Angiogenesis and vascular remodelling in normal and cancerous tissues

Vascular development and homeostasis are underpinned by two fundamental features: the generation of new vessels to meet the metabolic demands of under-perfused regions and the elimination of vessels that do not sustain flow. In this paper we develop the first multiscale model of vascular tissue growth that combines blood flow, angiogenesis, vascular remodelling and the subcellular and tissue scale dynamics of multiple cell populations. Simulations show that vessel pruning, due to low wall shear stress, is highly sensitive to the pressure drop across a vascular network, the degree of pruning increasing as the pressure drop increases. In the model, low tissue oxygen levels alter the internal dynamics of normal cells, causing them to release vascular endothelial growth factor (VEGF), which stimulates angiogenic sprouting. Consequently, the level of blood oxygenation regulates the extent of angiogenesis, with higher oxygenation leading to fewer vessels. Simulations show that network remodelling (and de novo network formation) is best achieved via an appropriate balance between pruning and angiogenesis. An important factor is the strength of endothelial tip cell chemotaxis in response to VEGF. When a cluster of tumour cells is introduced into normal tissue, as the tumour grows hypoxic regions form, producing high levels of VEGF that stimulate angiogenesis and cause the vascular density to exceed that for normal tissue. If the original vessel network is sufficiently sparse then the tumour may remain localised near its parent vessel until new vessels bridge the gap to an adjacent vessel. This can lead to metastable periods, during which the tumour burden is approximately constant, followed by periods of rapid growth.     

The Single Substitution I259T,Conserved in the Plasminogen Activator Pla of Pandemic Yersinia pestis Branches,Enhances Fibrinolytic Activity

