Fordyce Davidson

• BSc (Hons) PhD FIMA
• Professor of Mathematics at University of Dundee

Extracellular proteases are a class of public good that support growth of Bacillus subtilis when nutrients are in a polymeric form. Bacillus subtilis biofilm matrix molecules are another class of public good that are needed for biofilm formation and are prone to exploitation. In this study, we investigated the role of extracellular proteases in B....

Public goods support the development of microbial communities but are prone to exploitation. The extracellular matrix molecules of Bacillus subtilis are examples of public goods that are produced through the division of labour and support biofilm formation. Another class of public good that supports B. subtilis growth when nutrients are in a polyme...

Microbes encounter a wide range of polymeric nutrient sources in various environmental settings, which require processing to facilitate growth. Bacillus subtilis, a bacterium found in the rhizosphere and broader soil environment, is highly adaptable and resilient due to its ability to utilise diverse sources of carbon and nitrogen. Here, we explore...

Bacteria encounter polymeric nutrient sources that need to be processed to support growth. Bacillus subtilis is a bacterium known for its adaptability and resilience within the rhizosphere and broader soil environment. Here we explore the role that a suite of extracellular proteases plays in supporting growth of B. subtilis when an extracellular he...

Biofilms are consortia of microorganisms that form collectives through the excretion of extracellular matrix compounds. The importance of biofilms in biological, industrial and medical settings has long been recognized due to their emergent properties and impact on surrounding environments. In laboratory situations, one commonly used approach to st...

Blood components are a perishable resource that play a crucial role in clinical medicine. The blood component inventory is managed by transfusion services, who ultimately aim to balance supply with demand so as to ensure availability whilst minimising waste. Whilst the blood component inventory problem has been the focus of theoretical approaches f...

Single-species bacterial colony biofilms often present recurring morphologies that are thought to be of benefit to the population of cells within and known to be dependent on the self-produced extracellular matrix. However, much remains unknown in terms of the developmental process at the single cell level. Here, we design and implement systematic...

Single-species bacterial colony biofilms often present recurring morphologies that are thought to be of benefit to the population of cells within and known to be dependent on the self-produced extracellular matrix. However, much remains unknown in terms of the developmental process at the single cell level. Here, we design and implement systematic...

Range expansion is the spatial spread of a population into previously unoccupied regions. Understanding range expansion is important for the study and successful management of ecosystems, with applications ranging from controlling bacterial biofilm formation in industrial and medical environments to large scale conservation programmes for species u...

Bacteria can form dense communities called biofilms, where cells are embedded in a self-produced extracellular matrix. Exploiting competitive interactions between strains within the biofilm context can have potential applications in biological, medical, and industrial systems. By combining mathematical modelling with experimental assays, we reveal...

Range expansion is the spatial spread of a population into previously unoccupied regions. Understanding range expansion is important for the study and successful manipulation and management of ecosystems, with applications ranging from controlling bacterial biofilm formation in industrial and medical environments to large scale conservation program...

Bacteria typically form dense communities called biofilms, where cells are embedded in a self-produced extracellular matrix. Competitive interactions between strains within the biofilm context are studied due to their potential applications in biological, medical, and industrial systems. Combining mathematical modelling with experimental assays, we...

It is well known that biofilms are one of the most widespread forms of life on Earth, capable of colonising almost any environment from humans to metals.

We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodeling, such as during fast growth, develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes are faster than viscoelastic relaxation, wrinkles that are formed due to remodeling...

Translation is a key step in the synthesis of proteins. Accordingly, cells have evolved an intricate array of control mechanisms to regulate this process. By constructing a multicomponent mathematical framework we uncover how translation may be controlled via interacting feedback loops. Our results reveal that this interplay gives rise to a remarka...

Biofilm formation by Bacillus subtilis is a communal process that culminates in the formation of architecturally complex multicellular communities. Here we reveal that the transition of the biofilm into a nonexpanding phase constitutes a distinct step in the process of biofilm development. Using genetic analysis we show that B. subtilis strains lac...

