Impaired dynamics of precapillary sphincters and pericytes at first-order capillaries predict reduced neurovascular function in the aging mouse brain.

The microvascular inflow tract, comprising the penetrating arterioles, precapillary sphincters and first-order capillaries, is the bottleneck for brain blood flow and energy supply. Exactly how aging alters the structure and function of the microvascular inflow tract remains unclear. By in vivo four-dimensional two-photon imaging, we reveal an age-dependent decrease in vaso-responsivity accompanied by a decrease in vessel density close to the arterioles and loss of vascular mural cell processes, although the number of mural cell somas and their alpha smooth muscle actin density were preserved. The age-related reduction in vascular reactivity was mostly pronounced at precapillary sphincters, highlighting their crucial role in capillary blood flow regulation. Mathematical modeling revealed impaired pressure and flow control in aged mice during vasoconstriction. Interventions that preserve dynamics of cerebral blood vessels may ameliorate age-related decreases in blood flow and prevent brain frailty.

Precapillary sphincters and pericytes at first-order capillaries as key regulators for brain capillary perfusion.

Rises in local neural activity trigger local increases of cerebral blood flow, which is essential to match local energy demands. However, the specific location of microvascular flow control is incompletely understood. Here, we used two-photon microscopy to observe brain microvasculature in vivo. Small spatial movement of a three-dimensional (3D) vasculature makes it challenging to precisely measure vessel diameter at a single x-y plane. To overcome this problem, we carried out four-dimensional (x-y-z-t) imaging of brain microvessels during exposure to vasoactive molecules in order to constrain the impact of brain movements on the recordings. We demonstrate that rises in synaptic activity, acetylcholine, nitric oxide, cyclic guanosine monophosphate, ATP-sensitive potassium channels, and endothelin-1 exert far greater effects on brain precapillary sphincters and first-order capillaries than on penetrating arterioles or downstream capillaries, but with similar kinetics. The high level of responsiveness at precapillary sphincters and first-order capillaries was matched by a higher level of α-smooth muscle actin in pericytes as compared to penetrating arterioles and downstream capillaries. Mathematical modeling based on 3D vasculature reconstruction showed that precapillary sphincters predominantly regulate capillary blood flow and pressure as compared to penetrating arterioles and downstream capillaries. Our results confirm a key role for precapillary sphincters and pericytes on first-order capillaries as sensors and effectors of endothelium- or brain-derived vascular signals.

Conceptualizing conduction as a pliant electrical response: impact of gap junctions and ion channels.

Vasomotor responses conduct among resistance arteries to coordinate blood flow delivery pursuant to energetic demand. Conduction is set by the electrical and mechanical properties of vascular cells, the former tied to how gap junctions and ion channels distribute and dissipate charge, respectively. These membrane proteins are subject to modulation; thus, conduction could be viewed as "pliant" to the current regulatory state. This study used in silico approaches to conceptualize electrical pliancy and to illustrate how gap junctional and ion channel properties distinctly impact conduction along a single skeletal muscle artery or a branching cerebrovascular network. Initial simulations revealed how vascular cells encoded with electrotonic properties best reproduced spreading behavior; the endothelium's importance as a charge source and a longitudinal conduit was readily observed. Alterations in gap junctional conductance produced unique electrical fingerprints: 1) decreased endothelial coupling impaired longitudinal but enhanced radial spread, and 2) reduced myoendothelial coupling limited radial but enhanced longitudinal spread. Subsequent simulations illustrated how tuning ion channel activity, e.g., inward rectifying- and voltage-gated K+ channels, modified charge dissipation, resting membrane potential, and the spread of the electrical phenomenon. Restricting ion channel tuning to a network subregion then revealed how electrical spread could be locally shaped in accordance with the aggregate changes in membrane resistance. In summary, our analysis frames and reimagines electrical conduction as a pliable process, with subtle regulatory changes to membrane proteins shaping network spread and tissue perfusion.NEW & NOTEWORTHY Conducted vasomotor responses depend on initiation and spread of electrical phenomena along arterial walls and their translation into contractile responses. Using computational approaches, we show how subtle but widespread regulation of gap junctions and ion channels can modulate the range and amplitude of electrical spread. Ion channels are regulated by endocrine and mechanical signals and may differ regionally in networks. Subregional electrical changes are not spatially confined but may affect electrical conduction in neighboring regions.

