Walking, hopping and jumping: a model of transcription factor dynamics on DNA

We present a model of how transcription factors scan DNA to find their specific binding sites. Following the classical work of Winter et al. (1981), our model assumes two modes of transcription factor dynamics. Adjacent moves, where the proteins make a single step movement to one side, or short walks where the transcription factors slide along the DNA several binding sites at a time. The purpose of this article is twofold. Firstly, we discuss how such a system can be efficiently modeled computationally. Secondly, we analyse how the mean first binding times of transcription factors to their specific time depends on key parameters of the system

Evolving strategies for single-celled organisms in multi-nutrient environments

When micro-organisms are in environments with multiple nutrients, they often preferentially utilise one first. A second is only utilised once the first is exhausted. Such a two-phase growth pattern is known as diauxic growth. Experimentally, this manifests itself through two distinct exponential growth phases separated by a lag phase of arrested growth. The dura- tion of the lag phase can be quite substantial. From an evolu- tionary point of view the existence of a lag phase is somewhat puzzling because it implies a substantial loss of growth op- portunity. Mutants with shorter lag phases would be prone to outcompete those with longer phases. Yet in nature, diauxic growth with lag phases appears to be a robust phenomenon. We introduce a model of the evolution of diauxic growth that captures the basic interactions regulating it in bacteria. We observe its evolution without a lag phase. We conclude that the lag phase is an adaptation that is only beneficial when fit- ness is averaged over a large number of environments

Evolving Biological Systems: Evolutionary Pressure to Inefficiency

The evolution of quantitative details (i.e. “parameter values”) of biological systems is highly under-researched. We use evolutionary algorithms to co-evolve parameters for a generic but biologically plausible topological differential equation model of nutrient uptake. In our model, evolving cells compete for a finite pool of nutrient resources. From our investigations it emerges that the choice of values is very important for the properties of the biological system. Our analysis also shows that clonal populations that are not subject to competition from other species best grow at a very slow rate. However, if there is co-evolutionary pressure, that is, if a population of clones has to compete with other cells, then the fast growth is essential, so as not to leave resources to the competitor. We find that this strategy, while favoured evolutionarily, is inef- ficient from an energetic point of view, that is less growth is achieved per unit of input nutrient. We conclude, that competition can lead to an evolutionary pressure towards inefficiency

A search algorithm for a class of optimal finite-precision controller realization problems with saddle points

With game theory, we review the optimal digital controller realization problems that maximize a finite word length (FWL) closed-loop stability measure. For a large class of these optimal FWL controller realization problems which have saddle points, a minimax-based search algorithm is derived for finding a global optimal solution. The algorithm consists of two stages. In the first stage, the closed form of a transformation set is constructed which contains global optimal solutions. In the second stage, a subgradient approach searches this transformation set to obtain a global optimal solution. This algorithm does not suffer from the usual drawbacks associated with using direct numerical optimization methods to tackle these FWL realization problems. Furthermore, for a small class of optimal FWL controller realization problems which have no saddle point, the proposed algorithm also provides useful information to help solve them

The role of ERK5 signalling in macrophage behaviour during wound healing

Over 150 million individuals worldwide are affected by impaired wound healing, which can lead to chronic wound pathologies that often require lower limb amputations. Impaired wound healing is particularly prevalent in two growing demographics: aged and diabetic populations. Impaired wound healing continues to persist due to a lack of viable treatment options, exacerbated by an incomplete understanding of the mechanisms of wound healing. Research in this area has highlighted a significant role of dysregulated immune cells in impaired wound healing. We aimed to investigate the role of a key immune cell in wound healing: macrophages and how a known regulator of macrophages in other contexts, ERK5, influences wound healing, using genetic and therapeutic manipulations targeted at ERK5, both in vitro and in vivo. Genetic in vivo hyperactivation of ERK5 causes a persistent inflammatory profile in wounds, which aligned with similar observations of aberrant ERK5 signalling contributing to inflammation driven cancer progression. In contrast, genetic inactivation caused a brief increase in inflammation followed by an earlier shift to the resolution phase of wound healing as confirmed by flow cytometry and histology. This increase in reparative wound signalling in response to targeting ERK5 was also observed in human systems, using an in vitro keratinocyte model treated with a novel compound that targets and degrades ERK5, called OS1. Furthermore, using OS1 we were able to prime M0 THP-1 macrophages towards a reparative M2-like phenotype. This OS1-mediated pro-healing wound phenotype was recapitulated in vivo, where topical treatment with OS1 (inducing ERK5 loss in the entire wound) increased the rate of wound closure and was associated with an influx of M2-like macrophages and an earlier switch to the resolution phase of wound healing. This work is the first ever evaluation of the in vivo role of ERK5 in wound healing. We discovered that ERK5 signalling drives macrophage polarisation and immune infiltration during wound healing. The findings have the potential to improve diagnosis, stratification and treatment of chronic wounds. This study also provides evidence of the need to deviate from the traditional approach to target ERK5 via kinase inhibitors, since OS1-mediated degradation of ERK5, unlike ERK5 kinase inhibitors, was able to recapitulate the immune phenotypes of ERK5 genetic ablation models. Overall, this work highlights the potential for OS1 to be used to treat patients with impaired wound healing, such as those associated with diabetes

Optimal realizations of floating-point implemented digital controllers with finite word length considerations.

The closed-loop stability issue of finite word length (FWL) realizations is investigated for digital controllers implemented in floating-point arithmetic. Unlike the existing methods which only address the effect of the mantissa bits in floating-point implementation to the sensitivity of closed-loop stability, the sensitivity of closed-loop stability is analysed with respect to both the mantissa and exponent bits of floating-point implementation. A computationally tractable FWL closed-loop stability measure is then defined, and the method of computing the value of this measure is given. The optimal controller realization problem is posed as searching for a floating-point realization that maximizes the proposed FWL closed-loop stability measure, and a numerical optimization technique is adopted to solve for the resulting optimization problem. Simulation results show that the proposed design procedure yields computationally efficient controller realizations with enhanced FWL closed-loop stability performance