Confinement Regulates Complex Biochemical Networks: Initiation of Blood Clotting by “Diffusion Acting”

This study shows that environmental confinement strongly affects the activation of nonlinear reaction networks, such as blood coagulation (clotting), by small quantities of activators. Blood coagulation is sensitive to the local concentration of soluble activators, initiating only when the activators surpass a threshold concentration, and therefore is regulated by mass transport phenomena such as flow and diffusion. Here, diffusion was limited by decreasing the size of microfluidic chambers, and it was found that microparticles carrying either the classical stimulus, tissue factor, or a bacterial stimulus, Bacillus cereus, initiated coagulation of human platelet-poor plasma only when confined. A simple analytical argument and numerical model were used to describe the mechanism for this phenomenon: confinement causes diffusible activators to accumulate locally and surpass the threshold concentration. To interpret the results, a dimensionless confinement number, Cn, was used to describe whether a stimulus was confined, and a Damköhler number, Da₂, was used to describe whether a subthreshold stimulus could initiate coagulation. In the context of initiation of coagulation by bacteria, this mechanism can be thought of as “diffusion acting”, which is distinct from “diffusion sensing”. The ability of confinement and diffusion acting to change the outcome of coagulation suggests that confinement should also regulate other biological “on” and “off” processes that are controlled by thresholds.     

Rate of mixing controls rate and outcome of autocatalytic processes: theory and microfluidic experiments with chemical reactions and blood coagulation

This article demonstrates that the rate of mixing can regulate the rate and outcome of both biological and nonbiological autocatalytic reaction systems that display a threshold response to the concentration of an activator. Plug-based microfluidics was used to control the timing of reactions, the rate of mixing, and surface chemistry in blood clotting and its chemical model. Initiation of clotting of human blood plasma required addition of a critical concentration of thrombin. Clotting could be prevented by rapid mixing when thrombin was added near the critical concentration, and mixing also affected the rate of clotting when thrombin was added at concentrations far above the critical concentration in two clinical clotting assays for human plasma. This phenomenon was modeled by a simple mechanism—local and global competition between the clotting reaction, which autocatalytically produces an activator, and mixing, which removes the activator. Numerical simulations showed that the Damköhler number, which describes this competition, predicts the effects of mixing. Many biological systems are controlled by thresholds, and these results shed light on the dynamics of these systems in the presence of spatial heterogeneities and provide simple guidelines for designing and interpreting experiments with such systems.     

Long-term persistence of species and the SLOSS problem

The single large or several small (SLOSS) problem has been addressed in a large number of empirical and theoretical studies, but no coherent conclusion has yet been reached. Here I study the SLOSS problem in the context of metapopulation dynamics. I assume that there is a fixed total amount A(0) of habitat available, and I derive formulas for the optimal number n and area A of habitat patches, where n=A(0)/A. I consider optimality in two ways. First, I attempt to maximize the time to metapopulation extinction, which is a relevant measure for metapopulation viability for rare and threatened species. Second, I attempt to maximize the metapopulation capacity of the habitat patch network, which corresponds both with maximizing the distance to the deterministic extinction threshold and with maximizing the fraction of occupied patches. I show that in the typical case, a small number of large patches maximizes the metapopulation capacity, while an intermediate number of habitat patches maximizes the time to extinction. The main conclusion stemming from the analysis is that the optimal number of patches is largely affected by the relationship between habitat patch area and rates of immigration, emigration and local extinction. Here this relationship is summarized by a single factor zeta, termed the patch area scaling factor.     

