A proposed fractional-order Gompertz model and its application to tumour growth data.

A fractional-order Gompertz model of orders between 0 and 2 is proposed. The main purpose of this investigation is to determine whether the ordinary or proposed fractional Gompertz model would best fit our experimental dataset. The solutions for the proposed model are obtained using fundamental concepts from fractional calculus. The closed-form equations of both the proposed model and the ordinary Gompertz model are calibrated using an experimental dataset containing tumour growth volumes of a Rhabdomyosarcoma tumour in a mouse. With regard to the proposed model, the order, within the interval mentioned, that resulted in the best fit to the data was used in a further investigation into the prediction capability of the model. This was compared to the prediction capability of the ordinary Gompertz model. The result of the investigation was that a fractional-order Gompertz model of order 0.68 produced a better fit to our experimental dataset than the well-known ordinary Gompertz model.

The "firing cannons" of Dipodascopsis uninucleata var. uninucleata.

According to literature, the elongated ascospores of Dipodascopsis uninucleata var. uninucleata exhibit smart movement when forcefully ejected from bottle-shaped asci. This type of movement is defined as the unique patterns of non-random movement of ascospores with specialized morphology thereby facilitating release from asci. Smart movement is required to actively release ascospores individually through the narrow ascus neck, without causing an obstruction and blocking ascospore release. However, little is known about the propulsion mechanism of this cannon-type release system. We show that asci of this yeast contain a central channel (barrel) filled with ascospores. These are surrounded by a sheath-like structure that lines the inner surface of the ascus wall. We found that this sheath is responsible for forcing the naked ascospores out of the ascus by exerting turgor pressure from the bottom towards the tip of the ascus. This cannon firing system is in contrast to that found in Dipodascus geniculatus, where no sheaths lining the ascus interior were observed. Instead, sheaths were found enveloping each ascospore.