Truncated fractional moments of stable laws

Expressions are given for the truncated fractional moments $E X_+^p$ of a general stable law. These involve families of special functions that arose out of the study of multivariate stable densities and probabilities. As a particular case, an expression is given for $E(X-a)_+$ when $\alpha > 1$

Continuity of symmetric stable processes

AbstractThe path continuity of a symmetric p-stable process is examined in terms of any stochastic integral representation for the process. When 0 < p < 1, we give necessary and sufficient conditions for path continuity in terms of any (every) representation. When 1 ≤ p < 2, we extend the known sufficiency condition in terms of metric entropy and offer a conjecture for the stable version of the Dudley-Fernique theorem. Finally, necessary and sufficient conditions for path continuity are given in terms of continuity at a point for 0 < p < 2

Controlling the Size and Shape of Polypeptide Colloidal Particles: Temperature Dependence of Particle Formation

A promising approach for developing new drug delivery vehicles is by using stimuli responsive hydrogel nanoparticles. Polypeptide surfactants designed in our lab have been shown to form micellar particles of varying sizes and shapes depending on the solution salt concentration. These responsive polypeptide surfactants consist of a small charged protein domain (foldon) with three elastin-like polypeptide (ELP) chains forming a three-armed star polymer. The size and shape of the micelles they form is dependent on the ratio of total ELP volume to head group area. By introducing linear ELP into the ELP-foldon solution, the total volume of ELP in the aggregate would be increased if the linear ELP is incorporated in the micelle. This method could control the particle size and shape. To determine if the linear and three-armed ELPs co-assemble, we have observed aggregation as a function of temperature using turbidity measurements in a UV-vis spectrometer. We have found that higher concentrations of linear ELP increases the difference in transition temperature between the linear and three-armed ELP. At these higher ratios, the linear ELP aggregates prior to micelle formation. When the ELP-foldon subsequently passes through its critical micelle temperature, they break down the linear ELP aggregates resulting in smaller colloidal emulsions. Light scattering will be used to characterize the size and shape of these aggregates.https://engagedscholarship.csuohio.edu/u_poster_2013/1016/thumbnail.jp

Controlling the Size and Shape of Polypeptide Colloidal Particles: Temperature Dependence of Particle Formation

A promising approach for developing new drug delivery vehicles is by using stimuli responsive hydrogel nanoparticles. Polypeptide surfactants designed in our lab have been shown to form micellar particles of varying sizes and shapes depending on the solution salt concentration. These responsive polypeptide surfactants consist of a small charged protein domain (foldon) with three elastin-like polypeptide (ELP) chains forming a three-armed star polymer. The size and shape of the micelles they form is dependent on the ratio of total ELP volume to head group area. By introducing linear ELP into the ELP-foldon solution, the total volume of ELP in the aggregate would be increased if the linear ELP is incorporated in the micelle. This method could control the particle size and shape. To determine if the linear and three-armed ELPs co-assemble, we have observed aggregation as a function of temperature using turbidity measurements in a UV-vis spectrometer. We have found that higher concentrations of linear ELP increases the difference in transition temperature between the linear and three-armed ELP. At these higher ratios, the linear ELP aggregates prior to micelle formation. When the ELP-foldon subsequently passes through its critical micelle temperature, they break down the linear ELP aggregates resulting in smaller colloidal emulsions. Light scattering will be used to characterize the size and shape of these aggregates.https://engagedscholarship.csuohio.edu/u_poster_2013/1016/thumbnail.jp

Testosterone causes both prosocial and antisocial status-enhancing behaviors in human males

