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Abstract Reaction networks are commonly used within the mathematical biology and mathematical chemistry communities to model the dynamics of interacting species. These models differ from the typical graphs found in random graph theory since their vertices are constructed from elementary building blocks, i.e. the species. We consider these networks in an Erdös–Rényi framework and, under suitable assumptions, derive a threshold function for the network to have a deficiency of zero, which is a property of great interest in the reaction network community. Specifically, if the number of species is denoted by n and the edge probability by $p_n$ , then we prove that the probability of a random binary network being deficiency zero converges to 1 if $p_n\ll r(n)$ as $n \to \infty$ , and converges to 0 if $p_n \gg r(n)$ as $n \to \infty$ , where $r(n)=\frac{1}{n^3}$ . 

Abstract A high-throughput drug screen revealed that veratridine (VTD), a natural plant alkaloid, induces expression of the anti-cancer protein UBXN2A in colon cancer cells. UBXN2A suppresses mortalin, a heat shock protein, with dominant roles in cancer development including epithelial–mesenchymal transition (EMT), cancer cell stemness, drug resistance, and apoptosis. VTD-dependent expression of UBXN2A leads to the deactivation of mortalin in colon cancer cells, making VTD a potential targeted therapy in malignant tumors with high levels of mortalin. VTD was used clinically for the treatment of hypertension in decades past. However, the discovery of newer antihypertensive drugs and concerns over potential neuro- and cardiotoxicity ended the use of VTD for this purpose. The current study aims to determine the safety and efficacy of VTD at doses sufficient to induce UBXN2A expression in a mouse model. A set of flow-cytometry experiments confirmed that VTD induces both early and late apoptosis in a dose-dependent manner. In vivo intraperitoneal (IP) administration of VTD at 0.1 mg/kg every other day (QOD) for 4 weeks effectively induced expression of UBXN2A in the small and large intestines of mice. Liquid chromatography–tandem mass spectrometry (LC–MS/MS) assays on tissues collected from VTD-treated animals demonstrated VTD concentrations in the low pg/mg range. To address concerns regarding neuro- and cardiotoxicity, a comprehensive set of behavioral and cardiovascular assessments performed on C57BL/6NHsd mice revealed that VTD generates no detectable neurotoxicity or cardiotoxicity in animals receiving 0.1 mg/kg VTD QOD for 30 days. Finally, mouse xenograft experiments in athymic nude mice showed that VTD can suppress tumor growth. The main causes for the failure of experimental oncologic drug candidates are lack of sufficient safety and efficacy. The results achieved in this study support the potential utility of VTD as a safe and efficacious anti-cancer molecule. 

The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an important practical question is: what is the rate of convergence of the distribution of the process to the stationary distribution? With the exception of ^[1] pertaining to models whose state space is restricted to the non-negative integers, there has been a notable lack of results related to this rate of convergence in the reaction network literature. This paper begins the process of filling that hole in our understanding. In this paper, we characterize this rate of convergence, via the mixing times of the processes, for two classes of stochastically modeled reaction networks. Specifically, by applying a Foster-Lyapunov criteria we establish exponential ergodicity for two classes of reaction networks introduced in ^[2]. Moreover, we show that for one of the classes the convergence is uniform over the initial state.

 

Prosthetic limbs that are completely implanted within skin (i.e., endoprostheses) could permit direct, physical muscle–prosthesis attachment to restore more natural sensorimotor function to people with amputation. The objective of our study was to test, in a rabbit model, the feasibility of replacing the lost foot after hindlimb transtibial amputation by implanting a novel rigid foot–ankle endoprosthesis that is fully covered with skin. We first conducted a pilot, non-survival surgery in two rabbits to determine the maximum size of the skin flap that could be made from the biological foot–ankle. The skin flap size was used to determine the dimensions of the endoprosthesis foot segment. Rigid foot–ankle endoprosthesis prototypes were successfully implanted in three rabbits. The skin incisions healed over a period of approximately 1 month after surgery, with extensive fur regrowth by the pre-defined study endpoint of approximately 2 months post surgery. Upon gross inspection, the skin surrounding the endoprosthesis appeared normal, but a substantial subdermal fibrous capsule had formed around the endoprosthesis. Histology indicated that the structure and thickness of the skin layers (epidermis and dermis) were similar between the operated and non-operated limbs. A layer of subdermal connective tissue representing the fibrous capsule surrounded the endoprosthesis. In the operated limb of one rabbit, the subdermal connective tissue layer was approximately twice as thick as the skin on the medial (skin = 0.43 mm, subdermal = 0.84 mm), ventral (skin = 0.80 mm, subdermal = 1.47 mm), and lateral (skin = 0.76 mm, subdermal = 1.42 mm) aspects of the endoprosthesis. Our results successfully demonstrated the feasibility of implanting a fully skin-covered rigid foot–ankle endoprosthesis to replace the lost tibia–foot segment of the lower limb. Concerns include the fibrotic capsule which could limit the range of motion of jointed endoprostheses. Future studies include testing of endoprosthetics, as well as materials and pharmacologic agents that may suppress fibrous encapsulation.

 

Foraging outcomes dictate the nutritional resources available to an organism and may vary with intrinsic factors, like age. Thus, understanding how age affects foraging performance, alone or in interaction with extrinsic factors (like environmental quality), improves our understanding of aging processes in the wild. We examined how foraging traits, measured across five breeding seasons, change with age, environmental variation, and their interaction in Nazca boobies (Sula granti), a pelagic seabird in Galápagos. We evaluated the hypotheses that (1) foraging performance is better in middle‐aged birds than in young ones, and that (2) foraging performance is better in middle‐aged birds than in old ones. Furthermore, favorable environmental conditions will either (3) attenuate age differences in foraging performance (by relieving constraints on young, inexperienced and old, senescent age classes), or (4) accentuate age differences (if middle‐aged birds can exploit abundant resources better than other age classes can). Incubating birds tagged with GPS loggers (N = 815) provided data on foraging performance (e.g., total distance traveled, mass gained) to evaluate interactions between age and environmental variation (e.g., sea surface temperature). Poor environmental conditions associated with the cool phase of the El Niño‐Southern Oscillation increased foraging effort, including foraging distance and duration, for example. Across age classes, foraging boobies responded similarly to environmental variation except for female mass gain rate: age‐related declines in mass gain rate were reduced under favorable environmental conditions. Birds of different ages also searched in somewhat distinct areas in the poor conditions of 2016, but not in other years. In several foraging traits, including foraging duration and distance, female boobies showed predicted early‐life improvement and late‐life decline, following the established pattern for reproductive traits in this species. Thus, deficits in resource acquisition (this study) may contribute to the poor survival and reproductive outcomes previously observed in old Nazca boobies, particularly in females.