Theoretical insights into bacterial chemotaxis

Research into understanding bacterial chemotactic systems has become a paradigm for Systems Biology. Experimental and theoretical researchers have worked hand-in-hand for over 40 years to understand the intricate behavior driving bacterial species, in particular how such small creatures, usually not more than 5 µm in length, detect and respond to small changes in their extracellular environment. In this review we highlight the importance that theoretical modeling has played in providing new insight and understanding into bacterial chemotaxis. We begin with an overview of the bacterial chemotaxis sensory response, before reviewing the role of theoretical modeling in understanding elements of the system on the single cell scale and features underpinning multiscale extensions to population models. WIREs Syst Biol Med 2012 doi: 10.1002/wsbm.1168 For further resources related to this article, please visit the WIREs website.

Mathematics as a tool in the Life Sciences

Teaching mathematics to students in the biological sciences is often fraught with difficulty. Students often discover mathematics to be a very 'dry' subject in which it is difficult to see the motivation of learning it given its often abstract application. In this paper I advocate the use of mathematical modelling as a method for engaging students in understanding the use of mathematics in helping to solve problems in the Biological Sciences. The concept of mathematics as a laboratory tool is introduced and the importance of presenting students with relevant, real-world examples of applying mathematics in the Biological Sciences is discussed.

Blueberry supplementation induces spatial memory improvements and region-specific regulation of hippocampal BDNF mRNA expression in young rats

Rationale: Flavonoid-rich foods have been shown to be able to reverse age-related cognitive deficits in memory and learning in both animals and humans. However, to date, there have been only a limited number of studies investigating the effects of flavonoid-rich foods on cognition in young/healthy animals. Objectives: The aim of this study was to investigate the effects of a blueberry-rich diet in young animals using a spatial working memory paradigm, the delayed non-match task, using an eight-arm radial maze. Furthermore, the mechanisms underlying such behavioural effects were investigated. Results: We show that a 7-week supplementation with a blueberry diet (2 % w/w) improves the spatial memory performance of young rats (2 months old). Blueberry-fed animals also exhibited a faster rate of learning compared to those on the control diet. These behavioural outputs were accompanied by the activation of extracellular signal-related kinase (ERK1/2), increases in total cAMP-response element binding protein (CREB) and elevated levels of pro- and mature brain-derived neurotrophic factor (BDNF) in the hippocampus. Changes in hippocampal CREB correlated well with memory performance. Further regional analysis of BDNF gene expression in the hippocampus revealed a specific increase in BDNF mRNA in the dentate gyrus and CA1 areas of hippocampi of blueberry-fed animals. Conclusions: The present study suggests that consumption of flavonoid-rich blueberries has a positive impact on spatial learning performance in young healthy animals, and these improvements are linked to the activation of ERK–CREB– BDNF pathway in the hippocampus.

Neuroprotective effects of phenolic antioxidant tBHQ associate with inhibition of FoxO3a nuclear translocation and activity

The Forkhead transcription factor, FoxO3a induces genomic death responses in neurones following translocation from the cytosol to the nucleus. Nuclear translocation of FoxO3a is triggered by trophic factor withdrawal, oxidative stress and the stimulation of extrasynaptic NMDA receptors. Receptor activation of phosphatidylinositol 3-kinase (PI3K) – Akt signalling pathways retains FoxO3a in the cytoplasm thereby inhibiting the transcriptional activation of death promoting genes. We hypothesised that phenolic antioxidants such as tert-Butylhydroquinone (tBHQ), which is known to stimulate PI3K-Akt signalling, would inhibit FoxO3a translocation and activity. Treatment of cultured cortical neurones with NMDA increased the nuclear localisation of FoxO3a, reduced the phosphorylation of FoxO3a, increased caspase activity and upregulated Fas ligand expression. In contrast the phenolic antioxidant tBHQ caused retention of FoxO3a in the cytosol coincident with enhanced PI3K- dependent phosphorylation of FoxO3a. tBHQ-induced nuclear exclusion of FoxO3a was associated with reduced FoxO-mediated transcriptional activity. Exposure of neurones to tBHQ inhibited NMDA-induced nuclear translocation of FoxO3a prevented NMDA-induced upregulation of FoxO-mediated transcriptional activity, blocked caspase activation and protected neurones from NMDA-induced excitotoxic death. Collectively, these data suggest that phenolic antioxidants such as tBHQ oppose stress-induced activation of FoxO3a and therefore have potential neuroprotective utility in neurodegeneration.