Conceptualizing Conduction as a Pliant Vasomotor response: Impact of Ca2+ fluxes and Ca2+ Sensitization.

Coordinating blood flow to active tissue requires vasomotor responses to conduct among resistance arteries. Vasomotor spread is governed by the electrical and mechanical properties of vessels; the latter being linked to the sigmoid relations between membrane potential (VM), [Ca2+], and smooth muscle contractility. Proteins guiding electrical-to-tone translation are subject to regulation; thus, vasomotor conduction could be viewed as "pliant" to the current regulatory state. Using simple in silico approaches, we explored vasomotor pliancy and how the regulation of contractility impacts conduction along a skeletal muscle artery and a branching cerebrovascular network. Initial simulations revealed how limited electromechanical linearity affects the translation of electrical spread into arterial tone. Subtle changes to the VM-[Ca2+] or [Ca2+]-diameter relationship, akin to regulatory alterations in Ca2+ influx and Ca2+ sensitivity, modified the distance and amplitude of the conducted vasomotor response. Simultaneous changes to both relationships, consistent with agonist stimulation, augmented conduction although the effect varied with stimulus strength and polarity (depolarization vs hyperpolarization). Final simulations using our cerebrovascular network revealed how localized changes to the VM-[Ca2+] or [Ca2+]-diameter relationships could regionally shape conduction without interfering with the electrical spread. We conclude that regulatory changes to key effector proteins (e.g. L-type Ca2+ channels, myosin light chain phosphatase), integral to voltage translation, not only impact conducted vasomotor tone but likely blood flow delivery to active tissues.

Stimulation history affects vasomotor responses in rat mesenteric arterioles.

Resistance vessels regulate blood flow by continuously adjusting activity of the wall smooth muscle cells. These cells integrate a variety of stimuli from blood, endothelium, autonomic nerves, and surrounding tissues. Each stimulus elicits an intracellular signaling cascade that eventually influences activation of the contractile machinery. The characteristic time scale of each cascade and the sharing of specific reactions between cascades provide for complex behavior when a vessel receives multiple stimuli. Here, we apply sequential stimulation with invariant concentrations of vasoconstrictor (norepinephrine/methoxamine) and vasodilator (SNAP/carbacol) to rat mesenteric vessels in the wire myograph to show that (1) time elapsed between addition of two vasoactive drugs and (2) the sequence of addition may significantly affect final force development. Furthermore, force oscillations (vasomotion) often appear upon norepinephrine administration. Using computational modeling in combination with nitric oxide (NO) inhibition/NO addition experiments, we show that (3) amplitude and number of oscillating vessels increase over time, (4) the ability of NO to induce vasomotion depends on whether it is applied before or after norepinephrine, and (5) emergence of vasomotion depends on the prior dynamical state of the system; in simulations, this phenomenon appears as "hysteresis." These findings underscore the time-dependent nature of vascular tone generation which must be considered when evaluating the vasomotor effects of multiple, simultaneous stimuli in vitro or in vivo.

Electrical Communication in Lymphangions.

Contractions of lymphangions, i.e., the segment between two one-way lymphatic valves, generate the pressure gradients that propel lymph back to the circulation. Each lymphangion is comprised of an inner sheet of lymphatic endothelial cells circumscribed by one or more layers of lymphatic muscle cells (LMCs). Each contraction is produced by an LMC action potential (AP) that propagates via gap junctions along the lymphangion. Yet, electrical coupling within and between cell layers and the impact on AP waves is poorly understood. Here, we combine studies in rat and mouse lymphatic vessels with mathematical modeling to show that initiation of AP waves depends on high input resistance (low current drain), whereas propagation depends on morphology and sufficient LMC:LMC coupling. Simulations show that 1) myoendothelial coupling is insignificant to facilitate AP generation and sustain an experimentally measured cross-junctional potential difference of 25 mV, i.e., AP waves propagate along the LMC layer only; 2) LMC:LMC resistance is estimated around 2-10 MΩ but depends on vessel structure and cell-cell coupling, e.g., some degree of LMC overlap protects AP waves against LMC decoupling; 3) the propensity of AP wave initiation is highest around the valves, where the density of LMCs is low; and 4) a single pacemaker cell embedded in the LMC layer must be able to generate very large currents to overcome the current drain from the layer. However, the required current generation to initiate an AP wave is reduced upon stimulation of multiple adjacent LMCs. With stimulation of all LMCs, AP waves can also arise from heterogeneity in the electrical activity of LMCs. The findings advance our understanding of the electrical constraints that underlie initiation of APs in the LMC layer and make testable predictions about how morphology, LMC excitability, and LMC:LMC electrical coupling interact to determine the ability to initiate and propagate AP waves in small lymphatic vessels.