Catheter associated urinary tract infection (CAUTI) presents a significant health problem worldwide and is associated with increased morbidity and mortality. Herein, a silver-polytetrafluoroethylene (Ag-PTFE) nanocomposite coating for catheters was developed via a facile wet chemistry method. Benefiting from the synergistic effect of Ag and PTFE, t...

We show that a viscoelastic thin sheet driven out of equilibrium by active structural remodelling develops a rich variety of shapes as a result of a competition between viscous relaxation and activity. In the regime where active processes are faster than viscoelastic relaxation, wrinkles that are formed due to remodelling are unable to relax to a c...

Biofilm formation by Bacillus subtilis is a communal process that culminates in the formation of architecturally complex multicellular communities. Here we reveal that the transition of the biofilm into a non-expanding phase constitutes a distinct step in the process of biofilm development. Using genetic analysis we show that B. subtilis strains la...

Background: Catheter-associated urinary tract infections (CAUTIs) are among the most common hospital-acquired infections, leading to increased morbidity and mortality. A major reason for this is that urinary catheters are not yet capable of preventing CAUTIs. Aim: To develop an anti-infective urinary catheter. Methods: An efficient silver-poly...

In this paper, we investigate the role of cell death in promoting pattern formation within bacterial biofilms. To do this we utilise an extension of the model proposed by Dockery and Klapper [13], and consider the effects of two distinct death rates. Equations describing the evolution of a moving biofilm interface are derived, and properties of ste...

Chemotaxis, the directed motion of cells or organisms up chemical gradients, is a ubiquitous signal-response mechanism in nature with examples ranging from the movement of bacteria to the formation of blood capillary networks. In this paper, we investigate the existence and stability of steady state solutions to a system of partial differential equ...

Phytophthora infestans is a highly destructive plant pathogen. It was the cause of the infamous Irish potato famine in the nineteenth century and remains to this day a significant global problem with associated costs estimated at $3 billion annually. Key to the success of this pathogen is the dispersal of free-swimming cells called zoospores. A poo...

Thigmotropism is the ability of an organism to respond to a topographical stimulus by altering its axis of growth. The thigmotropic response of the model fungus Neurospora crassa was quantified using microfabricated glass slides with ridges of defined height. We show that the polarity machinery at the hyphal tip plays a role in the thigmotropic res...

Cell differentiation is ubiquitous and facilitates division of labour and development. Bacteria are capable of "multicellular" behaviours that benefit the bacterial community as a whole. A striking example of bacterial differentiation occurs throughout the formation of a biofilm. During Bacillus subtilis biofilm formation a subpopulation of cells d...

In general, prokaryotes are considered to be single-celled organisms that lack internal membrane-bound organelles. However, many bacteria produce proteinaceous microcompartments that serve a similar purpose; that is to concentrate specific enzymatic reactions together or to shield the wider cytoplasm from toxic metabolic intermediates. In this work...

Growth by cell elongation is a morphological process that transcends taxonomic kingdoms. Examples of this polarised growth form include hyphal tip growth in actinobacteria and filamentous fungi and pollen tube development. The biological processes required to produce polarisation in each of these examples are very different. However, commonality of...

Bacteria have elaborate signalling mechanisms to ensure a behavioural response that is most likely to enhance survival in a changing environment. It is becoming increasingly apparent that as part of this response, bacteria are capable of cell differentiation and can generate multiple, mutually exclusive co-existing cell states. These cell states ar...

DegU and exoprotesase levels as predicted by the minimal system. The solutions of the minimal system for I0 = 0 as functions of the phosphorylation ratio . (A) DegU and (B) exoprotease. The dots represent the levels of DegU and exoprotease for values of set at l and h, respectively. All other parameter values from Table 1. (TIFF)

Steady state signal response curves for the minimal system: e ects of increasing I0. The cubic curve given in (S9) plotted as a function of the DegU level U for diering values of I0. Zeros of this cubic represent steady states of the minimal problem. (A) The general shape of the cubics over the range of values of U considered: I0 = 0, 10−6, 10−5, 1...

