Mathematical Modelling in Biomedicine: A Primer for the Curious and the Skeptic.

In most disciplines of natural sciences and engineering, mathematical and computational modelling are mainstay methods which are usefulness beyond doubt. These disciplines would not have reached today's level of sophistication without an intensive use of mathematical and computational models together with quantitative data. This approach has not been followed in much of molecular biology and biomedicine, however, where qualitative descriptions are accepted as a satisfactory replacement for mathematical rigor and the use of computational models is seen by many as a fringe practice rather than as a powerful scientific method. This position disregards mathematical thinking as having contributed key discoveries in biology for more than a century, e.g., in the connection between genes, inheritance, and evolution or in the mechanisms of enzymatic catalysis. Here, we discuss the role of computational modelling in the arsenal of modern scientific methods in biomedicine. We list frequent misconceptions about mathematical modelling found among biomedical experimentalists and suggest some good practices that can help bridge the cognitive gap between modelers and experimental researchers in biomedicine. This manuscript was written with two readers in mind. Firstly, it is intended for mathematical modelers with a background in physics, mathematics, or engineering who want to jump into biomedicine. We provide them with ideas to motivate the use of mathematical modelling when discussing with experimental partners. Secondly, this is a text for biomedical researchers intrigued with utilizing mathematical modelling to investigate the pathophysiology of human diseases to improve their diagnostics and treatment.

The role of cooperativity in a p53-miR34 dynamical mathematical model.

The objective of this study is to evaluate the role of cooperativity, captured by the Hill coefficient, in a minimal mathematical model describing the interactions between p53 and miR-34a. The model equations are analyzed for negative, none and normal cooperativity using a specific version of bifurcation theory and they are solved numerically. Special attention is paid to the sign of so-called first Lyapunov value. Interpretations of the results are given, both according to dynamic theory and in biological terms. In terms of cell signaling, we propose the hypothesis that when the outgoing signal of a system spends a physiologically significant amount of time outside of its equilibrium state, then the value of that signal can be sampled at any point along the trajectory towards that equilibrium and indeed, at multiple points. Coupled with non-linear behavior, such as that caused by cooperativity, this feature can account for a complex and varied response, which p53 is known for. From dynamical point of view, we found that when cooperativity is negative, the system has only one stable equilibrium point. In the absence of cooperativity, there is a single unstable equilibrium point with a critical boundary of stability. In the case with normal cooperativity, the system can have one, two, or three steady states with both, bi-stability and bi-instability occurring.

Can DNA barcoding be used to identify closely related Clunio Haliday, 1855 species (Diptera: Chironomidae, Orthocladiinae)?

DNA barcoding based on a fragment of mitochondrial Cytochrome C Oxidase subunit 1 gene (COI) was applied to the two chironomids Clunio balticus Heimbach (690 base pairs) and C. ponticus Michailova (691 base pairs). The two species differed by one deletion in the nucleotide sequence Adenine. However, the 658-nucleotide long sequences of DNA from the mitochondrial Cytochrome C Oxidase subunit 1 gene (COI) of C. balticus and C. ponticus were identical upon comparison. Further, they compared with homologous sequences for C. marinus Holiday and C. tsushimensis Tokunaga from the Barcode of Life (BOLD) database and the results plotted as a weighted graph, where C. tsushimensis, C. marinus and C. balticus C. ponticus formed three almost equidistant groups. From this, we established that the genetic distance between the respective COI sequences of C. balticus and C. ponticus is minimal, indicating a close relationship between the species indicative of recent common origin. However, the comparative analysis between C. tsushimensis, C. marinus, C. balticus and C. ponticus showed a wider divergence in their respective nucleotide sequences. Overall, our results emphasized that the COI region does not work well as a DNA barcode to identify species within the Clunio genus. Either longer sequences or a multifaceted methodological approach, including morphology, cytogenetic and ecology is needed to distinguish some members of Clunio genus.

Acute paediatric bite injuries treated on inpatient basis: a 10-year retrospective study and criteria for hospital admission.

The aim of this study was to evaluate the acute bite wounds in children treated on an inpatient basis over a 10-year period and the criteria for inpatient treatment. This study comprised all acute mammalian bite injuries in relation to all paediatric bite injuries seen at the Emergency Surgical Department (ESD). Inclusion criteria were: aged between 0-18 years; acute human or animal bite injuries (presenting for the first time); and inpatient treatment. Exclusion criteria were: bite wounds treated elsewhere and referred for complications; bites treated on an outpatient basis referred for complications; and all insect bites. Over 10 years, 12,948 children were seen at the ESD. There were 167 children (0.77%) with mammalian bite wounds. Twelve of them responded to the inclusion criteria. They presented 7.18% of all mammalian bite injuries and 0.09% of all paediatric emergency visits at the ESD. The average age was 3.82 ± 1.63 years (from 1.3-7 years). The time elapsed between the accident to the wound debridement was 118.64 ± 101.39 minutes. There were 10 dogs, one horse, and one rabbit bite. Surgical treatment comprised debridement, saline irrigation, and primary closure or reconstruction. All patients received antibiotics in the postoperative period. The average hospital stay was 5.92 ± 2.39 days. In one case a partial distal flap necrosis occurred. Animal bite injuries treated on an inpatient basis are predominantly dog bites in young children under 10 years of age, with deep, extended, and commonly multiple injuries. Only 7% of paediatric bite injuries require inpatient treatment.