Metabolite Clearance During Wakefulness and Sleep

Abstract

Mechanisms for elimination of metabolites from ISF include metabolism, blood–brain barrier transport and non-selective, perivascular efflux, this last being assessed by measuring the clearance of markers like inulin. Clearance describes elimination. Clearance of a metabolite generated within the brain is determined as its elimination rate divided by its concentration in interstitial fluid (ISF). However, the more frequently measured parameter is the rate constant for elimination determined as elimination rate divided by amount present, which thus depends on both the elimination processes and the distribution of the metabolite in the brain. The relative importance of the various elimination mechanisms depends on the particular metabolite. Little is known about the effects of sleep on clearance via metabolism or blood–brain barrier transport, but studies with inulin in mice comparing perivascular effluxes during sleep and wakefulness reveal a 4.2-fold increase in clearance. Amongst the important brain metabolites considered, CO₂ is eliminated so rapidly across the blood–brain barrier that clearance is blood flow limited and elimination quickly balances production. Glutamate is removed from ISF primarily by uptake into astrocytes and conversion to glutamine, but also by transport across the blood–brain barrier. Both lactate and amyloid-β are eliminated by metabolism, blood–brain barrier transport and perivascular efflux and both show decreased production, decreased ISF concentration and increased perivascular clearance during sleep. Taken altogether available data indicate that sleep increases perivascular and non-perivascular clearances for amyloid-β which reduces its concentration and may have long-term consequences for the formation of plaques and cerebral arterial deposits.

Appendices

Appendices

1.1 Appendix 1

The evidence that extramural perivascular spaces can exist is convincing as large particles can be introduced into them (see e.g. Carare et al. 2008) and during influx of fluorescent tracers the spaces protrude beyond the dimensions of the vessel walls (see e.g. Figs. 2 and 3 in Iliff et al. 2012). The case against their normal existence along arterioles and venules is largely that they are rarely seen in fixed, sectioned tissue. However, spaces, particularly labile spaces, are likely to be difficult to fix, so this type of evidence is not in itself compelling (see e.g. Fig. 2 in Bakker et al. 2016). Arbel-Ornath et al. (2013) used two-photon imaging to investigate the position of a 3 kDa dextran during efflux following injection into the parenchyma. Shortly after injection they saw fluorescence within the parenchyma, in perivascular spaces surrounding small arteries and, at lower concentration, between the smooth muscle cells.

There is extensive and convincing evidence that solutes can rapidly reach the basement membranes between the smooth muscle cells (see e.g. Carare et al. 2013a), but it has not been established whether the solutes reach these locations by movement along the basement membranes as favoured by Weller, Carare, Hawkes and colleagues (see e.g. Morris et al. 2016) or via movement along the vessels via extramural pathways and penetration from these into the basement membranes within the vessel wall. This is discussed in Section “Clearance via Perivascular Routes”. While it has been possible to observe solutes moving inwards via extramural periarterial spaces (Iliff et al. 2012) and outwards via some periarterial route (Dienel and Cruz 2008; Arbel-Ornath et al. 2013), so far it has not been possible to observe solutes progressing via either perivenular or specifically intramural periarterial routes.

1.2 Appendix 2

In several papers the time courses of the amount of Aβ remaining in the brain have been analysed using a scheme introduced by Shibata et al. (2000). In this an amount Aβ₀ of the Aβ is assumed to be introduced initially into the parenchyma in a soluble form. This soluble Aβ can either be effluxed with rate constant k1 or irreversibly converted to a retained form with rate constant k2. The prediction of this scheme for the time course can be derived as follows. If at any time t the amount of the soluble form in the brain is Aβs_t and that of the retained form is Aβr_t, then the total amount remaining is Aβ_t = Aβs_t + Aβr_t and the changes with time of the amounts are governed by

$$ \frac{{\mathrm{d}\mathrm{A}\upbeta \mathrm{s}}_t}{\mathrm{d}t}=-\left(k1+k2\right){\mathrm{A}\upbeta \mathrm{s}}_t $$

(7)

and

$$ \frac{{\mathrm{d}\mathrm{A}\upbeta \mathrm{r}}_t}{\mathrm{d}t}=k2{\mathrm{A}\upbeta \mathrm{s}}_t $$

(8)

The first of these differential equations has as its solution

$$ {\mathrm{A}\upbeta \mathrm{s}}_t={\mathrm{A}\upbeta}_0{e}^{-\left(k1+k2\right)t}, $$

(9)

which then allows the second to be solved,

$$ {\mathrm{A}\upbeta \mathrm{r}}_t={\mathrm{A}\upbeta}_0a1\left(1-{e}^{-\left(k1+k2\right)t}\right) $$

(10)

and thus

$$ {\mathrm{A}\upbeta}_t={\mathrm{A}\upbeta}_0\left[a1+a2{e}^{-\left(k1+k2\right)t}\right] $$

(11)

where a1 = k2/(k1 + k2) is the fraction of the Aβ that is eventually converted to the retained form and a2 = 1 − a1 is the fraction eventually effluxed. This is to be compared with the versions of the solutions for Aβ_t that have been used in various studies. The version presented by Shibata et al. (2000)

$$ {\mathrm{A}\upbeta}_t={\mathrm{A}\upbeta}_0\left[a1+a2\right]{e}^{-k1t} $$

(12)

was also used by Deane et al. (2004), Bell et al. (2007) and Deane et al. (2008) (Abhay Sagare, personal communication). Storck et al. (2016) used a partially corrected version

$$ {\mathrm{A}\upbeta}_t={\mathrm{A}\upbeta}_0\left[a1+a2\right]{e}^{-\left(k1+k2\right)t}. $$

(13)

Use of Eqs. (12) or (13) may have affected the estimates of the fractions of Aβ effluxed and retained. In Shibata et al., it may have led to a small overestimate of the rate constant for efflux. In Bell et al., the fraction retained was small, i.e. k2 ≪ k1, and Eq. (12) is then almost the same as Eq. (11). However, the units stated in the methods section of that paper for k1 and k2 were pmol min⁻¹ g⁻¹ while those actually used in the calculations were min⁻¹ as in Shibata et al. The values reported in Tables 1 and 2 are calculated rates of efflux with the units stated, pmol min⁻¹ g⁻¹. These rates were calculated as the initial amount present, ~13 pmol/g ISF (assuming the mass of ISF is 1/10th that of the tissue), times the corresponding rate constant obtained using Eq. (12) (Abhay Sagare, personal communication).