Mathematical model for low density lipoprotein (LDL) endocytosis by hepatocytes

Model for random internalization of nanoparticles by cells

We propose a stochastic model for the internalization of nanoparticles by cells formulating cellular uptake as a compound Poisson process with a random probability of success. This is an alternative approach to the one presented by Rees et al. [Nat. Commun. 10, 2341 (2019)2041-172310.1038/s41467-018-07882-8] who explained overdispersion in nanoparticle uptake and associated negative binomial distribution by considering a Poisson distribution for particle arrival and a gamma-distributed cell area. In our stochastic model, the formation of new pits is represented by the Poisson process, whereas the capturing process and the population heterogeneity are described by a random Bernoulli process with a beta-distributed probability of success. The random probability of success generates ensemble-averaged conditional transition probabilities that increase with the number of newly formed pits (self-reinforcement). As a result, an ensemble-averaged nanoparticle uptake can be represented as a Polya process. We derive an explicit formula for the distribution of the random number of pits containing nanoparticles. In the limit of the fast nucleation and low probability of nanoparticle capture, we find the negative binomial distribution.

Intercellular pathways of cancer treatment-related cardiotoxicity and their therapeutic implications: the paradigm of radiotherapy

Advances in cancer therapeutics have improved patient survival rates. However, cancer survivors may suffer from adverse events either at the time of therapy or later in life. Cardiovascular diseases (CVD) represent a clinically important, but mechanistically understudied complication, which interfere with the continuation of best-possible care, induce life-threatening risks, and/or lead to long-term morbidity. These concerns are exacerbated by the fact that targeted therapies and immunotherapies are frequently combined with radiotherapy, which induces durable inflammatory and immunogenic responses, thereby providing a fertile ground for the development of CVDs. Stressed and dying irradiated cells produce 'danger' signals including, but not limited to, major histocompatibility complexes, cell-adhesion molecules, proinflammatory cytokines, and damage-associated molecular patterns. These factors activate intercellular signaling pathways which have potentially detrimental effects on the heart tissue homeostasis. Herein, we present the clinical crosstalk between cancer and heart diseases, describe how it is potentiated by cancer therapies, and highlight the multifactorial nature of the underlying mechanisms. We particularly focus on radiotherapy, as a case known to often induce cardiovascular complications even decades after treatment. We provide evidence that the secretome of irradiated tumors entails factors that exert systemic, remote effects on the cardiac tissue, potentially predisposing it to CVDs. We suggest how diverse disciplines can utilize pertinent state-of-the-art methods in feasible experimental workflows, to shed light on the molecular mechanisms of radiotherapy-related cardiotoxicity at the organismal level and untangle the desirable immunogenic properties of cancer therapies from their detrimental effects on heart tissue. Results of such highly collaborative efforts hold promise to be translated to next-generation regimens that maximize tumor control, minimize cardiovascular complications, and support quality of life in cancer survivors.

Optimization of Extracellular Vesicle Release for Targeted Drug Delivery

Targeted drug delivery is a promising approach for many serious diseases, such as glioblastoma multiforme, one of the most common and devastating brain tumor. In this context, this work addresses the optimization of the controlled release of drugs which are carried by extracellular vesicles. Towards this goal, we derive and numerically verify an analytical solution for the end-to-end system model. We then apply the analytical solution either to reduce the disease treatment time or to reduce the amount of required drugs. The latter is formulated as a bilevel optimization problem, whose quasiconvex/quasiconcave property is proved here. For solving the optimization problem, we propose and utilize a combination of bisection method and golden-section search. The numerical results demonstrate that the optimization can significantly reduce the treatment time and/or the required drugs carried by extracellular vesicles for a therapy compared to the steady state solution.

Computationally Modelling Cholesterol Metabolism and Atherosclerosis

Cardiovascular disease (CVD) is the leading cause of death globally. The underlying pathological driver of CVD is atherosclerosis. The primary risk factor for atherosclerosis is elevated low-density lipoprotein cholesterol (LDL-C). Dysregulation of cholesterol metabolism is synonymous with a rise in LDL-C. Due to the complexity of cholesterol metabolism and atherosclerosis mathematical models are routinely used to explore their non-trivial dynamics. Mathematical modelling has generated a wealth of useful biological insights, which have deepened our understanding of these processes. To date however, no model has been developed which fully captures how whole-body cholesterol metabolism intersects with atherosclerosis. The main reason for this is one of scale. Whole body cholesterol metabolism is defined by macroscale physiological processes, while atherosclerosis operates mainly at a microscale. This work describes how a model of cholesterol metabolism was combined with a model of atherosclerotic plaque formation. This new model is capable of reproducing the output from its parent models. Using the new model, we demonstrate how this system can be utilized to identify interventions that lower LDL-C and abrogate plaque formation.