Evaluating empirical scaling relations of pattern metrics with simulated landscapes

Landscape patterns demonstrate scale-dependent properties that have been parsimoniously described by empirical scaling functions. These functions, derived from multiple-scale analysis of real landscapes, are evaluated here for their generality and robustness via a series of simulated landscapes with known landscape patterns. A factorial design was used to generate these landscapes, varying the number of classes, class abundance distribution, and patch dispersion. The results confirm that the three types of scaling relations were both general and robust. Type I metrics were predictable with simple scaling functions (e.g. power laws or linear functions); Type II metrics showed stair-case like response patterns and were essentially not predictable; Type III metrics exhibited erratic response patterns that were unpredictable in most cases. However, significant differences were found between real and simulated landscapes when landscape extent was increased. Systematic changes in grain size show that the predictability of scaling relations increases with the number of classes, the evenness of class abundance distribution, and the aggregation of patch dispersion. However, random patch dispersion seemed to enhance the predictability of scaling relations when changing spatial extent.     

Immigration of olfactory searching insects into host plant patches: testing scaling rules for olfactory information

Herbivorous insects are commonly faced with host plants being distributed in scattered patches across a landscape. Immigration rates into habitat patches may strongly depend on the sensory cues used in the patch location process, and immigration rates of insects can be predicted based on the scaling of sensory cues. Here, we tested recent estimates of the scaling of olfactory information to patch size, which predicts a scaling coefficient ζ ≈ ?0.5 (A ^ζ , where A = patch size, ζ = scaling coefficient). We predicted that immigration rates of olfactory searching insects into patches of different sizes should scale according to the estimated slope. We investigated attraction of the weevils Cionus tuberculosus and Cionus scrophulariae to odors from figwort Scrophularia nodosa and quantified immigration rates of weevils into differently sized patches. We also investigated oviposition rates of the sawfly Tenthredo scrophulariae. The slope in the regression between density and patch size for herbivores was then compared with the predicted scaling coefficient. Using olfactometers, we found that weevils were attracted to figwort odors. Weevil densities were significantly affected by patch size, and the slope in the relationship between density and patch size was ζ = ?0.53. The slope in the relationship between larval densities of sawflies and patch size was less negative with a slope of ζ = ?0.15, indicating differences in search behavior compared with the weevils. The density–patch size relationship for the weevils closely matched the predicted slope and supported the previous estimations of the scaling of olfactory information to patch size.     

The review of contemporary ideas about the influence of flow rate on blood clotting

Normal blood clotting is vitally important for mammals. The diffusion-convection transfer of clotting factors plays a key role in blood clot formation. Since the shear rates of blood flow are very high (up to 7000 s⁻¹), clot formation critically depends on the flow rate. The methods of study of the flow effect on clotting are indirect and the processes are rather complex; therefore, mathematical models of this process are significant for interpretation of results and understanding of the mechanisms. The review expounds the main experimental data on the effect of flow on the blood clotting cascade, some hypotheses and mathematical models explaining different regimes of the functioning of this system. The review is focused on specific problems encountered by researchers in this field. Some of the experimental works have shown that flow decreases the size of the formed fibrin clot and that the dependence of clot formation period on the flow shear rate is a threshold function. However, there are also experimental evidence that the flow can increase production of clotting factors (factor Xa), which must be expressed in the procoagulant action of the flow. Mathematical models of different aspects of clotting give no unified predictions either. Nevertheless, the combined analysis of results of detailed modeling and experiments, in our opinion, may result in understanding of the mechanisms, which determine the behavior of clotting in a flow.     

The limiting behaviour of a mainland-island metapopulation

Stochastic patch occupancy models (SPOMs) are a class of discrete time Markov chains used to model the presence/absence of a population in a collection of habitat patches. This class of model is popular with ecologists due to its ability to incorporate important factors of the habitat patch network such as connectivity and distance between patches as well as heterogeneity in patch characteristics. We present an asymptotic examination of a simple type of SPOM called the mainland-island model. In this model a single patch called the mainland is connected to a large number of smaller patches called islands and each island is only connected to the mainland. We discuss the limiting behaviour of the SPOM as the number of islands increases and the size of the islands decrease relative to the mainland. We demonstrate that a variety of limiting behaviours is possible depending on the scaling of the island size and on the heterogeneity of habitat quality.     