The outer membrane plasminogen activator Pla of Yersinia pestis is a central virulence factor in plague. The primary structure of the Pla β-barrel is conserved in Y. pestis biovars Antiqua, Medievalis, and Orientalis, which are associated with pandemics of plague. The Pla molecule of the ancestral Y. pestis lineages Microtus and Angola carries the single amino acid change T259I located in surface loop 5 of the β-barrel. Recombinant Y. pestis KIM D34 or Escherichia coli XL1 expressing Pla T259I was impaired in fibrinolysis and in plasminogen activation. Lack of detectable generation of the catalytic light chain of plasmin and inactivation of plasmin enzymatic activity by the Pla T259I construct indicated that Microtus Pla cleaved the plasminogen molecule more unspecifically than did common Pla. The isoform pattern of the Pla T259I molecule was different from that of the common Pla molecule. Microtus Pla was more efficient than wild-type Pla in α₂-antiplasmin inactivation. Pla of Y. pestis and PgtE of Salmonella enterica have evolved from the same omptin ancestor, and their comparison showed that PgtE was poor in plasminogen activation but exhibited efficient antiprotease inactivation. The substitution ²⁵⁹IIDKT/TIDKN in PgtE, constructed to mimic the L5 region in Pla, altered proteolysis in favor of plasmin formation, whereas the reverse substitution ²⁵⁹TIDKN/IIDKT in Pla altered proteolysis in favor of α₂-antiplasmin inactivation. The results suggest that Microtus Pla represents an ancestral form of Pla that has evolved into a more efficient plasminogen activator in the pandemic Y. pestis lineages.Since the year 540, plague has killed some 200 million humans in three pandemics, i.e., the Justinian plague, the Black Death, and the modern plague (36). Genomic studies have estimated that the etiological agent, Yersinia pestis, evolved from the oral-fecal pathogen Yersinia pseudotuberculosis serotype O1b only shortly before the first pandemic, i.e., 5,000 to 20,000 years ago (1, 2, 46), which has made the bacterium a paradigm of the rapid evolution of a severe bacterial pathogen (57). At least four biovars of Y. pestis have been identified through metabolic and genomic studies; of these biovars, Antiqua, Medievalis, and Orientalis may be associated with the three plague pandemics, whereas the fourth biovar, Microtus, is associated with human-attenuated Y. pestis strains from two geographically distant infection foci in China (36, 59-61). A recent molecular analysis indicated that the biovars are not monophyletic and proposed the subdivision of Y. pestis into eight molecular groupings, which represent different evolutionary branches and histories and are only partially compatible with the biovars (1). Y. pestis evolved from Y. pseudotuberculosis along branch 0, which consists of “atypical” Y. pestis strains designated Angola, Microtus, and Pestoides; these are phylogenetically ancestral to the Antiqua, Medievalis, and Orientalis branches (1).As a disease, plague exhibits various pathologies. Bubonic plague is the zoonotic form of the disease, which is usually acquired by humans from the bite of a flea that has been infected through a blood meal on a diseased rodent (36). The bacteria invade at the intradermal flea bite site and migrate to lymphatic vessels and then to regional draining lymph nodes, where they multiply and cause the development of buboes (44). Without early treatment, bubonic plague progresses to life-threatening septicemic plague, and hematogenous spread of the bacterium to lungs leads to pneumonic plague, a rapidly fatal and highly contagious airborne disease. Occasional injection of Y. pestis cells by the flea directly into the circulatory system leads to primary septicemic plague (43).The plasminogen activator Pla is a cell surface protease encoded by the Y. pestis-specific plasmid pPCP1 (10, 48). Pla is essential in the pathogenesis of bubonic (43, 49) and pneumonic plague (28), whereas it has less of a role in primary septicemic plague (43, 49). The pla gene is highly transcribed in buboes of Y. pestis-infected mice (45), and Pla specifically potentiates migration of the bacteria to lymphatic tissue (43). Pla seems to have a different role in pneumonic plague, where it allows Y. pestis to replicate rapidly in the lungs, causing lethal fulminant pneumonia (28). Virulent Y. pestis strains lacking the Pla-encoding plasmid pPCP1 have been isolated in Asia (3), and they can be associated with primary septicemic plague (43).Pla is an aspartic protease (22, 55) that activates human plasminogen (Plg) to the serine protease plasmin (47) and inactivates the plasmin inhibitor α₂-antiplasmin (α₂AP), thus affecting the main control system for plasmin activity (22). Plg is an abundant circulating zymogen, and its activation is central in the pathogenesis of plague (13, 28, 43), and plasmin is a powerful serine protease associated with cell migration and degradation of fibrin clots (29, 32, 37). In accordance with this, Pla-mediated bacterial adherence directs uncontrolled plasmin proteolysis onto basement membranes to enhance bacterial metastasis through tissue barriers (25, 27), and fibrinolysis by Pla-generated plasmin activity plays a role in the pathogenesis of bubonic plague (8).Compared to those of other Y. pestis biovars, Microtus isolates have several unique genomic features that may be involved in their inherent inability to attack the human host, and specific losses of genes or gene functions are thought to be responsible for the human attenuation (59). Interestingly, the attenuation does not apply to the murine host. The predicted amino acid sequence of the Pla polypeptide is remarkably conserved: in the branches Antiqua, Medievalis, and Orientalis, the Pla sequences are completely identical, whereas a single amino acid substitution, T259I, has been detected in atypical Angola and Microtus strains (6, 38, 50). A genetic analysis of 260 isolates of Y. pestis showed that the T259I substitution in Pla is shared by all isolates of biovar Microtus but absent in those of other biovars (59). Many of the Pestoides strains lack the pPCP1 plasmid and hence also the pla gene (12), and pla sequences from Pestoides are not available.Pla is a member of the omptin family of conserved outer membrane proteases/adhesins detected in several gram-negative bacterial pathogens (15, 17, 21). The omptins have the same molecular size, a β-barrel fold of 10 transmembrane β strands, and five surface-exposed loops, L1 to L5 (Fig. ​(Fig.1).1). The catalytic residues and the residues interacting with lipid A in the outer membrane are completely conserved (17, 21-23, 41, 55). The omptins cleave peptide substrates at basic residues (17) but show dramatic heterogeneity in the recognition of biologically important polypeptides, such as Plg, the antiprotease α₂AP, gelatin, and progelatinases. Analyses of hybrid proteins created between Pla and the omptins PgtE of Salmonella enterica and OmpT of Escherichia coli have indicated that the differing polypeptide substrate selectivity of omptins is dictated by sequence variation in the mobile loop structures of the β-barrel (22, 40). Residue T259 in Pla is located at surface loop 5 and oriented inward in the active-site groove of the Pla barrel, close to residue K262, where Pla is autoprocessed (22, 23) (Fig. ​(Fig.11).Open in a separate windowFIG. 1.Model of Pla structure (23) and location of residue Thr259. Side (top drawing) and top (bottom drawing) views of the transmembrane β-barrel are shown. L1 to L5 are the surface loops. Catalytic residues Asp84, Asp86, Asp206, and His208 are indicated in green, Thr259 is in red, and the autoprocessing site Lys262 is in yellow. OM is the outer membrane. (C) Amino acid sequence of residues 254 to 273 at L5 and the termini of β-strands 9 and 10 in Pla, Microtus Pla, and PgtE are shown.The omptin β-barrel has spread by horizontal gene transfer in gram-negative bacteria and adapted to the life-styles of host bacteria (15, 17, 21, 22, 40). Overall, the omptins give an example of an evolvable, robust enzyme fold (34) that easily acquires novel or improved functions. The fact that the single substitution T259I associates with ancestral Y. pestis Microtus and Angola populations suggests that Microtus Pla represents a form of the protein that preceded the common Pla protein. The central role of Plg activation in the pathogenesis of plague led us to analyze whether the single substitution T259I affects the fibrinolytic activities of the Pla molecule.     