Unusual isotope effect in the reaction of chlorosilylene with trimethylsilane-1-d: Absolute rate studies and quantum chemical and Rice–Ramsperger–Kassel–Marcus calculations provide strong evidence for the involvement of an intermediate complex

Time-resolved studies of chlorosilylene, ClSiH, generated by the 193 nm laser flash photolysis of 1-chloro-1- silacyclopent-3-ene, have been carried out to obtain rate constants for its bimolecular reaction with trimethylsilane-1-d, Me3SiD, in the gas phase. The reaction was studied at total pressures up to 100 Torr (with and without added SF6) over the temperature range of 295−407 K. The rate constants were found to be pressure independent and gave the following Arrhenius equation: log[(k/(cm3 molecule−1 s−1)] = (−13.22 ± 0.15) + [(13.20 ± 1.00) kJ mol−1]/(RT ln 10). When compared with previously published kinetic data for the reaction of ClSiH with Me3SiH, kinetic isotope effects, kD/kH, in the range from 7.4 (297 K) to 6.4 (407 K) were obtained. These far exceed values of 0.4−0.5 estimated for a single-step insertion process. Quantum chemical calculations (G3MP2B3 level) confirm not only the involvement of an intermediate complex, but also the existence of a low-energy internal isomerization pathway which can scramble the D and H atom labels. By means of Rice−Ramsperger−Kassel−Marcus modeling and a necessary (but small) refinement of the energy surface, we have shown that this mechanism can reproduce closely the experimental isotope effects. These findings provide the first experimental evidence for the isomerization pathway and thereby offer the most concrete evidence to date for the existence of intermediate complexes in the insertion reactions of silylenes.

The maximum rate of mammal evolution

How fast can a mammal evolve from the size of a mouse to the size of an elephant? Achieving such a large transformation calls for major biological reorganization. Thus, the speed at which this occurs has important implications for extensive faunal changes, including adaptive radiations and recovery from mass extinctions. To quantify the pace of large-scale evolution we developed a metric, clade maximum rate, which represents the maximum evolutionary rate of a trait within a clade. We applied this metric to body mass evolution in mammals over the last 70 million years, during which multiple large evolutionary transitions occurred in oceans and on continents and islands. Our computations suggest that it took a minimum of 1.6, 5.1, and 10 million generations for terrestrial mammal mass to increase 100-, and 1,000-, and 5,000- fold, respectively. Values for whales were down to half the length (i.e., 1.1, 3, and 5 million generations), perhaps due to the reduced mechanical constraints of living in an aquatic environment. When differences in generation time are considered, we find an exponential increase in maximum mammal body mass during the 35 million years following the Cretaceous–Paleogene (K–Pg) extinction event. Our results also indicate a basic asymmetry in macroevolution: very large decreases (such as extreme insular dwarfism) can happen at more than 10 times the rate of increases. Our findings allow more rigorous comparisons of microevolutionary and macroevolutionary patterns and processes. Keywords: haldanes, biological time, scaling, pedomorphosis

Response kinetics in the complex chemotaxis signalling pathway of Rhodobacter sphaeroides

Chemotaxis is one of the best characterised signalling systems in biology. It is the mechanism by which bacteria move towards optimal environments and is implicated in biofilm formation, pathogenesis and symbiosis. The properties of the bacterial chemosensory response have been described in detail for the single chemosensory pathway of Escherichia coli. We have characterised the properties of the chemosensory response of Rhodobacter sphaeroides, an -proteobacterium with multiple chemotaxis pathways, under two growth conditions allowing the effects of protein expression levels and cell architecture to be investigated. Using tethered cell assays we measured the responses of the system to step changes in concentration of the attractant propionate and show that, independently of the growth conditions, R. sphaeroides is chemotactic over at least five orders of magnitude and has a sensing profile following Weber’s law. Mathematical modelling also shows that, like E. coli, R. sphaeroides is capable of showing Fold-Change Detection (FCD). Our results indicate that general features of bacterial chemotaxis such as the range and sensitivity of detection, adaptation times, adherence to Weber’s law and the presence of FCD may be integral features of chemotaxis systems in general, regardless of network complexity, protein expression levels and cellular architecture across different species.