The effect of viewing eccentricity on enumeration

Visual acuity and contrast sensitivity progressively diminish with increasing viewing eccentricity. Here we evaluated how visual enumeration is affected by visual eccentricity, and whether subitizing capacity, the accurate enumeration of a small number (～3) of items, decreases with more eccentric viewing. Participants enumerated gratings whose (1) stimulus size was constant across eccentricity, and (2) whose stimulus size scaled by a cortical magnification factor across eccentricity. While we found that enumeration accuracy and precision decreased with increasing eccentricity, cortical magnification scaling of size neutralized the deleterious effects of increasing eccentricity. We found that size scaling did not affect subitizing capacities, which were nearly constant across all eccentricities. We also found that size scaling modulated the variation coefficients, a normalized metric of enumeration precision, defined as the standard deviation divided by the mean response. Our results show that the inaccuracy and imprecision associated with increasing viewing eccentricity is due to limitations in spatial resolution. Moreover, our results also support the notion that the precise number system is restricted to small numerosities (represented by the subitizing limit), while the approximate number system extends across both small and large numerosities (indexed by variation coefficients) at large eccentricities.     

Allometric density responses in butterflies: the response to small and large patches by small and large species

Species are differentially affected by habitat fragmentation as a consequence of differences in mobility, area requirements, use of the matrix, and responses to edges. A quantitative understanding of these differences is essential not only for conservation biology but also for basic ecological theory. Here, we examine density responses by butterflies to patch size and use a quantitative theory on the scaling of population density with patch size to interpret results. Theory suggests that the density distribution of mobile species along a patch size gradient should depend on the scaling of net migration rates, whereas the density distribution of less mobile species should depend more on local growth. Using data from 11 localities in three European countries, we calculated the slope in the relationship between patch size and population density. These slopes were evaluated in relation to butterfly traits and matrix composition. As estimates of butterfly mobility we used both wing span and expert mobility rankings. The slope of the density–area relationship changed as predicted with wing span and the association of species to grasslands. Large and highly mobile species had a negative slope, similarly for grassland specialists and generalist species, and the slope matched quantitative predictions based on the scaling of net migration rates. Small and less mobile grassland specialists had a slope that was less negative than the slope of large and mobile grassland specialists, whereas the slope did not change with size for generalist species. These analyses suggest that the variability in response among butterfly species to patch size could be explained by accounting for body size/mobility and habitat associations among species. A caveat is that edge effects are not explicitly included in the model analysis, and future research should aim to combine area and edge effects in a common theoretical framework.     

Dimensional analysis of nerve models

General equations for (i) a uniform patch of nerve membrane, (ii) a continuous (unmyelinated) axon and (iii) a noded (myelinated) axon are analyzed using dimensional analysis. The original dimensioned equations are transformed to dimensionless equations. These equations contain dimensionless constants called similarity parameters which are functions of the physical constants or parameters of the system. (The similarity parameters are analogous to such quantities as the Reynolds number and Mach number used in fluid dynamics.) There is one similarity parameter for each of cases (i) and (ii), and four for case (iii). All dimensioned systems having the same values of all the similarity parameters form a similarity class.Once a quantity such as threshold stimulus or conduction velocity is computed for one member of any similarity class, the same quantity can be easily computed for any other member of the same class, by a simple formula containing the physical constants of the system, called a generating equation, or by an even simpler expression of proportionality, called a scaling relation.     

Integration of Acoustic Radiation Force and Optical Imaging for Blood Plasma Clot Stiffness Measurement

