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

The conducted vascular response as a mediator of hypercapnic cerebrovascular reactivity: A modelling study

It is well established that the cerebral blood flow (CBF) shows exquisite sensitivity to changes in the arterial blood partial pressure of CO2 ( [Formula: see text] ), which is reflected by an index termed cerebrovascular reactivity. In response to elevations in [Formula: see text] (hypercapnia), the vessels of the cerebral microvasculature dilate, thereby decreasing the vascular resistance and increasing CBF. Due to the challenges of access, scale and complexity encountered when studying the microvasculature, however, the mechanisms behind cerebrovascular reactivity are not fully understood. Experiments have previously established that the cholinergic release of the Acetylcholine (ACh) neurotransmitter in the cortex is a prerequisite for the hypercapnic response. It is also known that ACh functions as an endothelial-dependent agonist, in which the local administration of ACh elicits local hyperpolarization in the vascular wall; this hyperpolarization signal is then propagated upstream the vascular network through the endothelial layer and is coupled to a vasodilatory response in the vascular smooth muscle (VSM) layer in what is known as the conducted vascular response (CVR). Finally, experimental data indicate that the hypercapnic response is more strongly correlated with the CO2 levels in the tissue than in the arterioles. Accordingly, we hypothesize that the CVR, evoked by increases in local tissue CO2 levels and a subsequent local release of ACh, is responsible for the CBF increase observed in response to elevations in [Formula: see text] . By constructing physiologically grounded dynamic models of CBF and control in the cerebral vasculature, ones that integrate the available knowledge and experimental data, we build a new model of the series of signalling events and pathways underpinning the hypercapnic response, and use the model to provide compelling evidence that corroborates the aforementioned hypothesis. If the CVR indeed acts as a mediator of the hypercapnic response, the proposed mechanism would provide an important addition to our understanding of the repertoire of metabolic feedback mechanisms possessed by the brain and would motivate further in-vivo investigation. We also model the interaction of the hypercapnic response with dynamic cerebral autoregulation (dCA), the collection of mechanisms that the brain possesses to maintain near constant CBF despite perturbations in pressure, and show how the dCA mechanisms, which otherwise tend to be overlooked when analysing experimental results of cerebrovascular reactivity, could play a significant role in shaping the CBF response to elevations in [Formula: see text] . Such in-silico models can be used in tandem with in-vivo experiments to expand our understanding of cerebrovascular diseases, which continue to be among the leading causes of morbidity and mortality in humans.

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.

A stepwise approach to resolving small ionic currents in vascular tissue

Arterial membrane potential (V_m) is set by an active interplay among ion channels whose principal function is to set contractility through the gating of voltage-operated Ca²⁺ channels. To garner an understanding of this electrical parameter, the activity of each channel must be established under near-physiological conditions, a significant challenge given their small magnitude. The inward rectifying K⁺ (K_IR) channel is illustrative of the problem, as its outward "physiological" component is almost undetectable. This study describes a stepwise approach to dissect small ionic currents at physiological V_m using endothelial and smooth muscle cells freshly isolated from rat cerebral arteries. We highlight three critical steps, beginning with the voltage clamping of vascular cells bathed in physiological solutions while maintaining a giga-ohm seal. K_IR channels are then inhibited (micromolar Ba²⁺) so that a difference current can be created, once Ba²⁺ traces are corrected for the changing seal resistance and subtle instrument drift, pulling the reversal potential rightward. The latter is a new procedure and entails the alignment of whole cell current traces at a voltage where K_IR is silent and other channels exhibit limited activity. We subsequently introduced corrected and uncorrected currents into computer models of the arterial wall to show how these subtle adjustments markedly impact the importance of K_IR in V_m and arterial tone regulation. We argue that this refined approach can be used on an array of vascular ion channels to build a complete picture of how they dynamically interact to set arterial tone in key organs like the brain.NEW & NOTEWORTHY This work describes a stepwise approach to resolve small ionic currents involved in controlling V_m in resistance arteries. Using this new methodology, we particularly resolved the outward component of the K_IR current in native vascular cells, voltage clamped in near-physiological conditions. This novel approach can be applied to any other vascular currents and used to better interpret how vascular ion channels cooperate to control arterial tone.