Dietary levels of pure flavonoids improve spatial memory performance and increase hippocampal brain-derived neurotrophic factor.

Evidence suggests that flavonoid-rich foods are capable of inducing improvements in memory and cognition in animals and humans. However, there is a lack of clarity concerning whether flavonoids are the causal agents in inducing such behavioral responses. Here we show that supplementation with pure anthocyanins or pure flavanols for 6 weeks, at levels similar to that found in blueberry (2% w/w), results in an enhancement of spatial memory in 18 month old rats. Pure flavanols and pure anthocyanins were observed to induce significant improvements in spatial working memory (p = 0.002 and p = 0.006 respectively), to a similar extent to that following blueberry supplementation (p = 0.002). These behavioral changes were paralleled by increases in hippocampal brain-derived neurotrophic factor (R = 0.46, p<0.01), suggesting a common mechanism for the enhancement of memory. However, unlike protein levels of BDNF, the regional enhancement of BDNF mRNA expression in the hippocampus appeared to be predominantly enhanced by anthocyanins. Our data support the claim that flavonoids are likely causal agents in mediating the cognitive effects of flavonoid-rich foods.

The selected poetry and prose of Vittorio Sereni

2013 centenary corrected paperback edition of a 2006 publication, with introduction, co-translations, and notes

Causal relationship between obesity and vitamin D status: bi-directional mendelian randomization analysis of multiple cohorts

BACKGROUND: Obesity is associated with vitamin D deficiency, and both are areas of active public health concern. We explored the causality and direction of the relationship between body mass index (BMI) and 25-hydroxyvitamin D [25(OH)D] using genetic markers as instrumental variables (IVs) in bi-directional Mendelian randomization (MR) analysis. METHODS AND FINDINGS: We used information from 21 adult cohorts (up to 42,024 participants) with 12 BMI-related SNPs (combined in an allelic score) to produce an instrument for BMI and four SNPs associated with 25(OH)D (combined in two allelic scores, separately for genes encoding its synthesis or metabolism) as an instrument for vitamin D. Regression estimates for the IVs (allele scores) were generated within-study and pooled by meta-analysis to generate summary effects. Associations between vitamin D scores and BMI were confirmed in the Genetic Investigation of Anthropometric Traits (GIANT) consortium (n = 123,864). Each 1 kg/m(2) higher BMI was associated with 1.15% lower 25(OH)D (p = 6.52×10⁻²⁷). The BMI allele score was associated both with BMI (p = 6.30×10⁻⁶²) and 25(OH)D (-0.06% [95% CI -0.10 to -0.02], p = 0.004) in the cohorts that underwent meta-analysis. The two vitamin D allele scores were strongly associated with 25(OH)D (p≤8.07×10⁻⁵⁷ for both scores) but not with BMI (synthesis score, p = 0.88; metabolism score, p = 0.08) in the meta-analysis. A 10% higher genetically instrumented BMI was associated with 4.2% lower 25(OH)D concentrations (IV ratio: -4.2 [95% CI -7.1 to -1.3], p = 0.005). No association was seen for genetically instrumented 25(OH)D with BMI, a finding that was confirmed using data from the GIANT consortium (p≥0.57 for both vitamin D scores). CONCLUSIONS: On the basis of a bi-directional genetic approach that limits confounding, our study suggests that a higher BMI leads to lower 25(OH)D, while any effects of lower 25(OH)D increasing BMI are likely to be small. Population level interventions to reduce BMI are expected to decrease the prevalence of vitamin D deficiency.