Despite the life-preserving function blood clotting serves in the body, inadequate or excessive blood clot stiffness has been associated with life-threatening diseases such as stroke, hemorrhage, and heart attack. The relationship between blood clot stiffness and vascular diseases underscores the importance of quantifying the magnitude and kinetics of blood’s transformation from a fluid to a viscoelastic solid. To measure blood plasma clot stiffness, we have developed a method that uses ultrasound acoustic radiation force (ARF) to induce micron-scaled displacements (1-500 μm) on microbeads suspended in blood plasma. The displacements were detected by optical microscopy and took place within a micro-liter sized clot region formed within a larger volume (2 mL sample) to minimize container surface effects. Modulation of the ultrasound generated acoustic radiation force allowed stiffness measurements to be made in blood plasma from before its gel point to the stage where it was a fully developed viscoelastic solid. A 0.5 wt % agarose hydrogel was 9.8-fold stiffer than the plasma (platelet-rich) clot at 1 h post-kaolin stimulus. The acoustic radiation force microbead method was sensitive to the presence of platelets and strength of coagulation stimulus. Platelet depletion reduced clot stiffness 6.9 fold relative to platelet rich plasma. The sensitivity of acoustic radiation force based stiffness assessment may allow for studying platelet regulation of both incipient and mature clot mechanical properties.     

How insects sense olfactory patches – the spatial scaling of olfactory information

When searching for resources in heterogeneous environments, animals must rely on their abilities to detect the resources via their sensory systems. However, variation in the strength of the sensory cue may be mediated by the physical size of the resource patch. Patch detection of insects are often predicted by the scaling of sensory cues to patch size, where visual cues has been proposed to scale proportional to the diameter of the patch. The scaling properties of olfactory cues are, however, virtually unknown. Here, we investigated scaling rules for olfactory information in a gradient of numbers of odour sources, relevant to odour‐mediated attraction under field conditions. We recorded moth antennal responses to sex pheromones downwind from pheromone patches and estimated the slope in the scaling relationship between the effective length of the odour plumes and the number of odour sources. These measurements showed that the effective plume length increased proportional to the square root of the number of odour sources. The scaling relationship, as estimated in the field experiment, was then evaluated against field data of the slope in the relationship between trap catch and release rate of chemical attractants for a wide range of insects. This meta‐analysis revealed an average slope largely consistent with the estimated scaling relationship between the effective plume length and the number of odour sources. This study is the first to estimate the scaling properties of olfactory cues empirically and has implications for understanding and predicting the spatial distributions of insects searching by means of olfactory cues in heterogeneous environments.     

Positive feedback loops for factor V and factor VII activation supply sensitivity to local surface tissue factor density during blood coagulation

Blood coagulation is triggered not only by surface tissue factor (TF) density but also by surface TF distribution. We investigated recognition of surface TF distribution patterns during blood coagulation and identified the underlying molecular mechanisms. For these investigations, we employed 1), an in vitro reaction-diffusion experimental model of coagulation; and 2), numerical simulations using a mathematical model of coagulation in a three-dimensional space. When TF was uniformly immobilized over the activating surface, the clotting initiation time in normal plasma increased from 4 min to >120 min, with a decrease in TF density from 100 to 0.7 pmol/m². In contrast, surface-immobilized fibroblasts initiated clotting within 3–7 min, independently of fibroblast quantity and despite a change in average surface TF density from 0.5 to 130 pmol/m². Experiments using factor V-, VII-, and VIII-deficient plasma and computer simulations demonstrated that different responses to these two TF distributions are caused by two positive feedback loops in the blood coagulation network: activation of the TF–VII complex by factor Xa, and activation of factor V by thrombin. This finding suggests a new role for these reactions: to supply sensitivity to local TF density during blood coagulation.     

Platelets promote coagulation factor XII-mediated proteolytic cascade systems in plasma

Blood coagulation factor XII (FXII, Hageman factor) is a plasma serine protease which is autoactivated following contact with negatively charged surfaces in a reaction involving plasma kallikrein and high-molecular-weight kininogen (contact phase activation). Active FXII has the ability to initiate blood clotting via the intrinsic pathway of coagulation and inflammatory reactions via the kallikrein-kinin system. Here we have determined FXII-mediated bradykinin formation and clotting in plasma. Western blotting analysis with specific antibodies against various parts of the contact factors revealed that limited activation of FXII is sufficient to promote plasma kallikrein activation, resulting in the conversion of high-molecular-weight kininogen and bradykinin generation. The presence of platelets significantly promoted FXII-initiated bradykinin formation. Similarly, in vitro clotting assays revealed that platelets critically promoted FXII-driven thrombin and fibrin formation. In summary, our data suggest that FXII-initiated protease cascades may proceed on platelet surfaces, with implications for inflammation and clotting.     