Intercellular Conduction Optimizes Arterial Network Function and Conserves Blood Flow Homeostasis During Cerebrovascular Challenges

OBJECTIVE

Cerebral arterial networks match blood flow delivery with neural activity. Neurovascular response begins with a stimulus and a focal change in vessel diameter, which by themselves is inconsequential to blood flow magnitude, until they spread and alter the contractile status of neighboring arterial segments. We sought to define the mechanisms underlying integrated vascular behavior and considered the role of intercellular electrical signaling in this phenomenon. Approach and Results: Electron microscopic and histochemical analysis revealed the structural coupling of cerebrovascular cells and the expression of gap junctional subunits at the cell interfaces, enabling intercellular signaling among vascular cells. Indeed, robust vasomotor conduction was detected in human and mice cerebral arteries after focal vessel stimulation: a response attributed to endothelial gap junctional communication, as its genetic alteration attenuated this behavior. Conducted responses were observed to ascend from the penetrating arterioles, influencing the contractile status of cortical surface vessels, in a simulated model of cerebral arterial network. Ascending responses recognized in vivo after whisker stimulation were significantly attenuated in mice with altered endothelial gap junctional signaling confirming that gap junctional communication drives integrated vessel responses. The diminishment in vascular communication also impaired the critical ability of the cerebral vasculature to maintain blood flow homeostasis and hence tissue viability after stroke.

CONCLUSIONS

Our findings highlight the integral role of intercellular electrical signaling in transcribing focal stimuli into coordinated changes in cerebrovascular contractile activity and expose, a hitherto unknown mechanism for flow regulation after stroke.

Membrane Lipid-K IR 2.x Channel Interactions Enable Hemodynamic Sensing in Cerebral Arteries

Objective—

Inward rectifying K + (K IR ) channels are present in cerebral arterial smooth muscle and endothelial cells, a tandem arrangement suggestive of a dynamic yet undiscovered role for this channel. This study defined whether distinct pools of cerebral arterial K IR channels were uniquely modulated by membrane lipids and hemodynamic stimuli.

Approach and Results—

A Ba 2+ -sensitive K IR current was isolated in smooth muscle and endothelial cells of rat cerebral arteries; molecular analyses subsequently confirmed K IR 2.1/K IR 2.2 mRNA and protein expression in both cells. Patch-clamp electrophysiology next demonstrated that each population of K IR channels was sensitive to key membrane lipids and hemodynamic stimuli. In this regard, endothelial K IR was sensitive to phosphatidylinositol 4,5-bisphosphate content, with depletion impairing the ability of laminar shear stress to activate this channel pool. In contrast, smooth muscle K IR was sensitive to membrane cholesterol content, with sequestration blocking the ability of pressure to inhibit channel activity. The idea that membrane lipids help confer shear stress and pressure sensitivity of K IR channels was confirmed in intact arteries using myography. Virtual models integrating structural/electrical observations reconceptualized K IR as a dynamic regulator of membrane potential working in concert with other currents to set basal tone across a range of shear stresses and intravascular pressures.

Conclusions—

The data show for the first time that specific membrane lipid-K IR interactions enable unique channel populations to sense hemodynamic stimuli and drive vasomotor responses to set basal perfusion in the cerebral circulation.

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 Multicellular Vascular Model of the Renal Myogenic Response

The myogenic response is a key autoregulatory mechanism in the mammalian kidney. Triggered by blood pressure perturbations, it is well established that the myogenic response is initiated in the renal afferent arteriole and mediated by alterations in muscle tone and vascular diameter that counterbalance hemodynamic perturbations. The entire process involves several subcellular, cellular, and vascular mechanisms whose interactions remain poorly understood. Here, we model and investigate the myogenic response of a multicellular segment of an afferent arteriole. Extending existing work, we focus on providing an accurate—but still computationally tractable—representation of the coupling among the involved levels. For individual muscle cells, we include detailed Ca2+ signaling, transmembrane transport of ions, kinetics of myosin light chain phosphorylation, and contraction mechanics. Intercellular interactions are mediated by gap junctions between muscle or endothelial cells. Additional interactions are mediated by hemodynamics. Simulations of time-independent pressure changes reveal regular vasoresponses throughout the model segment and stabilization of a physiological range of blood pressures (80–180 mmHg) in agreement with other modeling and experimental studies that assess steady autoregulation. Simulations of time-dependent perturbations reveal irregular vasoresponses and complex dynamics that may contribute to the complexity of dynamic autoregulation observed in vivo. The ability of the developed model to represent the myogenic response in a multiscale and realistic fashion, under feasible computational load, suggests that it can be incorporated as a key component into larger models of integrated renal hemodynamic regulation.