Differential expression profile of miRNAs between stable and vulnerable plaques of carotid artery stenosis patients

Plaque vulnerability is associated with the degree of carotid artery stenosis (CS) and the risk of stroke. MicroRNAs (miRNAs) exert critical functions in disease progression, although only a few miRNAs have been well identified in CS. Therefore, this study aimed to investigate the differential expression profile of miRNAs and their potential functions in plaques of CS patients. Three CS patients with stable plaques and three patients with vulnerable plaques who underwent carotid endarterectomy were enrolled in this study. Differentially expressed miRNAs (DEmiRNAs) between patients with stable and vulnerable plaques were determined using small RNA sequencing. Target genes of DEmiRNAs were predicted and submitted to functional analyses. Validation of dysregulated DEmiRNAs was determined using quantitative real-time polymerase chain reaction (qRT-PCR). After sequencing, 76 DEmiRNAs were identified in vulnerable plaques, including 53 upregulated miRNAs and 23 downregulated miRNAs. Next, 23,495 target genes of the identified DEmiRNAs were predicted and functionally analyzed. This indicated that the target genes of the identified DEmiRNAs were mainly enriched in protein phosphorylation, transcription, nitrogen compound metabolism, endocytosis and autophagy, and related to signaling pathways of Hippo, MAPK, insulin, TGF-β, FoxO, AMPK and p53. Furthermore, qRT-PCR results for six miRNAs showed that five (83%) of them (hsa-miR-511-5p, hsa-miR-150-5p, hsa-miR-378a-5p, hsa-miR-365b-5p and hsa-miR-6511b-5p) were consistent with the sequencing results. Differential expression profiles and potential function of miRNAs associated with plaque stability in CS patients are identified for the first time, which should help to understand the regulatory mechanism of plaque stability in CS.

Acute exposure of minimally ox-LDL elicits survival responses by downregulating the mediators of NLRP3 inflammasome in cultured RAW 264.7 macrophages

Lipid burden in macrophages driven by oxidized LDL (oxLDL) accelerates the foam cell formation and the activation of sterile inflammatory responses aggravating the atherosclerosis. However, there is limited information on the mediators and the pathways involved in the possible survival responses, especially at the initial phase, by lipid-burden in macrophage cells on encountering oxLDL. The present study was designed to assess the expression status of major mediators involved in the NLRP3 inflammasome pathway of sterile inflammation and the cellular responses in oxLDL-challenged cultured RAW 264.7 macrophage cells. Ox-LDL-treated RAW 264.7 macrophage cells displayed a decreased expression of the key sterile inflammatory mediators, TLR4, TLR2, ASC, NLRP3 and IL-18 at protein and transcript levels; however, displayed increased level of IL-1β, RAGE and TREM1 at protein level. Biological responses including lipid uptake, lipid peroxidation, cellular hypertrophy, mitochondrial density, and mitochondrial membrane potential were significantly increased in oxLDL-treated macrophages. Moreover, superoxide production was significantly decreased in the oxLDL-treated macrophages compared to the control. Overall, the findings revealed the expression status of key sterile mediators and the macrophage response during the initial phase of oxLDL exposure tend toward the prevention of inflammation. Further understanding would open novel translational opportunities in the management of atherosclerosis.

Control of Cholesterol Metabolism Using a Systems Approach

Simple Summary

Cholesterol is the main sterol in mammals that is essential for healthy cell functionining. It plays a key role in metabolic regulation and signaling, it is a precursor molecule of bile acids, oxysterols, and all steroid hormones. It also contributes to the structural makeup of the membranes. Its homeostasis is tightly controlled since it can harm the body if it is allowed to reach abnormal blood concentrations. One of the diseases associated with elevated cholesterol levels being the major cause of morbidities and mortalities worldwide, is atherosclerosis. In this study, we have developed a model of the cholesterol metabolism taking into account local inflammation and oxidative stress. The aim was to investigate the impact of the interplay of those processes and cholesterol metabolism disturbances on the atherosclerosis development and progression. We have also analyzed the effect of combining different classes of drugs targeting selected components of cholesterol metabolism.

