Efficient parameter sensitivity computation for spatially extended reaction networks.

Reaction-diffusion models are widely used to study spatially extended chemical reaction systems. In order to understand how the dynamics of a reaction-diffusion model are affected by changes in its input parameters, efficient methods for computing parametric sensitivities are required. In this work, we focus on the stochastic models of spatially extended chemical reaction systems that involve partitioning the computational domain into voxels. Parametric sensitivities are often calculated using Monte Carlo techniques that are typically computationally expensive; however, variance reduction techniques can decrease the number of Monte Carlo simulations required. By exploiting the characteristic dynamics of spatially extended reaction networks, we are able to adapt existing finite difference schemes to robustly estimate parametric sensitivities in a spatially extended network. We show that algorithmic performance depends on the dynamics of the given network and the choice of summary statistics. We then describe a hybrid technique that dynamically chooses the most appropriate simulation method for the network of interest. Our method is tested for functionality and accuracy in a range of different scenarios.

An adaptive multi-level simulation algorithm for stochastic biological systems.

Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms (SSA) to estimate system statistics. The Gillespie algorithm is exact, but computationally costly as it simulates every single reaction. As such, approximate stochastic simulation algorithms such as the tau-leap algorithm are often used. Potentially computationally more efficient, the system statistics generated suffer from significant bias unless tau is relatively small, in which case the computational time can be comparable to that of the Gillespie algorithm. The multi-level method [Anderson and Higham, "Multi-level Monte Carlo for continuous time Markov chains, with applications in biochemical kinetics," SIAM Multiscale Model. Simul. 10(1), 146-179 (2012)] tackles this problem. A base estimator is computed using many (cheap) sample paths at low accuracy. The bias inherent in this estimator is then reduced using a number of corrections. Each correction term is estimated using a collection of paired sample paths where one path of each pair is generated at a higher accuracy compared to the other (and so more expensive). By sharing random variables between these paired paths, the variance of each correction estimator can be reduced. This renders the multi-level method very efficient as only a relatively small number of paired paths are required to calculate each correction term. In the original multi-level method, each sample path is simulated using the tau-leap algorithm with a fixed value of τ. This approach can result in poor performance when the reaction activity of a system changes substantially over the timescale of interest. By introducing a novel adaptive time-stepping approach where τ is chosen according to the stochastic behaviour of each sample path, we extend the applicability of the multi-level method to such cases. We demonstrate the efficiency of our method using a number of examples.

Deriving appropriate boundary conditions, and accelerating position-jump simulations, of diffusion using non-local jumping.

In this paper we explore lattice-based position-jump models of diffusion, and the implications of introducing non-local jumping; particles can jump to a range of nearby boxes rather than only to their nearest neighbours. We begin by deriving conditions for equivalence with traditional local jumping models in the continuum limit. We then generalize a previously postulated implementation of the Robin boundary condition for a non-local process of arbitrary maximum jump length, and present a novel implementation of flux boundary conditions, again generalized for a non-local process of arbitrary maximum jump length. In both these cases we validate our results using stochastic simulation. We then proceed to consider two variations on the basic diffusion model: a hybrid local/non-local scheme suitable for models involving sharp concentration gradients, and the implementation of biased jumping. In all cases we show that non-local jumping can deliver substantial time savings for stochastic simulations.

Identification of Neural Crest and Neural Crest-Derived Cancer Cell Invasion and Migration Genes Using High-throughput Screening and Deep Attention Networks.

Background: Cell migration and invasion are well-coordinated processes in development and disease but remain poorly understood. We previously showed that highly migratory neural crest (NC) cells share a 45-gene panel with other cell invasion phenomena, including cancer. To identify critical genes of the 45-gene panel, we performed a high-throughput siRNA screen and used statistical and deep learning methods to compare NC- versus non-NC-derived human cell lines. Results: We find 14 out of 45 genes significantly reduces c8161 melanoma cell migration; only 4 are shared with HT1080 fibrosarcoma cells (BMP4, ITGB1, KCNE3, RASGRP1). Deep learning attention network analysis identified distinct cell-cell interaction patterns and significant alterations after BMP4 or RASGRP1 knockdown in c8161 cells. Addition of recombinant proteins to the culture media identified 5 out of the 10 known secreted molecules stimulate c8161 cell migration, including BMP4. BMP4 siRNA knockdown inhibited c8161 cell invasion in vivo and in vitro ; however, its addition to the culture media rescued c8161 cell invasion. Conclusion: A high-throughput screen and deep learning rapidly distilled a 45-gene panel to a small subset of genes that appear critical to melanoma cell invasion and warrant deeper in vivo functional analysis for their role in driving the neural crest.

