Exact sharp-fronted solutions for nonlinear diffusion on evolving domains

Models of diffusive processes that occur on evolving domains are frequently employed to describe biological and physical phenomena, such as diffusion within expanding tissues or substrates. Previous investigations into these models either report numerical solutions or require an assumption of linear diffusion to determine exact solutions. Unfortunately, numerical solutions do not reveal the relationship between the model parameters and the solution features. Additionally, experimental observations typically report the presence of sharp fronts, which are not captured by linear diffusion. Here we address both limitations by presenting exact sharp-fronted solutions to a model of degenerate nonlinear diffusion on a growing domain. We obtain the solution by identifying a series of transformations that converts the model of nonlinear diffusion on a growing domain to the porous medium equation on a fixed domain, which admits known exact solutions. We determine expressions for critical time scales and domain growth rates such that the diffusive population never reaches the domain boundaries and hence the solution remains valid

Exact solutions for diffusive transport on heterogeneous growing domains

From the smallest biological systems to the largest cosmological structures, spatial domains undergo expansion and contraction. Within these growing domains, diffusive transport is a common phenomenon. Mathematical models have been widely employed to investigate diffusive processes on growing domains. However, a standard assumption is that the domain growth is spatially uniform. There are many relevant examples where this is not the case, such as the colonisation of growing gut tissue by neural crest cells. As such, it is not straightforward to disentangle the individual roles of heterogeneous growth and diffusive transport. Here we present exact solutions to models of diffusive transport on domains undergoing spatially non-uniform growth. The exact solutions are obtained via a combination of transformation, convolution and superposition techniques. We verify the accuracy of these solutions via comparison with simulations of a corresponding lattice-based random walk. We explore various domain growth functions, including linear growth, exponential growth and contraction, and oscillatory growth. Provided the domain size remains positive, we find that the derived solutions are valid. The exact solutions reveal the relationship between model parameters, such as the diffusivity and the type and rate of domain growth, and key statistics, such as the survival and splitting probabilities

Predicting population extinction in lattice-based birth-death-movement models

The question of whether a population will persist or go extinct is of key interest throughout ecology and biology. Various mathematical techniques allow us to generate knowledge regarding individual behaviour, which can be analysed to obtain predictions about the ultimate survival or extinction of the population. A common model employed to describe population dynamics is the lattice-based random walk model with crowding (exclusion). This model can incorporate behaviour such as birth, death and movement, while including natural phenomena such as finite size effects. Performing sufficiently many realisations of the random walk model to extract representative population behaviour is computationally intensive. Therefore, continuum approximations of random walk models are routinely employed. However, standard continuum approximations are notoriously incapable of making accurate predictions about population extinction. Here, we develop a new continuum approximation, the state space diffusion approximation, which explicitly accounts for population extinction. Predictions from our approximation faithfully capture the behaviour in the random walk model, and provides additional information compared to standard approximations. We examine the influence of the number of lattice sites and initial number of individuals on the long-term population behaviour, and demonstrate the reduction in computation time between the random walk model and our approximation

Molecular Communication for Quorum Sensing Inspired Cooperative Drug Delivery

A cooperative drug delivery system is proposed, where quorum sensing (QS), a density-dependent bacterial behavior coordination mechanism, is employed by synthetic bacterium-based nanomachines (B-NMs) for controllable drug delivery. In our proposed system, drug delivery is only triggered when there are enough QS molecules, which in turn only happens when there are enough B-NMs. This makes the proposed system can be used to achieve a high release rate of drug molecules from a high number of B-NMs when the population density of B-NMs may not be known. Analytical expressions for i) the expected activation probability of the B-NM due to randomly-distributed B-NMs and ii) the expected aggregate absorption rate of drug molecules due to randomly-distributed QS activated B-NMs are derived. Analytical results are verified by particle-based simulations. The derived results can help to predict and control the impact of environmental factors (e.g. diffusion coefficient and degradation rate) on the absorption rate of drug molecules since rigorous diffusion-based molecular channels are considered. Our results show that the activation probability at the B-NM increases as this B-NM is located closer to the center of the B-NM population and the aggregate absorption rate of the drug molecules non-linearly increases as the population density increases.Comment: 9 pages; 9 figure

Unpacking the Allee effect: determining individual-level mechanisms that drive global population dynamics