Abstract

Cholesterol is an essential component of mammalian cells and is involved in many fundamental physiological processes; hence, its homeostasis in the body is tightly controlled, and any disturbance has serious consequences. Disruption of the cellular metabolism of cholesterol, accompanied by inflammation and oxidative stress, promotes the formation of atherosclerotic plaques and, consequently, is one of the leading causes of death in the Western world. Therefore, new drugs to regulate disturbed cholesterol metabolism are used and developed, which help to control cholesterol homeostasis but still do not entirely cure atherosclerosis. In this study, a Petri net-based model of human cholesterol metabolism affected by a local inflammation and oxidative stress, has been created and analyzed. The use of knockout of selected pathways allowed us to observe and study the effect of various combinations of commonly used drugs on atherosclerosis. The analysis results led to the conclusion that combination therapy, targeting multiple pathways, may be a fundamental concept in the development of more effective strategies for the treatment and prevention of atherosclerosis.

Modeling cholesterol metabolism and atherosclerosis

Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.

Cellular factors involved in the hepatitis C virus life cycle

The hepatitis C virus (HCV), an obligatory intracellular pathogen, highly depends on its host cells to propagate successfully. The HCV life cycle can be simply divided into several stages including viral entry, protein translation, RNA replication, viral assembly and release. Hundreds of cellular factors involved in the HCV life cycle have been identified over more than thirty years of research. Characterization of these cellular factors has provided extensive insight into HCV replication strategies. Some of these cellular factors are targets for anti-HCV therapies. In this review, we summarize the well-characterized and recently identified cellular factors functioning at each stage of the HCV life cycle.

Cholesterol Regulation in Age-Related Macular Degeneration: A Framework for Mathematical Modelling of Drusen Biogenesis

In age-related macular degeneration (AMD), there is, in common with many other age-related diseases, the need to distinguish between changes in the ageing eye that lead to disease and those changes that are considered part of a healthy, ageing eye. Various studies investigating the multitude of mechanisms involved in the aetiology of AMD exist within the field of ophthalmology and related medical fields, yet many aspects of it remain poorly understood and only a limited number of therapies are available. A recent study relates drusen's topographically cellular characteristics to the neural retina's metabolic needs and associated cholesterol involvement within the retina. In particular, there is a need to fully understand the maintenance of cholesterol homeostasis in the retina to prevent normal ageing processes from being perturbed towards maculopathy. Here, we present an extensive review of the clinical and physiological features of the ageing retina, as well as mechanisms implicated in pathology, synthesised from a vast body of the published literature. We use this novel synthesis to construct a comprehensive process schematic, encompassing all key species and physiological processes such as nutrients, waste and lipoprotein management. We are therefore able to express these processes in a mathematical language via a comprehensive modelling framework, comprising a set of twenty-three equations spanning three distinct biological compartments. This very general modelling framework may now be adapted to more focused studies on individual mechanisms, processes or components underlying of the many facets of AMD. As an example of such a focused application, we conclude this article with a one-compartment, four-species model of the retinal pigment epithelium, which considers the parametric conditions under which either cholesterol homeostasis or unregulated accumulation of cholesterol may obtain in the ageing eye.

A mathematical model to estimate cholesterylester transfer protein (CETP) triglycerides flux in human plasma

Background

Cholesterylester transfer protein (CETP) modulates the composition of various lipoproteins associated with cardiovascular disease. Despite its central role in lipoprotein metabolism, its mode of action is still not fully understood. Here we present a simple way to estimate CETP-mediated lipid fluxes between different lipoprotein fractions.

Results

The model derived adequately describes the observed findings, especially regarding low- and high dense lipoproteins (LDL and HDL), delivering correlation coefficients of R² = 0.567 (p < 0.001) and R² = 0.466 (p < 0.001), respectively. These estimated fluxes correlate best among all other measured concentrations and ‘lipid per lipoprotein’ ratios to the observed fluxes.

Conclusion

Our model approach is independent of CETP-action’s exact mechanistic mode. It is simple and easy to apply, and may be a useful tool in revealing CETP’s ambiguous role in lipid metabolism. The model mirrors a diffusion-like exchange of triglycerides between lipoproteins. Cholesteryl ester and triglyceride concentrations measured in HDL, LDL and VLDL are sufficient to apply the model on a plasma sample.