Distinct mechanisms underlie pattern formation in the skin and skin appendages

Patterns form with the break of homogeneity and lead to the emergence of new structure or arrangement. There are different physiological and pathological mechanisms that lead to the formation of patterns. Here, we first introduce the basics of pattern formation and their possible biological basis. We then discuss different categories of skin patterns and their potential underlying molecular mechanisms. Some patterns, such as the lines of Blaschko and Naevus, are based on cell lineage and genetic mosaicism. Other patterns, such as regionally specific skin appendages, can be set by distinct combinatorial molecular codes, which in turn may be set by morphogenetic gradients. There are also some patterns, such as the arrangement of hair follicles (hair whorls) and fingerprints, which involve genetics as well as stochastic epigenetic events based on physiochemical principles. Many appendage primordia are laid out in developmental waves. In the adult, some patterns, such as those involving cycling hair follicles, may appear as traveling waves in mice. Since skin appendages can renew themselves in regeneration, their size and shape can still change in the adult via regulation by hormones and the environment. Some lesion patterns are based on pathological changes involving the above processes and can be used as diagnostic criteria in medicine. Understanding the different mechanisms that lead to patterns in the skin will help us appreciate their full significance in morphogenesis and medical research. Much remains to be learned about complex pattern formation, if we are to bridge the gap between molecular biology and organism phenotypes.     

Mathematical modelling of tumour acidity

Acid-mediated tumour invasion is receiving increasing experimental and clinical attention. Previous models proposed to describe this phenomenon failed to capture key properties of the system, such as the existence of the benign steady state, or predicted incorrectly the size of the inter-tissue gap. Here we show that taking proper account of quiescence ameliorates these drawbacks as well as revealing novel behaviour. The simplicity of the model allows us to fully identify the key parameters controlling different aspects of behaviour.     

Enzyme kinetics at high enzyme concentration

We re-visit previous analyses of the classical Michaelis-Menten substrate-enzyme reaction and, with the aid of the reverse quasi-steady-state assumption, we challenge the approximation d[C]/dt ≈ 0 for the basic enzyme reaction at high enzyme concentration. For the first time, an approximate solution for the concentrations of the reactants uniformly valid in time is reported. Numerical simulations are presented to verify this solution. We show that an analytical approximation can be found for the reactants for each initial condition using the appropriate quasi-steady-state assumption. An advantage of the present formalism is that it provides a new procedure for fitting experimental data to determine reaction constants. Finally, a new necessary criterion is found that ensures the validity of the reverse quasi-steady-state assumption. This is verified numerically.     

Towards whole-organ modelling of tumour growth

Multiscale approaches to modelling biological phenomena are growing rapidly. We present here some recent results on the formulation of a theoretical framework which can be developed into a fully integrative model for cancer growth. The model takes account of vascular adaptation and cell-cycle dynamics. We explore the effects of spatial inhomogeneity induced by the blood flow through the vascular network and of the possible effects of p27 on the cell cycle. We show how the model may be used to investigate the efficiency of drug-delivery protocols.     

Bulletin of mathematical biology—facts,figures and comparisons

The Society for Mathematical Biology (SMB) owns the Bulletin of Mathematical Biology (BMB). This is an international journal devoted to the interface of mathematics and biology. At the 2003 SMB annual meeting in Dundee the Society asked the editor of the BMB to produce an analysis of impact factor, subject matter of papers, submission rates etc. Other members of the society were interested in the handling times of articles and wanted comparisons with other (appropriate) journals. In this article we present a brief history of the journal and report on how the journal impact factor has grown substantially in the last few years. We also present an analysis of subject areas of published papers over the past two years. We finally present data on times from receipt of paper to acceptance, acceptance to print (and to online publication) and compare these data with some other journals. This is an expanded version of a report published in the Society for Mathematical Biology Newsletter, Volume 16, Number 3, pp. 9–12, 2003. These authors contributed equally.     

Response kinetics of tethered bacteria to stepwise changes in nutrient concentration

We examined the changes in swimming behaviour of the bacterium Rhodobacter sphaeroides in response to stepwise changes in a nutrient (propionate), following the pre-stimulus motion, the initial response and the adaptation to the sustained concentration of the chemical. This was carried out by tethering motile cells by their flagella to glass slides and following the rotational behaviour of their cell bodies in response to the nutrient change. Computerised motion analysis was used to analyse the behaviour. Distributions of run and stop times were obtained from rotation data for tethered cells. Exponential and Weibull fits for these distributions, and variability in individual responses are discussed. In terms of parameters derived from the run and stop time distributions, we compare the responses to stepwise changes in the nutrient concentration and the long-term behaviour of 84 cells under 12 propionate concentration levels from 1 nM to 25 mM. We discuss traditional assumptions for the random walk approximation to bacterial swimming and compare them with the observed R. sphaeroides motile behaviour.     

A model for colour pattern formation in the butterfly wing of Papilio dardanus

The butterfly Papilio dardanus is well known for the spectacular phenotypic polymorphism in the female of the species. We show that numerical simulations of a reaction diffusion model on a geometrically accurate wing domain produce spatial patterns that are consistent with many of those observed on the butterfly. Our results suggest that the wing coloration is due to a simple underlying stripe-like pattern of some pigment-inducing morphogen. We focus on the effect of key factors such as parameter values for mode selection, threshold values which determine colour, wing shape and boundary conditions. The generality of our approach should allow us to investigate other butterfly species. The relationship between these key factors and gene activities is discussed in the context of recent biological advances.