Steady state signal response curves for the full system. Steady state solutions of system (S1)-(S6) as functions of the signal parameter kph. Left columns (blue) show response for kdeph = 0.05s−1 and right columns (yellow) for kdeph = 0.005s−1. (A) From the top: kph vs DegU; kph vs DegUP; kph vs dimer of DegUP; kph vs DegU +DegUP+dimer; kph vs E. (...

Structure of system signal-response curves as predicted by the minimal system. The solutions of the minimal system (S7)–(S9) for I0 = 0 as functions of the phosphorylation ratio . (A) DegU : U+ (black), U− (blue) and U 0 (red) (U− + 50 is shown for ease of visualisation); (B) DegUP : P+, (black), P− (blue) and P 0 (red); (C) Dimer of DegUP : D+ (bl...

Extrinsic noise e ects on steady state protein levels: uniform signal variance. Output from system (S1)-(S6) subject to uniformly distributed signal strength/perception computed using the Gillespie SSA. Data from 1000 simulations is shown in each case. Histograms show levels of (A) DegU and (B) exoprotease at time t = 17hrs with the signal strength...

E ects of initial cell profile on final system response to intrinsic noise in the signal transduction pathway. Output from system (S1)-(S6) for three initial system configurations. Histograms show levels of DegU and exoprotease at five time points as computed using the Gillespie SSA. Data from 1000 simulations is shown in each case with output show...

E ects of initial cell profile on final system response to extrinsic noise in the signal. Output from system (S1)-(S6) for three initial system configurations. Histograms show levels of DegU and exoprotease at four time points as computed using the Gillespie SSA. Data from 1000 simulations is shown in each case. (A) All cells initially OFF (DegU =...

Selective Heterogeneity in Extracellular 1 Protease Production. (PDF)

Transient dynamics of DegU and Exoprotease as predicted by the full system. The level of DegU and exoprotease as predicted by the full system (S1)-(S6). Transient response as mediated by the phosphorylation rate kph (A and B) and the initial data (C and D). All parameter values from Table 1 except (A) DegU and (B) exoprotease response for kph = 0.0...

Dynamics of the minimal system. Solutions U of (S9) with the left hand side replaced by dU/dt as functions of time. All initial values of U above approximately 11 molecules per cell result in the system tending to the steady state, U+ ( 430 molecules per cell for the parameter values used here). (A) I0 = 10−10 and U(0) = 10 (black), U(0) = 15 (blue...

In this paper we model how the interaction of two species that compete for a common resource can be controlled by the introduction of a third species. This third species in the model can be considered as a bio-control agent. The aim here is to investigate whether the bio-control agent can slow, stall or even reverse the advance of one species into...

The indeterminate growth habit of fungal mycelial can produce massive organisms spanning kilometres, whereas the hypha, the modular building block of these structures, is only a few microns in diameter. The qualitative and quantitative relationship between these scales is difficult to establish using experimental methods alone and a large number of...

In this paper, we discuss a class of bistable reaction-diffusion systems used to model the competitive interaction of two species. The interactions are assumed to be of classic "Lotka-Volterra" type and we will consider a particular problem with relevance to applications in population dynamics: essentially, we study under what conditions the interp...

This contribution is based on the six presentations given at the Special Interest Group meeting on Mathematical modelling of fungal growth and function held during IMC9. The topics covered aspects of fungal growth ranging across several orders of magnitude of spatial and temporal scales from the bio-mechanics of spore ejection, vesicle trafficking...

In this paper we consider the spectral properties of a class of non-local operators, with par-3 ticular emphasis on properties of the associated eigenfunctions. The operators studied here are bounded 4 perturbations of linear (local) differential operators. The non-local perturbation is in the form of an 5 integral term. It is shown here that the s...

We study a class of bistable reaction-diffusion systems used to model two competing species. Systems in this class possess two uniform stable steady states representing semi-trivial solutions. Principally, we are interested in the case where the ratio of the diffusion coefficients is small, i.e. in the near-degenerate case. First, limiting argument...