Electronic supplementary material

The online version of this article (10.1186/s12918-019-0679-x) contains supplementary material, which is available to authorized users.

The Interplay Between Cholesterol Metabolism and Intrinsic Ageing

The last few decades have witnessed remarkable progress in our understanding of ageing. From an evolutionary standpoint it is generally accepted that ageing is a non-adaptive process which is underscored by a decrease in the force of natural selection with time. From a mechanistic perspective ageing is characterized by a wide variety of cellular mechanisms, including processes such as cellular senescence, telomere attrition, oxidative damage, molecular chaperone activity, and the regulation of biochemical pathways by sirtuins. These biological findings have been accompanied by an unrelenting rise in both life expectancy and the number of older people globally. However, despite age being recognized demographically as a risk factor for healthspan, the processes associated with ageing are routinely overlooked in disease mechanisms. Thus, a central goal of biogerontology is to understand how diseases such as cardiovascular disease (CVD) are shaped by ageing. This challenge cannot be ignored because CVD is the main cause of morbidity in older people. A worthwhile way to examine how ageing intersects with CVD is to consider the effects ageing has on cholesterol metabolism, because dysregualted cholesterol metabolism is the key factor which underpins the pathology of CVD. The aim of this chapter is to outline a hypothesis which accounts for how ageing intersects with intracellular cholesterol metabolism. Moreover, we discuss the implications of this relationship for the onset of disease in the 'oldest old' (individuals ≥85 years of age). We conclude the chapter by discussing the important role mathematical modelling has to play in improving our understanding of cholesterol metabolism and ageing.

Correlated receptor transport processes buffer single-cell heterogeneity

Cells typically vary in their response to extracellular ligands. Receptor transport processes modulate ligand-receptor induced signal transduction and impact the variability in cellular responses. Here, we quantitatively characterized cellular variability in erythropoietin receptor (EpoR) trafficking at the single-cell level based on live-cell imaging and mathematical modeling. Using ensembles of single-cell mathematical models reduced parameter uncertainties and showed that rapid EpoR turnover, transport of internalized EpoR back to the plasma membrane, and degradation of Epo-EpoR complexes were essential for receptor trafficking. EpoR trafficking dynamics in adherent H838 lung cancer cells closely resembled the dynamics previously characterized by mathematical modeling in suspension cells, indicating that dynamic properties of the EpoR system are widely conserved. Receptor transport processes differed by one order of magnitude between individual cells. However, the concentration of activated Epo-EpoR complexes was less variable due to the correlated kinetics of opposing transport processes acting as a buffering system.

Cell surface receptors translate extracellular ligand concentrations to intracellular responses. Receptor transport between the plasma membrane and other cellular compartments regulates the number of accessible receptors at the plasma membrane that determines the strength of downstream pathway activation at a given ligand concentration. In cell populations, pathway activation strength and cellular responses vary between cells. Understanding origins of cell-to-cell variability is highly relevant for cancer research, motivated by the problem of fractional killing by chemotherapies and development of resistance in subpopulations of tumor cells. The erythropoietin receptor (EpoR) is a characteristic example of a receptor system that strongly depends on receptor transport processes. It is involved in several cellular processes, such as differentiation or proliferation, regulates the renewal of erythrocytes, and is expressed in several tumors. To investigate the involvement of receptor transport processes in cell-to-cell variability, we quantitatively characterized trafficking of EpoR in individual cells by combining live-cell imaging with mathematical modeling. Thereby, we found that EpoR dynamics was strongly dependent on rapid receptor transport and turnover. Interestingly, although transport processes largely differed between individual cells, receptor concentrations in cellular compartments were robust to variability in trafficking processes due to the correlated kinetics of opposing transport processes.

Cholesterol metabolism: A review of how ageing disrupts the biological mechanisms responsible for its regulation

Cholesterol plays a vital role in the human body as a precursor of steroid hormones and bile acids, in addition to providing structure to cell membranes. Whole body cholesterol metabolism is maintained by a highly coordinated balancing act between cholesterol ingestion, synthesis, absorption, and excretion. The aim of this review is to discuss how ageing interacts with these processes. Firstly, we will present an overview of cholesterol metabolism. Following this, we discuss how the biological mechanisms which underpin cholesterol metabolism are effected by ageing. Included in this discussion are lipoprotein dynamics, cholesterol absorption/synthesis and the enterohepatic circulation/synthesis of bile acids. Moreover, we discuss the role of oxidative stress in the pathological progression of atherosclerosis and also discuss how cholesterol biosynthesis is effected by both the mammalian target of rapamycin and sirtuin pathways. Next, we examine how diet and alterations to the gut microbiome can be used to mitigate the impact ageing has on cholesterol metabolism. We conclude by discussing how mathematical models of cholesterol metabolism can be used to identify therapeutic interventions.