Modelling Aedes aegypti mosquito control via transgenic and sterile insect techniques: endemics and emerging outbreaks.

The invasion of pest insects often changes or destroys a native ecosystem, and can result in food shortages and disease endemics. Issues such as the environmental effects of chemical control methods, the economic burden of maintaining control strategies and the risk of pest resistance still remain, and mosquito-borne diseases such as malaria and dengue fever prevail in many countries, infecting over 100 million worldwide in 2010. One environmentally friendly method for mosquito control is the Sterile Insect Technique (SIT). This species-specific method of insect control relies on the mass rearing, sterilization and release of large numbers of sterile insects. An alternative transgenic method is the Release of Insects carrying a Dominant Lethal (RIDL). Our objective is to consider contrasting control strategies for two invasive scenarios via SIT and RIDL: an endemic case and an emerging outbreak. We investigate how the release rate and size of release region influence both the potential for control success and the resources needed to achieve it, under a range of conditions and control strategies, and we discuss advantageous strategies with respect to reducing the release resources and strategy costs (in terms of control mosquito numbers) required to achieve complete eradication of wild-type mosquitoes.

The dynamics of Turing patterns for morphogen-regulated growing domains with cellular response delays.

Since its conception in 1952, the Turing paradigm for pattern formation has been the subject of numerous theoretical investigations. Experimentally, this mechanism was first demonstrated in chemical reactions over 20 years ago and, more recently, several examples of biological self-organisation have also been implicated as Turing systems. One criticism of the Turing model is its lack of robustness, not only with respect to fluctuations in the initial conditions, but also with respect to the inclusion of delays in critical feedback processes such as gene expression. In this work we investigate the possibilities for Turing patterns on growing domains where the morphogens additionally regulate domain growth, incorporating delays in the feedback between signalling and domain growth, as well as gene expression. We present results for the proto-typical Schnakenberg and Gierer-Meinhardt systems: exploring the dynamics of these systems suggests a reconsideration of the basic Turing mechanism for pattern formation on morphogen-regulated growing domains as well as highlighting when feedback delays on domain growth are important for pattern formation.

Immunocytochemical identification of phenylalanine hydroxylase and albumin in cultured hepatoma cells and isolated rat hepatocytes.

Rhodamine-conjugated antibodies specific for phenylalanine hydroxylase and serum albumin were employed as cytochemical probes to identify these two proteins in H4 hepatoma cells and in isolated rat hepatocytes. Each fluorescent antibody stained the cells specifically and in a distinctive manner. In both cell types, albumin staining was discretely localized in cytoplasmic and in H4 cultures varied somewhat from cell to cell. Evidence from cultures of REB15 cells, a strain derived by cloning H4 cells in tyrosine-free medium, suggested that the staining variability of H4 cells could reflect a variability in phenylalanine hydroxylase content. Hydrocortisone-treated H4 cells and REB15 cultures contain increased amounts of phenylalanine hydroxylase; and all cells in the culture appear to be induced by the hormone. Evidence was presented to show that the albumin visualized within the isolated hepatocytes had been synthesized by these cells, and, furthermore, that quantitatively nearly all intracellular albumin in the isolated rat hepatocytes appeared to be entrained in the secretion pathway (analogous data already exist for H4 cells [Baker, R.E., and R. Shiman. 1979. J. Biol. Chem. 254:9633-9639]). By scoring specific fluorescence, 86 and 98% of the H4 cells and 89 and 98% of the isolated hepatocytes were found to contain phenylalanine hydroxylase and albumin, respectively. Therefore, almost all cells in each population appeared to synthesize both proteins. An implication of these findings is that in rat virtually all liver parenchymal cells must synthesize both phenylalanine hydroxylase and albumin.

Neuronal specification of cutaneous nerves through connections with skin grafts in the frog.

Skin grafts were rotated 180 degrees in frog tadpoles. After metamorphosis, cutaneous reflexes were tested, and the receptive fields of cutaneous nerves were mapped electrophysiologically. Accurately localized limb movements were elicited by mechanical stimulation of normal skin, or of dorsal skin reimplanted on the back after 180-degree rotation. Reflexes misdirected to the original site of the stimulated skin were elicited from dorsoventrally inverted grafts, but not from anteroposteriorly inverted grafts. In most cases, the local nerves supplied the grafts, and each nerve entered the skin within its own receptive field. This observation eliminated the possibility that misdirected reflexes were due to selective regrowth of cutaneous nerves. We concluded that cutaneous nerves formed central synaptic associations which were specified by their new terminal connections with grafted skin.