The spindle assembly checkpoint is a cell cycle surveillance mechanism that ensures the proper separation of chromosomes prior to cell division at mitosis. Aurora kinases play critical roles in mitotic progression and hence small-molecule inhibitors of Aurora kinases have been developed as a new class of potential anti-cancer drugs. In this paper w...

We study a scalar reaction-diffusion equation which contains a nonlocal term in the form of an integral convolution in the spatial variable and demonstrate, using asymptotic, analytical and numerical techniques, that this scalar equation is capable of producing spatio-temporal patterns. Fisher's equation is a particular case of this equation. An as...

Arguably the most dramatic phase in the cell cycle is mitosis, during which replicated chromosomes are sorted into two distinct sets. Aurora kinases are central to the accurate segregation of chromosomes during mitosis. Consequently, they have been selected as possible targets for cancer therapy. Anti-cancer drugs that target Aurora kinases are nor...

Fungi are agents of geochemical change in the environment and play important roles in the soil, the plant-root zone, and in rock and mineral habitats. Modelling may serve as a tool to quantify fungal weathering under natural conditions. This paper provides a review of existing mycelial growth models and examines how these can be adapted to describe...

Faithful separation of chromosomes prior to cell division at mitosis is a highly regulated process. One family of serine/threonine kinases that plays a central role in regulation is the Aurora family. Aurora B plays a role in the spindle assembly checkpoint, in part, by destabilizing the localization of BubR1 and Mad2 at centrosomes and responds to...

The results of a combined theoretical, numerical and experimental study of liquid oscillations in an asymmetric U-tube are presented. The configuration under investigation is analogous to that of the tuned liquid-column damper used to suppress oscillatory motion in large semi-supported structures. The liquid motion is described by a second-order or...

A defining characteristic of cancer is loss of control of accurate chromosome segregation resulting in aneuploidy, genetic instability and tumour progression, ultimately leading to invasive and metastatic phenotypes. A quantitative description of the underlying biological processes would be a valuable tool for developing chemotherapy that is select...

In this paper we consider a second order, Sturm-Liouville-type boundary-value operator of the form $$ L u := -[p u^{ abla}]^{Delta} + qu, $$ on an arbitrary, bounded time-scale $mathbb{T}$, for suitable functions $p,q$, together with suitable boundary conditions. We show that, with a suitable choice of domain, this operator can be formulated in the...

Let T⊂R be a bounded time-scale, with a=infT, b=supT. We consider the weighted, linear, eigenvalue problem−(puΔ)Δ(t)+q(t)uσ(t)=λw(t)uσ(t),t∈Tκ2,c00u(a)+c01uΔ(a)=0,c10u(ρ(b))+c11uΔ(ρ(b))=0, for suitable functions p, q and w and λ∈R. Problems of this type on time-scales have normally been considered in a setting involving Banach spaces of continuous...

In this paper the nature and validity of the mathematical formulation of Michaelis–Menten-type kinetics for enzyme-catalysed biochemical reactions is studied. Previous work has in the main concentrated on isolated, spatially uniform (well-mixed) reactions. The effects of substrate input and diffusion on this formulation, in particular, on the natur...

Thigmotropism (contour sensing) has been assigned an important role in both plant and human fungal pathogens. However, outside these systems, our knowledge of the function of thigmotropism in fungal growth control is relatively poor. Furthermore, the effects of environmental stress on thigmotropic responses have received scant attention. To try to...

Topographical sensing (thigmotropism) is an essential component of efficient fungal growth. It is an important element in the complex pathway of sensory and mechanical elements that drive and control the growing hyphal tip, a fuller understanding of which will bring the mycological community a step closer to complete comprehension of the hyphal gro...

In this paper, a delayed n-Species nonautonomous Lokta-Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. As a corollary, it is shown that the global asympt...

Fungi are of fundamental importance in the terrestrial environment. They have roles as decomposers, plant pathogens, symbionts, and in elemental cycles. Fungi are often dominant, and in soil can comprise the largest pool of biomass (including other microorganisms and invertebrates). They also play a role in maintenance of soil structure due to thei...