Investigating flavonoids as molecular templates for the design of small-molecule inhibitors of cell signaling

Epidemiological and clinical trials reveal compelling evidence for the ability of dietary flavonoids to lower cardiovascular disease risk. The mechanisms of action of these polyphenolic compounds are diverse, and of particular interest is their ability to function as protein and lipid kinase inhibitors. We have previously described structure-activity studies that reinforce the possibility for using flavonoid structures as templates for drug design. In the present study, we aim to begin constructing rational screening strategies for exploiting these compounds as templates for the design of clinically relevant, antiplatelet agents. We used the platelet as a model system to dissect the structural influence of flavonoids, stilbenes, anthocyanidins, and phenolic acids on inhibition of cell signaling and function. Functional groups identified as relevant for potent inhibition of platelet function included at least 2 benzene rings, a hydroxylated B ring, a planar C ring, a C ring ketone group, and a C-2 positioned B ring. Hydroxylation of the B ring with either a catechol group or a single C-4' hydroxyl may be required for efficient inhibition of collagen-stimulated tyrosine phosphorylated proteins of 125 to 130 kDa, but may not be necessary for that of phosphotyrosine proteins at approximately 29 kDa. The removal of the C ring C-3 hydroxyl together with a hydroxylated B ring (apigenin) may confer selectivity for 37 to 38 kDa phosphotyrosine proteins. We conclude that this study may form the basis for construction of maps of flavonoid inhibitory activity on kinase targets that may allow a multitargeted therapeutic approach with analogue counterparts and parent compounds.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in an hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main precursor of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homestasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

A moving mesh approach for modelling avascular tumour growth

A key step in many numerical schemes for time-dependent partial differential equations with moving boundaries is to rescale the problem to a fixed numerical mesh. An alternative approach is to use a moving mesh that can be adapted to focus on specific features of the model. In this paper we present and discuss two different velocity-based moving mesh methods applied to a two-phase model of avascular tumour growth formulated by Breward et al. (2002) J. Math. Biol. 45(2), 125-152. Each method has one moving node which tracks the moving boundary. The first moving mesh method uses a mesh velocity proportional to the boundary velocity. The second moving mesh method uses local conservation of volume fraction of cells (masses). Our results demonstrate that these moving mesh methods produce accurate results, offering higher resolution where desired whilst preserving the balance of fluxes and sources in the governing equations.

Modelling negative feedback networks for activating transcription factor 3 predicts a dominant role for miRNAs in immediate early gene regulation

Activating transcription factor 3 (Atf3) is rapidly and transiently upregulated in numerous systems, and is associated with various disease states. Atf3 is required for negative feedback regulation of other genes, but is itself subject to negative feedback regulation possibly by autorepression. In cardiomyocytes, Atf3 and Egr1 mRNAs are upregulated via ERK1/2 signalling and Atf3 suppresses Egr1 expression. We previously developed a mathematical model for the Atf3-Egr1 system. Here, we adjusted and extended the model to explore mechanisms of Atf3 feedback regulation. Introduction of an autorepressive loop for Atf3 tuned down its expression and inhibition of Egr1 was lost, demonstrating that negative feedback regulation of Atf3 by Atf3 itself is implausible in this context. Experimentally, signals downstream from ERK1/2 suppress Atf3 expression. Mathematical modelling indicated that this cannot occur by phosphorylation of pre-existing inhibitory transcriptional regulators because the time delay is too short. De novo synthesis of an inhibitory transcription factor (ITF) with a high affinity for the Atf3 promoter could suppress Atf3 expression, but (as with the Atf3 autorepression loop) inhibition of Egr1 was lost. Developing the model to include newly-synthesised miRNAs very efficiently terminated Atf3 protein expression and, with a 4-fold increase in the rate of degradation of mRNA from the mRNA/miRNA complex, profiles for Atf3 mRNA, Atf3 protein and Egr1 mRNA approximated to the experimental data. Combining the ITF model with that of the miRNA did not improve the profiles suggesting that miRNAs are likely to play a dominant role in switching off Atf3 expression post-induction.

Fold-change detection in a whole-pathway model of Escherichia coli chemotaxis

There has been recent interest in sensory systems that are able to display a response which is proportional to a fold change in stimulus concentration, a feature referred to as fold-change detection (FCD). Here, we demonstrate FCD in a recent whole-pathway mathematical model of Escherichia coli chemotaxis. FCD is shown to hold for each protein in the signalling cascade and to be robust to kinetic rate and protein concentration variation. Using a sensitivity analysis, we find that only variations in the number of receptors within a signalling team lead to the model not exhibiting FCD. We also discuss the ability of a cell with multiple receptor types to display FCD and explain how a particular receptor configuration may be used to elucidate the two experimentally determined regimes of FCD behaviour. All findings are discussed in respect of the experimental literature.