A power-law summarizes uptake dependence on host receptors | A power-law summarizes uptake dependence on host receptors |
A power-law summarizes uptake dependence on host receptors | The approximately linear relationship between the logarithm of uptake and host receptors indicates the power-law dependence. |
A power-law summarizes uptake dependence on host receptors | Sequential perturbation of Zipper model parameters shows that these changes can be mapped to changes in both power-law parameters (84C Fig). |
Abstract | Surprisingly, we found that the uptake probability of a single bacterium follows a simple power-law dependence on the concentration of integrins. |
Abstract | Furthermore, the value of a power-law parameter depends on the particular host-bacterium pair but not on bacterial concentration. |
Abstract | This power-law captures the complex, variable processes underlying bacterial invasion while also enabling differentiation of cell lines. |
Author Summary | A detailed but unwieldy mechanistic model describing individual host-pathogen receptor binding events is captured by a simple power-law dependence on the concentration of the host receptors. |
Author Summary | The power-law parameters capture characteristics of the host-bacterium pair interaction and can differentiate host cell lines. |
Introduction | Here, to characterize the fundamental property of bacterial uptake, we employ kinetic modeling and experiments that distill a simple power-law , relating uptake probability—the amount of bacteria per host cell scaled by the bacteria concentration—with host receptor levels. |
Introduction | We describe how different hosts and bacterial strains translate into different power-law parameters which serves as the basis of a novel, operational definition of cell type. |
Abstract | We, therefore, have developed a power-law based estimator to measure allele and haplotype diversity that accommodates heavy tails using the concepts of regular variation and occupancy distributions. |
Abstract | Finally, we compared the convergence of our power-law versus classical diversity estimators such as Capture recapture, Chao, ACE and Jackknife methods. |
Abstract | This suggests that power-law based estimators offer a valid alternative to classical diversity estimators and may have broad applicability in the field of population genetics. |
Author Summary | We here use a power-law methodology that accommodates heavy-tails to estimate both the population coverage by ethnicity in the US and the genetic diversity of alleles and haplotypes. |
Discussion | Therefore, we built our model around a truncated power-law for estimating the properties of infinite discrete distributions with regularly varying heavy tails [7,8,14]. |
Haplotype Distribution Formalism | However, in heavy tailed distributions (such as power-law distributions) the vast majority of haplotypes are very rare. |
Introduction | This power-law framework is useful for modeling the probability mass (and number) of A and H that are unseen in the sample and represented by the “invisible” tail of the distribution. |
Introduction | Last, we discuss broader applications of the power-law methodology outside HSCT for modeling species richness in the field of ecology, which is characterized by similar heavy-tailed distributions. |
Methodology Validation | Capture-recapture and power-law estimates were found to converge to the true value of H, but the capture-recapture method required a very deep sample of the population to attain accuracy whereas the power-law method converged quickly and offered accurate estimates, even with limited sampling (Fig 1B). |
Probability of New Haplotype Discovery | Thus, our current power-law methodology appears flawed for providing accurate estimates for the number of unique alleles and requires future modifications to accommodate the mixed data sources. |
A gradual increase in membrane resistance is critical to reduced fluctuation-based modulation of input-output responses in an eLlF model | Furthermore, over the range of 1—60 spikes/ s, the f-chrve of the eLIF using a value of AT of 15 mV can be accurately fit with a power-law function with an exponent of 1.78, which is within the range of values observed experimentally for stellate cells (Fig 3F). |
Analysis and statistics | For power-law and Boltzmann fits, we also confirmed fits in Origin 8.5 (OriginLab, Northampton, MA). |
Analysis and statistics | For the f-V curve, experimental and modeling results were fit using a power-law function: where f is the firing rate, p is the exponent of the fit reported in the results section, a and b are positive constants and VC is the minimal voltage required to elicit spike generation. |
Power-law scaling of stellate cell f-V curve without voltage fluctuations | Power-law scaling of stellate cell f-V curve without voltage fluctuations |
Power-law scaling of stellate cell f-V curve without voltage fluctuations | In the visual system, a power-law scaling between spike firing rate and membrane voltage of layer 11 pyramidal neurons is critical for gain control and contrast invariance [12,37]. |
Power-law scaling of stellate cell f-V curve without voltage fluctuations | Modeling has shown that a power-law scaling with an exponent near 2 between spike firing rate and voltage can arise from the combination of an intrinsic, steep and linear f-Vrelationship, and smoothing through Gaussian-distributed voltage fluctuations [3,19,34,47]. |
a co g-n —stellate v,, trajectory | Line indicates fit to a power-law function of the form shown in panel inset. |
a co g-n —stellate v,, trajectory | Surprisingly, we found that f-V curves were nonlinear and could be fit With a power-law function (Fig 2D; mean r2 = 0.95 i 0.02, range: 07—099) using an exponent (p) of 1.45 i 0.08 (Fig 2D; n = 19, range: 0.45—2.0, 17/19 had p values >1). |
a co g-n —stellate v,, trajectory | Contrary to previous assumptions [12,37], therefore, neuronal f-V curves can eXpress significant power-law scaling in the absence of any fluctuation-based smoothing. |