In this paper, a Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the prey and nonlocal delays due to gestation of the predator is investigated. In the case of a general domain, sufficient conditions are obtained for the global convergence of positive solutions of the proposed problem by using the energy function...

We consider a class of non-local boundary value problems of the type used to model a variety of physical and biological processes, from Ohmic heating to population dynamics. Of particular relevance therefore is the existence of positive solutions. We are interested in the existence of such solutions that arise as a direct consequence of the non-loc...

Fungi are of fundamental importance in terrestrial ecosystems playing important roles in decomposition, nutrient cycling, plant symbiosis and pathogenesis, and have significant potential in several areas of environmental biotechnology such as biocontrol and bioremediation. In all of these contexts, the fungi are growing in environments exhibiting s...

Recent advances in systems biology have driven many aspects of biological research in a direction heavily weighted towards computational, quantitative and predictive analysis, based on, or assisted by mathematical modelling. In particular, mathematical modelling has played a significant role in the development of our understanding of the growth and...

Topographical sensing (thigmotropism) is an essential component of efficient fungal growth. It is an important element in the complex pathway of sensory and mechanical elements that drive and control the growing hyphal tip, a fuller understanding of which will bring the mycological community a step closer to complete comprehension of the hyphal gro...

In most environments, the spatial distribution of nutrient resources is not uniform. Such heterogeneity is particularly evident in mineral soils, where an additional level of spatial complexity prevails owing to the complex pore network in the solid phases of the soil. Mycelial fungi are well adapted to growth in such spatially complex environments...

In this paper, we first investigate a stage-structured competitive model with time delays, harvesting, and nonlocal spatial effect. By using an iterative technique recently developed by Wu and Zou (Wu J, Zou X. Travelling wave fronts of reaction–diffusion systems with delay. J Dynam Differen Equat 2001;13:651–87), sufficient conditions are establis...

In this paper we consider the spectral properties of a class of non-local uniformly elliptic operators, which arise from the study of non-local uniformly elliptic partial differential equations. Such equations arise naturally in the study of a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics...

A delayed periodic Lotka-Volterra type population model with m predators and n preys is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of...

In this article we consider the spectral properties of a class of non-local operators that arise from the study of non-local reaction-diffusion equations. Such equations are used to model a variety of physical and biological systems with examples ranging from Ohmic heating to population dynamics. The operators studied here are bounded perturbations...

A Lotka–Volterra type reaction–diffusion predator–prey model with stage structure for the predator and time delay due to maturity is investigated. By successively modifying the coupled lower–upper solution pairs, sufficient conditions independent of the effect of spatial diffusion are derived for the global convergence of positive solutions to the...

A three-species Lotka–Volterra type food chain model with stage structure and time delays is investigated. It is assumed in the model that the individuals in each species may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators (immature top predators) do not...

We reconsider the basic formulation of second-order, two-point, Sturm-Liouville-type boundary value problems on time scales. Although this topic has received extensive attention in recent years, we present some simple examples which show that there are certain difficulties with the formulation of the problem as usually used in the literature. These...

A delayed Lotka–Volterra type predator-prey model with stage structure for predator and prey dispersal in two-patch environments is investigated. It is assumed that immature individuals and mature individuals of predator species are divided by a fixed age, and that immature predators do not feed on prey and do not have the ability to reproduce; on...

A periodic ratio-dependent predator–prey model with time delays and stage structure for both prey and predator is investigated. It is assumed that immature individuals and mature individuals of each species are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the perma...

In this paper we investigate the validity of a quasi-steady state assumption in approximating Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions that are subject to periodic substrate input.

A two-species Lotka-Volterra type competition model with stage structures for both species is proposed and investigated. In our model, the individuals of each species are classified as belonging either the immature or the mature. First, we consider the stage-structured model with constant coefficients. By constructing suitable Lyapunov functions, s...

A delayed periodic Holling-type predator–prey model without instantaneous negative feedback is investigated. By using the continuation theorem of coincidence degree theory and by constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive per...