A one-dimensional individual-based mechanical model of cell movement in heterogeneous tissues and its coarse-grained approximation.

Mechanical heterogeneity in biological tissues, in particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult to explore relationships between cellular-level properties and tissue-level outcomes when biological experiments are performed at a single scale only. To overcome this difficulty, we develop a multi-scale mathematical model which provides a clear framework to explore these connections across biological scales. Starting with an individual-based mechanical model of cell movement, we subsequently derive a novel coarse-grained system of partial differential equations governing the evolution of the cell density due to heterogeneous cellular properties. We demonstrate that solutions of the individual-based model converge to numerical solutions of the coarse-grained model, for both slowly-varying-in-space and rapidly-varying-in-space cellular properties. We discuss applications of the model, such as determining relative cellular-level properties and an interpretation of data from a breast cancer detection experiment.

Plasticity in fast synaptic inhibition of adult oxytocin neurons caused by switch in GABA(A) receptor subunit expression.

We found that magnocellular oxytocin neurons in adult female rats exhibit an endogenous GABA(A) receptor subunit switch around parturition: a decrease in alpha1:alpha2 subunit mRNA ratio correlated with a decrease in allopregnanolone potentiation and increase in decay time constant of the GABA(A) receptor-mediated IPSCs in these cells. The causal relationship between changes in alpha1:alpha2 mRNA ratio and the ion channel kinetics was confirmed using in vitro antisense deletion. Further, GABA(A) receptors exhibited a tonic inhibitory influence upon oxytocin release in vivo, and allopregnanolone helped to restrain oxytocin neuron in vitro firing only before parturition, when the alpha1:alpha2 subunit mRNA ratio was still high. Such observations provide evidence for the physiological significance of GABA(A) receptor subunit heterogeneity and plasticity in the adult brain.

Isolation of the gene encoding the Saccharomyces cerevisiae centromere-binding protein CP1.

CP1 is a sequence-specific DNA-binding protein of the yeast Saccharomyces cerevisiae which recognizes the highly conserved DNA element I (CDEI) of yeast centromeres. We cloned and sequenced the gene encoding CP1. The gene codes for a protein of molecular weight 39,400. When expressed in Escherichia coli, the CP1 gene directed the synthesis of a CDEI-binding protein having the same gel mobility as purified yeast CP1. We have given the CP1 gene the genetic designation CEP1 (centromere protein 1). CEP1 was mapped and found to reside on chromosome X, 2.0 centimorgans from SUP4. Strains were constructed in which most of CEP1 was deleted. Such strains lacked detectable CP1 activity and were viable; however, CEP1 gene disruption resulted in a 35% increase in cell doubling time and a ninefold increase in the rate of mitotic chromosome loss. An unexpected consequence of CP1 gene disruption was methionine auxotrophy genetically linked to cep1. This result and the recent finding that CDEI sites in the MET25 promoter are required to activate transcription (D. Thomas, H. Cherest, and Y. Surdin-Kerjan, J. Mol. Biol. 9:3292-3298, 1989) suggest that CP1 is both a kinetochore protein and a transcription factor.

Function of the ski4p (Csl4p) and Ski7p proteins in 3'-to-5' degradation of mRNA.

One of two general pathways of mRNA decay in the yeast Saccharomyces cerevisiae occurs by deadenylation followed by 3'-to-5' degradation of the mRNA body. Previous results have shown that this degradation requires components of the exosome and the Ski2p, Ski3p, and Ski8p proteins, which were originally identified due to their superkiller phenotype. In this work, we demonstrate that deletion of the SKI7 gene, which encodes a putative GTPase, also causes a defect in 3'-to-5' degradation of mRNA. Deletion of SKI7, like deletion of SKI2, SKI3, or SKI8, does not affect various RNA-processing reactions of the exosome. In addition, we show that a mutation in the SKI4 gene also causes a defect in 3'-to-5' mRNA degradation. We show that the SKI4 gene is identical to the CSL4 gene, which encodes a core component of the exosome. Interestingly, the ski4-1 allele contains a point mutation resulting in a mutation in the putative RNA binding domain of the Csl4p protein. This point mutation strongly affects mRNA degradation without affecting exosome function in rRNA or snRNA processing, 5' externally transcribed spacer (ETS) degradation, or viability. In contrast, the csl4-1 allele of the same gene affects rRNA processing but not 3'-to-5' mRNA degradation. We identify csl4-1 as resulting from a partial-loss-of-function mutation in the promoter of the CSL4 gene. These data indicate that the distinct functions of the exosome can be separated genetically and suggest that the RNA binding domain of Csl4p may have a specific function in mRNA degradation.

