Bjørn Olav Hald

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.

Influence of cyanide on diauxic oscillations in yeast

Coherent glycolytic oscillations in Saccharomyces cerevisiae are a multicellular property induced by addition of glucose to a starved cell population of sufficient density. However, initiation of oscillations requires an additional perturbation, usually addition of cyanide. The fate of cyanide during glycolytic oscillations has not previously been studied, and is the subject of the present paper. Using a cyanide electrode, a substantial decrease in cyanide concentration was observed. In the pH range 6–7, we found experimentally that the electrode behaves reasonably well, provided changes in pH are taken into account. To our knowledge, use of a cyanide electrode to study cyanide dynamics in living biological systems is new. Cyanide was found to enter starving yeast cells in only negligible amounts, and did not react significantly with glucose. Thus, cyanide consumption must be explained by reactions with glycolytic intermediates and evaporation. Evaporation and reaction with the signalling substance, extracellular acetaldehyde (ACAx) only explains the observed cyanide removal if [ACAx] is improbably high. Furthermore, differences in NADH traces upon cyanide addition before or after glucose addition strongly suggest that cyanide also reacts with intracellular carbonyl‐containing metabolites. We show that cyanide reacts with pyruvate (Pyr) and dihydroxyacetone phosphate in addition to ACA, and estimate their rate constants. Our results strongly suggest that the major routes of cyanide removal during glycolysis are reactions with pyruvate and ACA. Cyanide removal by all carbonyl‐containing intermediates led to a lower mean [ACAx], thereby increasing the amplitude of [ACAx] oscillations.

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.

Quantitative evaluation of respiration induced metabolic oscillations in erythrocytes

The changes in the partial pressures of oxygen and carbon dioxide (P(O(2)) and P(CO(2))) during blood circulation alter erythrocyte metabolism, hereby causing flux changes between oxygenated and deoxygenated blood. In the study we have modeled this effect by extending the comprehensive kinetic model by Mulquiney and Kuchel [P.J. Mulquiney, and P.W. Kuchel. Model of 2,3-bisphosphoglycerate metabolism in the human erythrocyte based on detailed enzyme kinetic equations: equations and parameter refinement, Biochem. J. 1999, 342, 581-596.] with a kinetic model of hemoglobin oxy-/deoxygenation transition based on an oxygen dissociation model developed by Dash and Bassingthwaighte [R. Dash, and J. Bassingthwaighte. Blood HbO(2) and HbCO(2) dissociation curves at varied O(2), CO(2), pH, 2,3-DPG and temperature levels, Ann. Biomed. Eng., 2004, 32(12), 1676-1693.]. The system has been studied during transitions from the arterial to the venous phases by simply forcing P(O(2)) and P(CO(2)) to follow the physiological values of venous and arterial blood. The investigations show that the system passively follows a limit cycle driven by the forced oscillations of P(O(2)) and is thus inadequately described solely by steady state consideration. The metabolic system exhibits a broad distribution of time scales. Relaxations of modes with hemoglobin and Mg(2+) binding reactions are very fast, while modes involving glycolytic, membrane transport and 2,3-BPG shunt reactions are much slower. Incomplete slow mode relaxations during the 60 s period of the forced transitions cause significant overshoots of important fluxes and metabolite concentrations - notably ATP, 2,3-BPG, and Mg(2+). The overshoot phenomenon arises in consequence of a periodical forcing and is likely to be widespread in nature - warranting a special consideration for relevant systems.

KIR channels tune electrical communication in cerebral arteries

The conducted vasomotor response reflects electrical communication in the arterial wall and the distance signals spread is regulated by three factors including resident ion channels. This study defined the role of inward-rectifying K+ channels (KIR) in governing electrical communication along hamster cerebral arteries. Focal KCl application induced a vasoconstriction that conducted robustly, indicative of electrical communication among cells. Inhibiting dominant K+ conductances had no attenuating effect, the exception being Ba2+ blockade of KIR. Electrophysiology and Q-PCR analysis of smooth muscle cells revealed a Ba2+-sensitive KIR current comprised of KIR2.1/2.2 subunits. This current was surprisingly small and when incorporated into a model, failed to account for the observed changes in conduction. We theorized a second population of KIR channels exist and consistent with this idea, a robust Ba2+-sensitive KIR2.1/2.2 current was observed in endothelial cells. When both KIR currents were incorporated into, and then inhibited in our model, conduction decay was substantive, aligning with experiments. Enhanced decay was ascribed to the rightward shift in membrane potential and the increased feedback arising from voltage-dependent-K+ channels. In summary, this study shows that two KIR populations work collaboratively to govern electrical communication and the spread of vasomotor responses along cerebral arteries.