We present a solid theoretical foundation for interpreting the origin of Allee effects by providing the missing link in understanding how local individual-based mechanisms translate to global population dynamics. Allee effects were originally proposed to describe population dynamics that cannot be explained by exponential and logistic growth models. However, standard methods often calibrate Allee effect models to match observed global population dynamics without providing any mechanistic insight. By introducing a stochastic individual-based model, with proliferation, death and motility rates that depend on local density, we present a modelling framework that translates particular global Allee effects to specific individual-based mechanisms. Using data from ecology and cell biology, we unpack individual-level mechanisms implicit in an Allee effect model and provide simulation tools for others to repeat this analysis

Psoriasis drug development and GWAS interpretation through in silico analysis of transcription factor binding sites

BackgroundPsoriasis is a cytokine‐mediated skin disease that can be treated effectively with immunosuppressive biologic agents. These medications, however, are not equally effective in all patients and are poorly suited for treating mild psoriasis. To develop more targeted therapies, interfering with transcription factor (TF) activity is a promising strategy.MethodsMeta‐analysis was used to identify differentially expressed genes (DEGs) in the lesional skin from psoriasis patients (n = 237). We compiled a dictionary of 2935 binding sites representing empirically‐determined binding affinities of TFs and unconventional DNA‐binding proteins (uDBPs). This dictionary was screened to identify “psoriasis response elements” (PREs) overrepresented in sequences upstream of psoriasis DEGs.ResultsPREs are recognized by IRF1, ISGF3, NF‐kappaB and multiple TFs with helix‐turn‐helix (homeo) or other all‐alpha‐helical (high‐mobility group) DNA‐binding domains. We identified a limited set of DEGs that encode proteins interacting with PRE motifs, including TFs (GATA3, EHF, FOXM1, SOX5) and uDBPs (AVEN, RBM8A, GPAM, WISP2). PREs were prominent within enhancer regions near cytokine‐encoding DEGs (IL17A, IL19 and IL1B), suggesting that PREs might be incorporated into complex decoy oligonucleotides (cdODNs). To illustrate this idea, we designed a cdODN to concomitantly target psoriasis‐activated TFs (i.e., FOXM1, ISGF3, IRF1 and NF‐kappaB). Finally, we screened psoriasis‐associated SNPs to identify risk alleles that disrupt or engender PRE motifs. This identified possible sites of allele‐specific TF/uDBP binding and showed that PREs are disproportionately disrupted by psoriasis risk alleles.ConclusionsWe identified new TF/uDBP candidates and developed an approach that (i) connects transcriptome informatics to cdODN drug development and (ii) enhances our ability to interpret GWAS findings. Disruption of PRE motifs by psoriasis risk alleles may contribute to disease susceptibility.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/155494/1/ctm2s4016901500545-sup-0001.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155494/2/ctm2s4016901500545-sup-0018.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155494/3/ctm2s4016901500545-sup-0002.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155494/4/ctm2s4016901500545.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/155494/5/ctm2s4016901500545-sup-0009.pd

Photosystem II Peripheral Accessory Chlorophyll Mutants in Chlamydomonas reinhardtii. Biochemical Characterization and Sensitivity to Photo-Inhibition

In addition to the four chlorophylls (Chls) involved in primary charge separation, the photosystem II (PSII) reaction center polypeptides, D1 and D2, coordinate a pair of symmetry-related, peripheral accessory Chls. These Chls are axially coordinated by the D1-H118 and D2-H117 residues and are in close association with the proximal Chl antennae proteins, CP43 and CP47. To gain insight into the function(s) of each of the peripheral Chls, we generated site-specific mutations of the amino acid residues that coordinate these Chls and characterized their energy and electron transfer properties. Our results demonstrate that D1-H118 and D2-H117 mutants differ with respect to: (a) their relative numbers of functional PSII complexes, (b) their relative ability to stabilize charge-separated states, (c) light-harvesting efficiency, and (d) their sensitivity to photo-inhibition. The D2-H117N and D2-H117Q mutants had reduced levels of functional PSII complexes and oxygen evolution capacity as well as reduced light-harvesting efficiencies relative to wild-type cells. In contrast, the D1-H118Q mutant was capable of near wild-type rates of oxygen evolution at saturating light intensities. The D1-H118Q mutant also was substantially more resistant to photo-inhibition than wild type. This reduced sensitivity to photo-inhibition is presumably associated with a reduced light-harvesting efficiency in this mutant. Finally, it is noted that the PSII peripheral accessory Chls have similarities to a to a pair of Chls also present in the PSI reaction center complex