Allometric plasticity in a polyphenic beetle

Abstract 1. Environmental conditions, such as variation in nutrition, commonly contribute to morphological variation among individuals by affecting body size and the expression of certain morphological traits; however the scaling relationship between a morphological trait and body size over a range of body sizes is generally assumed not to change in response to environmental fluctuation (allometric plasticity), but instead to be constant and diagnostic for a particular trait and species or population. The work reported here examined diet‐induced allometric plasticity in the polyphenic beetle Onthophagus taurus Schreber (1759) (Coleoptera: Scarabaeidae). 2. Male O. taurus vary in body size depending on larval nutrition. Only males above a critical body size threshold express fully developed horns; males smaller than this threshold develop only rudimentary horns or no horns at all. 3. Field populations that naturally utilise two different resources for feeding larvae (horse dung vs. cow manure) exhibited significant differences in the average scaling relationship between body size and male horn length over the same range of body sizes. Males collected from cow manure populations expressed consistently longer horns for a given body size than males collected from horse dung populations. 4. Males reared in the laboratory on horse dung or cow manure also exhibited significant differences in the average scaling relationship between body size and horn length. Differences between laboratory populations reared on horse dung or cow manure were of the same kind and magnitude as differences between field populations that utilise these different resources naturally. 5. These findings suggest that between‐population differences in scaling relationships between horn length and body size can be the product of differences in the quality of resources available to developing larvae. Results are discussed in the context of onthophagine mating systems and recent insights in the developmental and endocrine control of horn polyphenisms.     

How it all starts: Initiation of the clotting cascade

Abstract

The plasma coagulation system in mammalian blood consists of a cascade of enzyme activation events in which serine proteases activate the proteins (proenzymes and procofactors) in the next step of the cascade via limited proteolysis. The ultimate outcome is the polymerization of fibrin and the activation of platelets, leading to a blood clot. This process is protective, as it prevents excessive blood loss following injury (normal hemostasis). Unfortunately, the blood clotting system can also lead to unwanted blood clots inside blood vessels (pathologic thrombosis), which is a leading cause of disability and death in the developed world. There are two main mechanisms for triggering the blood clotting, termed the tissue factor pathway and the contact pathway. Only one of these pathways (the tissue factor pathway) functions in normal hemostasis. Both pathways, however, are thought to contribute to thrombosis. An emerging concept is that the contact pathway functions in host pathogen defenses. This review focuses on how the initiation phase of the blood clotting cascade is regulated in both pathways, with a discussion of the contributions of these pathways to hemostasis versus thrombosis.     

The role of membrane patch size and flow in regulating a proteolytic feedback threshold on a membrane: possible application in blood coagulation

Positive feedback controls in proteolytic systems are characterized by thresholds which are regulated by the concentration of the initial stimulus and the kinetic parameters for enzyme generation and inhibition. Significant complexity is added when a positive feedback is localized on a membrane in contact with a flowing medium, such as seen in the early steps of blood coagulation. A partial differential equation model of an archetypal feedback loop is examined in which a proteolytic enzyme catalyzes its own formation from a zymogen on a membrane in contact with a flowing medium. As predicted from prior solution-phase and membrane-phase analyses, the threshold conditions for activation of the system are regulated by the kinetics of enzyme generation and inhibition and by the density of reactant-binding sites on the membrane; but the present analysis also establishes how the feedback threshold is controlled by the flow rate of the adjacent medium and the physical size of the membrane patch on which the feedback loop is localized. For given systems of particular kinetic properties, lower flow rates or larger active patches of membrane can result in the activation threshold being exceeded, whereas higher flow rates or smaller membrane patches can prevent initiation. In addition to numerical simulation, a simplified non-flowing model is analyzed to formulate an approximate mathematical statement of the dependence of the minimum activatable patch size on the kinetic and other parameters.     