The Conducted Vasomotor Response: Function, Biophysical Basis, and Pharmacological Control

Arterial tone is coordinated among vessel segments to optimize nutrient transport and organ function. Coordinated vasomotor activity is remarkable to observe and depends on stimuli, sparsely generated in tissue, eliciting electrical responses that conduct lengthwise among electrically coupled vascular cells. The conducted response is the focus of this topical review, and in this regard, the authors highlight literature that advances an appreciation of functional significance, cellular mechanisms, and biophysical principles. Of particular note, this review stresses that conduction is enabled by a defined pattern of charge movement along the arterial wall as set by three key parameters (tissue structure, gap junctional resistivity, and ion channel activity). The impact of disease on conduction is carefully discussed, as are potential strategies to restore this key biological response and, along with it, the match of blood flow delivery with tissue energetic demand.

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.

Stimulation-induced increases in cerebral blood flow and local capillary vasoconstriction depend on conducted vascular responses

Significance Pericytes are located at the outside wall of capillaries. However, whether and how pericytes are involved in the regulation of blood flow in brain capillaries is still debated. We report that capillary vascular responses are mostly initiated and peak at near-arteriole capillaries. These vascular responses are conducted along capillaries at a speed of 5–20 µm/s. Conducted vascular responses in brain capillaries appear to involve pericytes, the mural cells of microvessels, and may be a novel modulator of vascular function in the brain. Functional neuroimaging, such as fMRI, is based on coupling neuronal activity and accompanying changes in cerebral blood flow (CBF) and metabolism. However, the relationship between CBF and events at the level of the penetrating arterioles and capillaries is not well established. Recent findings suggest an active role of capillaries in CBF control, and pericytes on capillaries may be major regulators of CBF and initiators of functional imaging signals. Here, using two-photon microscopy of brains in living mice, we demonstrate that stimulation-evoked increases in synaptic activity in the mouse somatosensory cortex evokes capillary dilation starting mostly at the first- or second-order capillary, propagating upstream and downstream at 5–20 µm/s. Therefore, our data support an active role of pericytes in cerebrovascular control. The gliotransmitter ATP applied to first- and second-order capillaries by micropipette puffing induced dilation, followed by constriction, which also propagated at 5–20 µm/s. ATP-induced capillary constriction was blocked by purinergic P2 receptors. Thus, conducted vascular responses in capillaries may be a previously unidentified modulator of cerebrovascular function and functional neuroimaging signals.

Gap Junctions Suppress Electrical but Not [Ca2+] 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.

Vascular flow reserve as a link between long‐term blood pressure level and physical performance capacity in mammals

Mean arterial pressure (MAP) is surprisingly similar across different species of mammals, and it is, in general, not known which factors determine the arterial pressure level. Mammals often have a pronounced capacity for sustained physical performance. This capacity depends on the vasculature having a flow reserve that comes into play as tissue metabolism increases. We hypothesize that microvascular properties allowing for a large vascular flow reserve is linked to the level of the arterial pressure.To study the interaction between network properties and network inlet pressure, we developed a generic and parsimonious computational model of a bifurcating microvascular network where diameter and growth of each vessel evolves in response to changes in biomechanical stresses. During a simulation, the network develops well‐defined arterial and venous vessel characteristics. A change in endothelial function producing a high precapillary resistance and thus a high vascular flow reserve is associated with an increase in network inlet pressure. Assuming that network properties are independent of body mass, and that inlet pressure of the microvascular network is a proxy for arterial pressure, the study provides a conceptual explanation of why high performing animals tend to have a high MAP.