosome formation
because of high flexibility lead to no systematically detectable effect of
sequence on looping, and begin to provide a picture of the distinctions between
the short length scale mechanics of nucleosome formation and looping.Comment: Nucleic Acids Research (2012); Published version available at
http://nar.oxfordjournals.org/cgi/content/abstract/gks473?
ijkey=6m5pPVJgsmNmbof&keytype=re
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