An investigation is made into controlling the natural frequency of tuned liquid column dampers (TLCDs) as a function of the geometry of the tank. A model is derived for free oscillations and the natural frequency is given as a function of the ratio of the vertical columns and the dimensions of the horizontal chamber. Asymmetric TLCDs are modelled i...

A delayed periodic ratio-dependent predator–prey model with prey dispersal and stage structure for predator is investigated. It is assumed that immature individuals and mature individuals of the predator species are divided by a fixed age, and that immature predators don't have the ability to attack prey, and that predator species is confined to on...

A delayed Lotka–Volterra type predator–prey model with stage structure for predator is investigated. It is assumed in the model that the individuals in the predator population may belong to one of two classes: the immatures and the matures, the age to maturity is presented by a time delay, and that the immature predators do not have the ability to...

Let T ⊂ ℝ be a time-scale, with a = inf T, b = sup T. We consider the nonlinear boundary value problem - [p(t)uΔ(t)]Δ + q(t) uσ(t) = λf(t, uσ(t)), on T, u(a) = u(b) = 0, where λ ∈ ℝ+ :=[0, ∞), and f : T × ℝ → ℝ satisfies the conditions f(t, ξ) > 0, (t, ξ) ∈ T × ℝ, f(t, ξ) > fξ (t, ξ) ξ, (t, ξ) ∈ T × ℝM+. We prove a strong maximum principle for the...

A ratio-dependent predator–prey model with stage structure for prey is investigated. First, sufficient conditions are derived for the uniform persistence and impermanence of the model. Next, by constructing appropriate Lyapunov functions, a set of easily verifiable sufficient conditions are obtained for the global asymptotic stability of nonnegativ...

A delayed three-species periodic Lotka-Volterra food-chain model without instantaneous negative feedback is investigated. By using R. E. Gaines and J. L. Mawhin’s [Coincidence degree and nonlinear differential equations. (1977; Zbl 0339.47031)] continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a s...

A discrete periodic two-species Lotka-Volterra predator-prey model with time delays is investigated. By using Gaines and Mawhin's continuation theorem of coincidence degree theory, a set of easily verifiable sufficient conditions are derived for the existence of positive periodic solutions of the model.

A delayed periodic predator–prey model with stage structure for predator is proposed. It is assumed that immature individuals and mature individuals of the predator are divided by a fixed age, and that immature predators do not have the ability to attack prey. Sufficient conditions are derived for the existence, uniqueness and global asymptotic sta...

A periodic cooperative model with time delays is investigated. By using the continuation theorem of coincidence degree theory and by constructing a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive periodic solutions of the system.

A periodic predator-prey model with stage structure for prey and time delays due to negative feedback and gestation of predator is proposed. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory, sufficient conditions are derived for the existence of positive periodic solutions to the proposed model. Numerical simulations a...

Responses of Rhizoctonia solani to spatial heterogeneity in sources of carbon, and associated translocation of carbon (C), were studied in a simple microcosm system comprising two discrete domains of agar gels separated on a glass slide and overlain with a porous membrane. Two arrangements of the gel pairs were used, one containing two equally larg...

A delayed predator-prey model with stage structure for the predator is proposed and investigated. Sufficient conditions are derived for persistence, the local and global asymptomatic stability of a positive equilibrium of the model. Numerical simulations are presented to illustrate the feasability of our main results.

A delayed periodic Lotka-Volterra type predator-prey model with prey dispersal in two-patch environments is investigated. By using R. E. Gaines and J. L. Mawhin’s [Coincidence degree and nonlinear differential equations. (1977; Zbl 0339.47031)] continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set o...

The nature and validity of the mathematical formulation of Michaelis-Menten type kinetics for enzyme-catalysed biochemical reactions is studied. Almost all previous work has concentrated on isolated reactions, i.e. those without input or other environmental influences. In this paper, we investigate the effects of substrate input on this formulation...

A periodic Lotka–Volterra predator–prey model with dispersion and time delays is investigated. By using Gaines and Mawhin’s continuation theorem of coincidence degree theory and by means of a suitable Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence, uniqueness and global stability of positive peri...