Factor XIII-dependent generation of 5th complement component(C5)-derived monocyte chemotactic factor coinciding with plasma clotting.

Blood coagulation or plasma clotting caused generation of a monocyte chemotactic factor(s) in vitro. The chemotactic factor, of which the apparent molecular mass was 75 kDa, shared antigenicity with complement C5 and possessed the affinity to monocytes, but not to polymorphonuclear leukocytes. The generation of the chemotactic factor was hindered in the presence of a thiol enzyme inhibitor, p-chloromercuriphenyl sulfonic acid, at the concentration of 1 mmol/l, although the gelation of plasma was apparently completed. Furthermore, the generation of chemotactic factor was not observed when a plasma deficient in blood coagulation factor XIII, which is a precursor of a thiol enzyme, plasma transglutaminase, was used; and the activity normally appeared when the deficient plasma was reconstituted with purified factor XIII or with a tissue transglutaminase prior to clotting. When the human sera were injected into guinea pig skin, the serum derived from normal plasma or from the reconstituted factor XIII deficient one caused mononuclear cell infiltration, however, the serum from the deficient plasma without reconstitution infiltrated to a significantly smaller extent. These results indicated that the complement system was initiated somehow during the clotting process resulting in the generation of the C5-derived monocyte chemotactic factor in cooperation with factor XIIIa (activated factor XIII).     

Transient dynamics in metapopulation response to perturbation

Transient time in population dynamics refers to the time it takes for a population to return to population-dynamic equilibrium (or close to it) following a perturbation in the environment or in population size. Depending on the direction of the perturbation, transient time may either denote the time until extinction (or until the population has decreased to a lower equilibrium level), or the recovery time needed to reach a higher equilibrium level. In the metapopulation context, the length of the transient time is set by the interplay between population dynamics and landscape structure. Assuming a spatially realistic metapopulation model, we show that transient time is a product of four factors: the strength of the perturbation, the ratio between the metapopulation capacity of the landscape and a threshold value determined by the properties of the species, and the characteristic turnover rate of the species, adjusted by a factor depending on the structure of the habitat patch network. Transient time is longest following a large perturbation, for a species which is close to the threshold for persistence, for a species with slow turnover, and in a habitat patch network consisting of only a few dynamically important patches. We demonstrate that the essential behaviour of the n-dimensional spatially realistic Levins model is captured by the one-dimensional Levins model with appropriate parameter transformations.     

Scaling of differentiation in networks: nervous systems,organisms, ant colonies,ecosystems, businesses,universities, cities,electronic circuits,and Legos

Nodes in networks are often of different types, and in this sense networks are differentiated. Here we examine the relationship between network differentiation and network size in networks under economic or natural selective pressure, such as electronic circuits (networks of electronic components), Legos (networks of Lego pieces), businesses (networks of employees), universities (networks of faculty), organisms (networks of cells), ant colonies (networks of ants), and nervous systems (networks of neurons). For each of these we find that (i) differentiation increases with network size, and (ii) the relationship is consistent with a power law. These results are explained by a hypothesis that, because nodes are costly to build and maintain in such "selected networks", network size is optimized, and from this the power-law relationship may be derived. The scaling exponent depends on the particular kind of network, and is determined by the degree to which nodes are used in a combinatorial fashion to carry out network-level functions. We find that networks under natural selection (organisms, ant colonies, and nervous systems) have much higher combinatorial abilities than the networks for which human ingenuity is involved (electronic circuits, Legos, businesses, and universities). A distinct but related optimization hypothesis may be used to explain scaling of differentiation in competitive networks (networks where the nodes themselves, rather than the entire network, are under selective pressure) such as ecosystems (networks of organisms).