Role of the Saccharomyces cerevisiae general regulatory factor CP1 in methionine biosynthetic gene transcription.

Saccharomyces cerevisiae general regulatory factor CP1 (encoded by the gene CEP1) is required for optimal chromosome segregation and methionine prototrophy. MET16-CYC1-lacZ reporter constructs were used to show that MET16 5'-flanking DNA contains a CP1-dependent upstream activation sequence (UAS). Activity of the UAS required an intact CP1-binding site, and the effects of cis-acting mutations on CP1 binding and UAS activity correlated. In most respects, MET16-CYC1-lacZ reporter gene expression mirrored that of chromosomal MET16; however, the endogenous gene was found to be activated in response to amino acid starvation (general control). The latter mechanism was both GCN4 and CP1 dependent. MET25 was also found to be activated by GCN4, albeit weakly. More importantly, MET25 transcription was strongly CP1 dependent in gcn4 backgrounds. The modulation of MET gene expression by GCN4 can explain discrepancies in the literature regarding CP1 dependence of MET gene transcription. Lastly, micrococcal nuclease digestion and indirect end labeling were used to analyze the chromatin structure of the MET16 locus in wild-type and cep1 cells. The results indicated that CP1 plays no major role in configuring chromatin structure in this region, although localized CP1-specific differences in nuclease sensitivity were detected.

The N terminus of the centromere H3-like protein Cse4p performs an essential function distinct from that of the histone fold domain.

Cse4p is an evolutionarily conserved histone H3-like protein that is thought to replace H3 in a specialized nucleosome at the yeast (Saccharomyces cerevisiae) centromere. All known yeast, worm, fly, and human centromere H3-like proteins have highly conserved C-terminal histone fold domains (HFD) but very different N termini. We have carried out a comprehensive and systematic mutagenesis of the Cse4p N terminus to analyze its function. Surprisingly, only a 33-amino-acid domain within the 130-amino-acid-long N terminus is required for Cse4p N-terminal function. The spacing of the essential N-terminal domain (END) relative to the HFD can be changed significantly without an apparent effect on Cse4p function. The END appears to be important for interactions between Cse4p and known kinetochore components, including the Ctf19p/Mcm21p/Okp1p complex. Genetic and biochemical evidence shows that Cse4p proteins interact with each other in vivo and that nonfunctional cse4 END and HFD mutant proteins can form functional mixed complexes. These results support different roles for the Cse4p N terminus and the HFD in centromere function and are consistent with the proposed Cse4p nucleosome model. The structure-function characteristics of the Cse4p N terminus are relevant to understanding how other H3-like proteins, such as the human homolog CENP-A, function in kinetochore assembly and chromosome segregation.

Analysis of primary structural determinants that distinguish the centromere-specific function of histone variant Cse4p from histone H3.

Cse4p is a variant of histone H3 that has an essential role in chromosome segregation and centromere chromatin structure in budding yeast. Cse4p has a unique 135-amino-acid N terminus and a C-terminal histone-fold domain that is more than 60% identical to histone H3 and the mammalian centromere protein CENP-A. Cse4p and CENP-A have biochemical properties similar to H3 and probably replace H3 in centromere-specific nucleosomes in yeasts and mammals, respectively. In order to identify regions of Cse4p that distinguish it from H3 and confer centromere function, a systematic site-directed mutational analysis was performed. Nested deletions of the Cse4p N terminus showed that this region of the protein contains at least one essential domain. The C-terminal histone-fold domain of Cse4p was analyzed by changing Cse4p amino acids that differ between Cse4p and H3 to the analogous H3 residues. Extensive substitution of contiguous Cse4p residues with H3 counterparts resulted in cell lethality. However, all large lethal substitution alleles could be subdivided into smaller viable alleles, many of which caused elevated rates of mitotic chromosome loss. The results indicate that residues critical for wild-type Cse4p function and high-fidelity chromosome transmission are distributed across the entire histone-fold domain. Our findings are discussed in the context of the known structure of H3 within the nucleosome and compared with previous results reported for CENP-A.