A generative modeling approach to connectivity-Electrical conduction in vascular networks.

The physiology of biological structures is inherently dynamic and emerges from the interaction and assembly of large collections of small entities. The extent of coupled entities complicates modeling and increases computational load. Here, microvascular networks are used to present a novel generative approach to connectivity based on the observation that biological organization is hierarchical and composed of a limited set of building blocks, i.e. a vascular network consists of blood vessels which in turn are composed by one or more cell types. Fast electrical communication is crucial to synchronize vessel tone across the vast distances within a network. We hypothesize that electrical conduction capacity is delimited by the size of vascular structures and connectivity of the network. Generation and simulation of series of dynamical models of electrical spread within vascular networks of different size and composition showed that (1) Conduction is enhanced in models harboring long and thin endothelial cells that couple preferentially along the longitudinal axis. (2) Conduction across a branch point depends on endothelial connectivity between branches. (3) Low connectivity sub-networks are more sensitive to electrical perturbations. In summary, the capacity for electrical signaling in microvascular networks is strongly shaped by the morphology and connectivity of vascular (particularly endothelial) cells. While the presented software can be used by itself or as a starting point for more sophisticated models of vascular dynamics, the generative approach can be applied to other biological systems, e.g. nervous tissue, the lymphatics, or the biliary system.

Cyanohydrin reactions enhance glycolytic oscillations in yeast.

Synchronous metabolic oscillations can be induced in yeast by addition of glucose and removal of extracellular acetaldehyde (ACAx). Compared to other means of ACAx removal, cyanide robustly induces oscillations, indicating additional cyanide reactions besides ACA to lactonitrile conversion. Here, (13)C NMR is used to confirm our previous hypothesis, that cyanide directly affects glycolytic fluxes through reaction with carbonyl-containing compounds. Intracellularly, at least 3 cyanohydrins were identified. Extracellularly, all signals could be identified and lactonitrile was found to account for ~66% of total cyanide removal. Simulations of our updated computational model show that intracellular cyanide reactions increase the amplitude of oscillations and that cyanide addition lowers [ACA] instantaneously. We conclude that cyanide provides the following means of inducing global oscillations: a) by reducing [ACAx] relative to oscillation amplitude, b) by targeting multiple intracellular carbonyl compounds during fermentation, and c) by acting as a phase resetting stimulus.

Origins of variation in conducted vasomotor responses.

Regulation of blood flow in the microcirculation depends on synchronized vasomotor responses. The vascular conducted response is a synchronous dilatation or constriction, elicited by a local electrical event that spreads along the vessel wall. Despite the underlying electrical nature, however, the efficacy of conducted responses varies significantly between different initiating stimuli within the same vascular bed as well as between different vascular beds following the same stimulus. The differences have stimulated proposals of different mechanisms to account for the experimentally observed variation. Using a computational approach that allows for introduction of structural and electrophysiological heterogeneity, we systematically tested variations in both arteriolar electrophysiology and modes of stimuli. Within the same vessel, our simulations show that conduction efficacy is influenced by the type of cell being stimulated and, in case of depolarization, by the stimulation strength. Particularly, simultaneous stimulation of both endothelial and vascular smooth muscle cells augments conduction. Between vessels, the specific electrophysiology determines membrane resistance and conduction efficiency-notably depolarization or radial currents reduce electrical spread. Random cell-cell variation, ubiquitous in biological systems, only cause small or no reduction in conduction efficiency. Collectively, our simulations can explain why CVRs from hyperpolarizing stimuli tend to conduct longer than CVRs from depolarizing stimuli and why agonists like acetylcholine induce CVRs that tend to conduct longer than electrical injections. The findings demonstrate that although substantial heterogeneity is observed in conducted responses, it can be largely ascribed to the origin of electrical stimulus combined with the specific electrophysiological properties of the arteriole. We conclude by outlining a set of "principles of electrical conduction" in the microcirculation.

