Robust homeostasis of cellular cholesterol is a consequence of endogenous antithetic integral control

Abstract

Although cholesterol is essential for cellular viability and proliferation, it is highly toxic in excess. The concentration of cellular cholesterol must therefore be maintained within tight tolerances, and is thought to be subject to a stringent form of homeostasis known as Robust Perfect Adaptation (RPA). While much is known about the cellular signalling interactions involved in cholesterol regulation, the specific chemical reaction network structures that might be responsible for the robust homeostatic regulation of cellular cholesterol have been entirely unclear until now. In particular, the molecular mechanisms responsible for sensing excess whole-cell cholesterol levels have not been identified previously, and no mathematical models to date have been able to capture an integral control implementation that could impose RPA on cellular cholesterol. Here we provide a detailed mathematical description of cholesterol regulation pathways in terms of biochemical reactions, based on an extensive review of experimental and clinical literature. We are able to decompose the associated chemical reaction network structures into several independent subnetworks, one of which is responsible for conferring RPA on several intracellular forms of cholesterol. Remarkably, our analysis reveals that RPA in the cholesterol concentration in the endoplasmic reticulum (ER) is almost certainly due to a well-characterised control strategy known as antithetic integral control which, in this case, involves the high-affinity binding of a multi-molecular transcription factor complex with cholesterol molecules that are excluded from the ER membrane. Our model provides a detailed framework for exploring the necessary biochemical conditions for robust homeostatic control of essential and tightly regulated cellular molecules such as cholesterol.

Keywords: cholesterol homeostasis; integral control; modularity; robust perfect adaptation; signalling network.

FIGURE 1

Schematic overview of molecular interactions associated with cholesterol regulation. ER cholesterol molecules (C _e ) that exceed the sequestration capacity of membrane phospholipids protrude into the ER lumen (C). These are sensed and sequestered by constitutively produced SREBP/Scap/Insig complex, S _ci (solid red line). Unbound S _ci releases three transcription factors (S _R , S _H , S _p ) into the nucleus to induce expression of LDLR (R), HMGCR (H _R ) and PCSK9 (P). Cholesterol delivered from blood-borne lipoproteins (C _L ) is taken up by LDLR, then engulfed and released via lysosomes to become free unesterified cholesterol (C _f ) that supplements the PM cholesterol pool (C _p ). Fluxes between PM cholesterol and ER membrane cholesterol (C _e ) establish a balance, while esterification of C _e into E further contribute to the overall regulation of cellular cholesterol concentration. PCSK9 binding to LDLR initiates degradation of both molecules via internalisation into lysosomes. Biosynthesis of cholesterol starts with the constitutive formation of HMG–CoA (H), to eventually be converted to C _e , a process initialised by the catalytic enzyme H _R . The rate–limiting step in endogenous production of cholesterol occurs when C _e inhibits catalytic activity via degradation of H _R . Black arrows indicate flux or upregulation, dashed arrows indicate de novo protein synthesis, blunt arrow heads indicate inhibition, round arrow head indicates catalytic target. Created with BioRender.com.

FIGURE 2

CRN graph structure for the cholesterol homeostasis network.

FIGURE 3

Subnetwork 1, with deficiency 1, confers RPA on the species C _e , C _p , C _f and E. Subnetwork 1 can be decomposed into algebraically independent Subnetworks 1A and 1B respectively. Subnetwork 1A contains species C _e , that regulates the transcription of cholesterol promoting processes, while Subnetwork 1B comprise the other three non–terminal complexes, C _p , C _f and E.

FIGURE 4

Subnetwork 2. Reactions in this Subnetwork contribute to the overarching controlling module but do not have any influence on the RPA capacity of the CRN as a whole. C _e is the only species common to both Independent Subnetworks, and thus connects independent CRN subnetworks 1 and 2.

FIGURE 5

Numerical simulation of Eqs 1–13, showing the system response to step changes in C _L . (A) Concentration of input variable, C _L . (B) For indicated persistent disturbances in the concentration of C _L , the concentration of the RPA–capable variables C _e , C _f , C _p and E transiently change, and then return to their respective fixed setpoints. (C) The non–RPA capable variables C, R and H arrive at steady-state values that depend on the value of C _L . (D) The non–RPA capable variables S _ci , S _r , H _R , S _p , P and S _h arrive at steady-state values that depend on the value of C _L . Parameters: k ₁ = 3, k ₂ = 2, k ₃ = 5, k ₄ = 4, k ₅ = 5, k ₆ = 1, k ₇ = 4, k ₈ = 3, k ₉ = 1, k ₁₀ = 1.2, k ₁₁ = 1, k ₁₂ = 9, k ₁₃ = 1, k ₁₄ = 1, k ₁₅ = 1, k ₁₆ = 1, p ₁ = 30, p ₂ = 4, p ₃ = 1.5, μ = 25, η = 10, α = 10, θ = 10. Initial values: S _ci (0) = 5, C(0) = 1, S _r (0) = 1, S _h (0) = 1, R(0) = 1, C _f (0) = 50, C _p (0) = 1, C _e (0) = 100, E(0) = 5, H _R (0) = 1, H(0) = 1, S _p (0) = 1, P(0) = 1.

FIGURE 6

Network schematic for the cellular cholesterol regulatory network. This network diagram captures the nature of the interactions among the thirteen species of the CRN, illustrating the overarching topology of the cellular cholesterol homeostatic machinery as a single Opposer module, with its characteristic feedback architecture. Grey arrows represent flux, or an activating/upregulating influence, while blunt arrow heads (flat bars) represent inhibition or a negative/downregulating influence. Solid circular line endings represent a catalytic reaction. The single opposer node, comprising the irreversible sequestration of cholesterol within the SREBP/Scap/Cholesterol complex (S _ci C) is represented by the green arrows.

FIGURE 7

Single opposer node for the cellular cholesterol regulatory network. The purple box highlights the sequestration process that implements a form of antithetic integral control, thereby constituting a single opposer node via a single linear coordinate change. These opposer interactions (indicated in red) confer RPA on the sensor molecule, C _e , which in turn imparts RPA to several upstream molecules (not shown).