Models in biology: ‘accurate descriptions of our pathetic thinking’

In this essay I will sketch some ideas for how to think about models in biology. I will begin by trying to dispel the myth that quantitative modeling is somehow foreign to biology. I will then point out the distinction between forward and reverse modeling and focus thereafter on the former. Instead of going into mathematical technicalities about different varieties of models, I will focus on their logical structure, in terms of assumptions and conclusions. A model is a logical machine for deducing the latter from the former. If the model is correct, then, if you believe its assumptions, you must, as a matter of logic, also believe its conclusions. This leads to consideration of the assumptions underlying models. If these are based on fundamental physical laws, then it may be reasonable to treat the model as ‘predictive’, in the sense that it is not subject to falsification and we can rely on its conclusions. However, at the molecular level, models are more often derived from phenomenology and guesswork. In this case, the model is a test of its assumptions and must be falsifiable. I will discuss three models from this perspective, each of which yields biological insights, and this will lead to some guidelines for prospective model builders

A study of the free amino acids in the liquid endosperm of coconut (Cocos nucifera)

On the basis of results obtained with paper Chromatographic and thin layer lonophoretic techniques, the paper describes the free amino acids in the liquid endosperm of coconut in two stages of maturit

Complex-linear invariants of biochemical networks

The nonlinearities found in molecular networks usually prevent mathematical analysis of network behaviour, which has largely been studied by numerical simulation. This can lead to difficult problems of parameter determination. However, molecular networks give rise, through mass-action kinetics, to polynomial dynamical systems, whose steady states are zeros of a set of polynomial equations. These equations may be analysed by algebraic methods, in which parameters are treated as symbolic expressions whose numerical values do not have to be known in advance. For instance, an "invariant" of a network is a polynomial expression on selected state variables that vanishes in any steady state. Invariants have been found that encode key network properties and that discriminate between different network structures. Although invariants may be calculated by computational algebraic methods, such as Gr\"obner bases, these become computationally infeasible for biologically realistic networks. Here, we exploit Chemical Reaction Network Theory (CRNT) to develop an efficient procedure for calculating invariants that are linear combinations of "complexes", or the monomials coming from mass action. We show how this procedure can be used in proving earlier results of Horn and Jackson and of Shinar and Feinberg for networks of deficiency at most one. We then apply our method to enzyme bifunctionality, including the bacterial EnvZ/OmpR osmolarity regulator and the mammalian 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase glycolytic regulator, whose networks have deficiencies up to four. We show that bifunctionality leads to different forms of concentration control that are robust to changes in initial conditions or total amounts. Finally, we outline a systematic procedure for using complex-linear invariants to analyse molecular networks of any deficiency.Comment: 36 pages, 6 figure

The rational parameterisation theorem for multisite post-translational modification systems

Post-translational modification of proteins plays a central role in cellular regulation but its study has been hampered by the exponential increase in substrate modification forms (“modforms”) with increasing numbers of sites. We consider here biochemical networks arising from post-translational modification under mass-action kinetics, allowing for multiple substrates, having different types of modification (phosphorylation, methylation, acetylation, etc.) on multiple sites, acted upon by multiple forward and reverse enzymes (in total number L), using general enzymatic mechanisms. These assumptions are substantially more general than in previous studies. We show that the steady-state modform concentrations constitute an algebraic variety that can be parameterised by rational functions of the L free enzyme concentrations, with coefficients which are rational functions of the rate constants. The parameterisation allows steady states to be calculated by solving L algebraic equations, a dramatic reduction compared to simulating an exponentially large number of differential equations. This complexity collapse enables analysis in contexts that were previously intractable and leads to biological predictions that we review. Our results lay a foundation for the systems biology of post-translational modification and suggest deeper connections between biochemical networks and algebraic geometry

Sri Lanka Malaria Maps

BACKGROUND: Despite a relatively good national case reporting system in Sri Lanka, detailed maps of malaria distribution have not been publicly available. METHODS: In this study, monthly records over the period 1995 – 2000 of microscopically confirmed malaria parasite positive blood film readings, at sub-district spatial resolution, were used to produce maps of malaria distribution across the island. Also, annual malaria trends at district resolution were displayed for the period 1995 – 2002. RESULTS: The maps show that Plasmodium vivax malaria incidence has a marked variation in distribution over the island. The incidence of Plasmodium falciparum malaria follows a similar spatial pattern but is generally much lower than that of P. vivax. In the north, malaria shows one seasonal peak in the beginning of the year, whereas towards the south a second peak around June is more pronounced. CONCLUSION: This paper provides the first publicly available maps of both P. vivax and P. falciparum malaria incidence distribution on the island of Sri Lanka at sub-district resolution, which may be useful to health professionals, travellers and travel medicine professionals in their assessment of malaria risk in Sri Lanka. As incidence of malaria changes over time, regular updates of these maps are necessary

Learning in Social Networks: Rationale and Ideas for Its Implementation in Higher Education

The internet has fast become a prevalent medium for collaboration between people and social networks, in particular, have gained vast popularity and relevance over the past few years. Within this framework, our paper will analyse the role played by social networks in current teaching practices. Specifically, we focus on the principles guiding the design of study activities which use social networks and we relate concrete experiences that show how they contribute to improving teaching and learning within a university environment