Gap junctions suppress electrical but not [Ca(2+)] heterogeneity in resistance arteries.

Despite stochastic variation in the molecular composition and morphology of individual smooth muscle and endothelial cells, the membrane potential along intact microvessels is remarkably uniform. This is crucial for coordinated vasomotor responses. To investigate how this electrical homogeneity arises, a virtual arteriole was developed that introduces variation in the activities of ion-transport proteins between cells. By varying the level of heterogeneity and subpopulations of gap junctions (GJs), the resulting simulations shows that GJs suppress electrical variation but can only reduce cytosolic [Ca(2+)] variation. The process of electrical smoothing, however, introduces an energetic cost due to permanent currents, one which is proportional to the level of heterogeneity. This cost is particularly large when electrochemically different endothelial-cell and smooth-muscle-cell layers are coupled. Collectively, we show that homocellular GJs in a passively open state are crucial for electrical uniformity within the given cell layer, but homogenization may be limited by biophysical or energetic constraints. Owing to the ubiquitous presence of ion transport-proteins and cell-cell heterogeneity in biological tissues, these findings generalize across most biological fields.

Less is more: minimal expression of myoendothelial gap junctions optimizes cell-cell communication in virtual arterioles.

Dysfunctional electrical signalling within the arteriolar wall is a major cause of cardiovascular disease. The endothelial cell layer constitutes the primary electrical pathway, co-ordinating contraction of the overlying smooth muscle cell (SMC) layer. As myoendothelial gap junctions (MEGJs) provide direct contact between the cell layers, proper vasomotor responses are thought to depend on a high, uniform MEGJ density. However, MEGJs are observed to be expressed heterogeneously within and among vascular beds. This discrepancy is addressed in the present study. As no direct measures of MEGJ conductance exist, we employed a computational modelling approach to vary the number, conductance and distribution of MEGJs. Our simulations demonstrate that a minimal number of randomly distributed MEGJs augment arteriolar cell-cell communication by increasing conduction efficiency and ensuring appropriate membrane potential responses in SMCs. We show that electrical coupling between SMCs must be tailored to the particular MEGJ distribution. Finally, observation of non-decaying mechanical conduction in arterioles without regeneration has been a long-standing controversy in the microvascular field. As heterogeneous MEGJ distributions provide for different conduction profiles along the cell layers, we demonstrate that a non-decaying conduction profile is possible in the SMC layer of a vessel with passive electrical properties. These intriguing findings redefine the concept of efficient electrical communication in the microcirculation, illustrating how heterogeneous properties, ubiquitous in biological systems, may have a profound impact on system behaviour and how acute local and global flow control is explained from the biophysical foundations.

Programming strategy for efficient modeling of dynamics in a population of heterogeneous cells.

MOTIVATION: Heterogeneity is a ubiquitous property of biological systems. Even in a genetically identical population of a single cell type, cell-to-cell differences are observed. Although the functional behavior of a given population is generally robust, the consequences of heterogeneity are fairly unpredictable. In heterogeneous populations, synchronization of events becomes a cardinal problem-particularly for phase coherence in oscillating systems. RESULTS: The present article presents a novel strategy for construction of large-scale simulation programs of heterogeneous biological entities. The strategy is designed to be tractable, to handle heterogeneity and to handle computational cost issues simultaneously, primarily by writing a generator of the 'model to be simulated'. We apply the strategy to model glycolytic oscillations among thousands of yeast cells coupled through the extracellular medium. The usefulness is illustrated through (i) benchmarking, showing an almost linear relationship between model size and run time, and (ii) analysis of the resulting simulations, showing that contrary to the experimental situation, synchronous oscillations are surprisingly hard to achieve, underpinning the need for tools to study heterogeneity. Thus, we present an efficient strategy to model the biological heterogeneity, neglected by ordinary mean-field models. This tool is well posed to facilitate the elucidation of the physiologically vital problem of synchronization. AVAILABILITY: The complete python code is available as Supplementary Information. CONTACT: bjornhald@gmail.com or pgs@kiku.dk SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Applicability of cable theory to vascular conducted responses.