Although popular discussion of testosterone’s influence on males often centers on aggression and antisocial behavior, contemporary theorists have proposed that it instead enhances behaviors involved in obtaining and maintaining a high social status. Two central distinguishing but untested predictions of this theory are that testosterone selectively increases status-relevant aggressive behaviors, such as responses to provocation, but that it also promotes nonaggressive behaviors, such as generosity toward others, when they are appropriate for increasing status. Here, we tested these hypotheses in healthy young males by injecting testosterone enanthate or a placebo in a double-blind, between-subjects, randomized design (n = 40). Participants played a version of the Ultimatum Game that was modified so that, having accepted or rejected an offer from the proposer, participants then had the opportunity to punish or reward the proposer at a proportionate cost to themselves. We found that participants treated with testosterone were more likely to punish the proposer and that higher testosterone levels were specifically associated with increased punishment of proposers who made unfair offers, indicating that testosterone indeed potentiates aggressive responses to provocation. Furthermore, when participants administered testosterone received large offers, they were more likely to reward the proposer and also chose rewards of greater magnitude. This increased generosity in the absence of provocation indicates that testosterone can also cause prosocial behaviors that are appropriate for increasing status. These findings are inconsistent with a simple relationship between testosterone and aggression and provide causal evidence for a more complex role for testosterone in driving status-enhancing behaviors in males

Monitoring Micelle Formation in Mixtures of Linear and Foldon-capped Polypeptides with Light Scattering Spectroscopy

Elastin-like polypeptide (ELP) polymers are ideal for producing environmentally responsive micellar systems because they exhibit a transition from being water-soluble at low temperatures to phase-separated at high temperatures. For application development of drug delivery vehicles and biosensing nanoparticles, it is important to prepare spherical micelles of controlled diameter and shape. Since at a given salt concentration, the headgroup area for each foldon should be constant, the size of the micelles is expected to be proportional to the volume of the linear ELP available per foldon headgroup. Therefore, adding linear ELPs to a system of ELP-foldon should result in changes of the micelle volume. At higher salts the electrostatic repulsion between headgroups is shielded, reducing the effective size of foldon headgroups, increasing the packing factor of micelles which leads to formation of non-spherical micelles. The effects of addition of linear ELPs on size, shape, and molecular weight of micelles at different salt concentrations were studied by a combination of Depolarized Dynamic Light Scattering (DDLS) and Static Light Scattering (SLS) Spectroscopies. The initial results on 50 μM ELPfoldon samples (at 25 mM salt) show that the apparent hydrodynamic radius of mixed micelles increases more than 5-fold as the amount of linear ELP raised from 0 to 50 μM. The size increase is accompanied by significant increase in depolarized scattering indicating the growing geometrical anisotropy of the micelles with increase of added linear ELP. In addition, the increase of the amount of linear ELP in the mixed micelles significantly increased the relative molecular weight of the micelles.https://engagedscholarship.csuohio.edu/u_poster_2014/1024/thumbnail.jp

Controlling Micelle Formation Using Mixtures of Linear and Foldon-capped Polypeptides (ELP): Measurements with UV-vis Spectroscopy

Polymer surfactants developed in our lab have a protein headgroup (foldon) and three elastin-like polypeptide (ELP) tails. They can form micelles smaller than 30 nm, which may be useful in developing targeted drug delivery vehicles. Specifically, ELPs are capped with foldon, which is a 27 amino acid sequence that folds as a homotrimer, resulting in a three-armed star polypeptide. This structure has been shown to form micelles above the transition temperature (Tt) of the ELP. The salt concentration affects the interaction between the headgroups affecting how the micelles assemble. At low salt concentrations the ELP-foldon will form spherical micelles; whereas, at higher salt concentrations the micelles are non-spherical, as is demonstrated by light scattering. When linear ELP is mixed with ELP foldon, it is expected that the ELP-foldon will stabilize small droplets of linear ELP in the form of a microemulsion. Different ratios of ELP-foldon to linear ELP were prepared and their transition behavior was characterized using turbidity measured with UV-vis spectroscopy. The turbidity increased at the Tt of the ELP, and then dropped substantially at the Tt of the ELPfoldon. Increased concentration of the linear ELP increased the measured turbidity level after both transitions, suggesting an increase in aggregate size. Light scattering was utilized to further characterize the size and shape of the aggregates formed.https://engagedscholarship.csuohio.edu/u_poster_2014/1013/thumbnail.jp