Travelling gradients in interacting morphogen systems.

Morphogen gradients are well known to play several important roles in development; however the mechanisms underlying the formation and maintenance of these gradients are often not well understood. In this work, we investigate whether the presence of a secondary morphogen can increase the robustness of the primary morphogen gradient to perturbation, thereby providing a more stable mechanism for development. We base our model around the interactions of Fibroblast Growth Factor 8 and retinoic acid, which have been shown to act as morphogens in many developmental systems. In particular, we investigate the formation of opposing gradients of these morphogens along the antero-posterior axis of vertebrate embryos, thereby controlling temporal and spatial aspects of axis segmentation and neuronal differentiation.

Variable species densities are induced by volume exclusion interactions upon domain growth.

In this work we study the effect of domain growth on spatial correlations in agent populations containing multiple species. This is important as heterogenous cell populations are ubiquitous during the embryonic development of many species. We have previously shown that the long-term behavior of an agent population depends on the way in which domain growth is implemented. We extend this work to show that, depending on the way in which domain growth is implemented, different species dominate in multispecies simulations. Continuum approximations of the lattice-based model that ignore spatial correlations cannot capture this behavior, while those that explicitly account for spatial correlations can. The results presented here show that the precise mechanism of domain growth can determine the long-term behavior of multispecies populations and, in certain circumstances, establish spatially varying species densities.

Using approximate Bayesian computation to quantify cell-cell adhesion parameters in a cell migratory process.

In this work, we implement approximate Bayesian computational methods to improve the design of a wound-healing assay used to quantify cell-cell interactions. This is important as cell-cell interactions, such as adhesion and repulsion, have been shown to play a role in cell migration. Initially, we demonstrate with a model of an unrealistic experiment that we are able to identify model parameters that describe agent motility and adhesion, given we choose appropriate summary statistics for our model data. Following this, we replace our model of an unrealistic experiment with a model representative of a practically realisable experiment. We demonstrate that, given the current (and commonly used) experimental set-up, our model parameters cannot be accurately identified using approximate Bayesian computation methods. We compare new experimental designs through simulation, and show more accurate identification of model parameters is possible by expanding the size of the domain upon which the experiment is performed, as opposed to increasing the number of experimental replicates. The results presented in this work, therefore, describe time and cost-saving alterations for a commonly performed experiment for identifying cell motility parameters. Moreover, this work will be of interest to those concerned with performing experiments that allow for the accurate identification of parameters governing cell migratory processes, especially cell migratory processes in which cell-cell adhesion or repulsion are known to play a significant role.

Coupling volume-excluding compartment-based models of diffusion at different scales: Voronoi and pseudo-compartment approaches.

Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations are a popular tool for modelling such phenomena deterministically, but it is often necessary to use stochastic models to accurately capture the behaviour of a system, especially when the number of diffusing particles is low. The stochastic models we consider in this paper are 'compartment-based': the domain is discretized into compartments, and particles can jump between these compartments. Volume-excluding effects (crowding) can be incorporated by blocking movement with some probability. Recent work has established the connection between fine- and coarse-grained models incorporating volume exclusion, but only for uniform lattices. In this paper, we consider non-uniform, hybrid lattices that incorporate both fine- and coarse-grained regions, and present two different approaches to describe the interface of the regions. We test both techniques in a range of scenarios to establish their accuracy, benchmarking against fine-grained models, and show that the hybrid models developed in this paper can be significantly faster to simulate than the fine-grained models in certain situations and are at least as fast otherwise.

How domain growth is implemented determines the long-term behavior of a cell population through its effect on spatial correlations.

Domain growth plays an important role in many biological systems, and so the inclusion of domain growth in models of these biological systems is important to understanding how these systems function. In this work we present methods to include the effects of domain growth on the evolution of spatial correlations in a continuum approximation of a lattice-based model of cell motility and proliferation. We show that, depending on the way in which domain growth is implemented, different steady-state densities are predicted for an agent population. Furthermore, we demonstrate that the way in which domain growth is implemented can result in the evolution of the agent density depending on the size of the domain. Continuum approximations that ignore spatial correlations cannot capture these behaviors, while those that account for spatial correlations do. These results will be of interest to researchers in developmental biology, as they suggest that the nature of domain growth can determine the characteristics of cell populations.