Conduction processes in the vasculature have traditionally been described using cable theory, i.e., locally induced signals decaying passively along the arteriolar wall. The decay is typically quantified using the steady-state length-constant, λ, derived from cable theory. However, the applicability of cable theory to blood vessels depends on assumptions that are not necessarily fulfilled in small arteries and arterioles. We have employed a morphologically and electrophysiologically detailed mathematical model of a rat mesenteric arteriole to investigate if the assumptions hold and whether λ adequately describes simulated conduction profiles. We find that several important cable theory assumptions are violated when applied to small blood vessels. However, the phenomenological use of a length-constant from a single exponential function is a good measure of conduction length. Hence, λ should be interpreted as a descriptive measure and not in light of cable theory. Determination of λ using cable theory assumes steady-state conditions. In contrast, using the model it is possible to probe how conduction behaves before steady state is achieved. As ion channels have time-dependent activation and inactivation, the conduction profile changes considerably during this dynamic period with an initially longer spread of current. This may have implications in relation to explaining why different agonists have different conduction properties. Also, it illustrates the necessity of using and developing models that handle the nonlinearity of ion channels.

BKCa and KV channels limit conducted vasomotor responses in rat mesenteric terminal arterioles.

Intracellular Ca(2+) signals underlying conducted vasoconstriction to local application of a brief depolarizing KCl stimulus was investigated in rat mesenteric terminal arterioles (<40 µm). Using a computer model of an arteriole segment comprised of coupled endothelial cells (EC) and vascular smooth muscle cells (VSMC) simulations of both membrane potential and intracellular [Ca(2+)] were performed. The "characteristic" length constant, λ, was approximated using a modified cable equation in both experiments and simulations. We hypothesized that K(+) conductance in the arteriolar wall limit the electrotonic spread of a local depolarization along arterioles by current dissipation across the VSMC plasma membrane. Thus, we anticipated an increased λ by inhibition of voltage-activated K(+) channels. Application of the BK(Ca) channel blocker iberiotoxin (100 nM) onto mesenteric arterioles in vitro and inhibition of BK(Ca) channel current in silico increased λ by 34% and 32%, respectively. Similarly, inhibition of K(V) channels in vitro (4-aminopyridine, 1 mM) or in silico increased λ by 41% and 21%, respectively. Immunofluorescence microscopy demonstrated expression of BK(Ca), Kv1.5, Kv2.1, but not Kv1.2, in VSMCs of rat mesenteric terminal arterioles. Our results demonstrate that inhibition of voltage-activated K(+) channels enhance vascular-conducted responses to local depolarization in terminal arterioles by increasing the membrane resistance of VSMCs. These data contribute to our understanding of how differential expression patterns of voltage-activated K(+) channels may influence conducted vasoconstriction in small arteriolar networks. This finding is potentially relevant to understanding the compromised microcirculatory blood flow in systemic vascular diseases such as diabetes mellitus and hypertension.

Modeling diauxic glycolytic oscillations in yeast.

Glycolytic oscillations in a stirred suspension of starved yeast cells is an excellent model system for studying the dynamics of metabolic switching in living systems. In an open-flow system the oscillations can be maintained indefinitely at a constant operating point where they can be characterized quantitatively by experimental quenching and bifurcation analysis. In this article, we use these methods to show that the dynamics of oscillations in a closed system is a simple transient version of the open-system dynamics. Thus, easy-setup closed-system experiments are also useful for investigations of central metabolism dynamics of yeast cells. We have previously proposed a model for the open system comprised of the primary fermentative reactions in yeast that quantitatively describes the oscillatory dynamics. However, this model fails to describe the transient behavior of metabolic switching in a closed-system experiment by feeding the yeast suspension with a glucose pulse-notably the initial NADH spike and final NADH rise. Another object of this study is to gain insight into the secondary low-flux metabolic pathways by feeding starved yeast cells with various metabolites. Experimental and computational results strongly suggest that regulation of acetaldehyde explains the observed behavior. We have extended the original model with regulation of pyruvate decarboxylase, a reversible alcohol dehydrogenase, and drainage of pyruvate. Using the method of time rescaling in the extended model, the description of the transient closed-system experiments is significantly improved.