A mathematical model of the human metabolic system and metabolic flexibility

In healthy subjects some tissues in the human body display metabolic flexibility, by this we mean the ability for the tissue to switch its fuel source between predominantly carbohydrates in the postprandial state and predominantly fats in the fasted state. Many of the pathways involved with human metabolism are controlled by insulin and insulin-resistant states such as obesity and type-2 diabetes are characterised by a loss or impairment of metabolic flexibility. In this paper we derive a system of 12 first-order coupled differential equations that describe the transport between and storage in different tissues of the human body. We find steady state solutions to these equations and use these results to nondimensionalise the model. We then solve the model numerically to simulate a healthy balanced meal and a high fat meal and we discuss and compare these results. Our numerical results show good agreement with experimental data where we have data available to us and the results show behaviour that agrees with intuition where we currently have no data with which to compare.

A mathematical model of the sterol regulatory element binding protein 2 cholesterol biosynthesis pathway

Cholesterol is one of the key constituents for maintaining the cellular membrane and thus the integrity of the cell itself. In contrast high levels of cholesterol in the blood are known to be a major risk factor in the development of cardiovascular disease. We formulate a deterministic nonlinear ordinary differential equation model of the sterol regulatory element binding protein 2 (SREBP-2) cholesterol genetic regulatory pathway in a hepatocyte. The mathematical model includes a description of genetic transcription by SREBP-2 which is subsequently translated to mRNA leading to the formation of 3-hydroxy-3-methylglutaryl coenzyme A reductase (HMGCR), a main regulator of cholesterol synthesis. Cholesterol synthesis subsequently leads to the regulation of SREBP-2 via a negative feedback formulation. Parameterised with data from the literature, the model is used to understand how SREBP-2 transcription and regulation affects cellular cholesterol concentration. Model stability analysis shows that the only positive steady-state of the system exhibits purely oscillatory, damped oscillatory or monotic behaviour under certain parameter conditions. In light of our findings we postulate how cholesterol homeostasis is maintained within the cell and the advantages of our model formulation are discussed with respect to other models of genetic regulation within the literature.

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We formulate and analyse a nonlinear ODE model of the SREBP2 pathway.

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The mathematical model exhibits stable limit cycles under certain parameter conditions.

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Negative feedbacks in the SREBP2 pathway may help regulate cholesterol homeostasis.

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Our model provides a more accurate formulation of genetic regulation using nonlinear ODEs.

Kinetic modeling of low density lipoprotein oxidation in arterial wall and its application in atherosclerotic lesions prediction

Oxidation of low-density lipoprotein (LDL) is one of the major factors in atherogenic process. Trapped oxidized LDL (Ox-LDL) in the subendothelial matrix is taken up by macrophage and leads to foam cell generation creating the first step in atherosclerosis development. Many researchers have studied LDL oxidation using in vitro cell-induced LDL oxidation model. The present study provides a kinetic model for LDL oxidation in intima layer that can be used in modeling of atherosclerotic lesions development. This is accomplished by considering lipid peroxidation kinetic in LDL through a system of elementary reactions. In comparison, characteristics of our proposed kinetic model are consistent with the results of previous experimental models from other researches. Furthermore, our proposed LDL oxidation model is added to the mass transfer equation in order to predict the LDL concentration distribution in intima layer which is usually difficult to measure experimentally. According to the results, LDL oxidation kinetic constant is an important parameter that affects LDL concentration in intima layer so that existence of antioxidants that is responsible for the reduction of initiating rates and prevention of radical formations, have increased the concentration of LDL in intima by reducing the LDL oxidation rate.

A whole-body mathematical model of cholesterol metabolism and its age-associated dysregulation

BACKGROUND

Global demographic changes have stimulated marked interest in the process of aging. There has been, and will continue to be, an unrelenting rise in the number of the oldest old ( >85 years of age). Together with an ageing population there comes an increase in the prevalence of age related disease. Of the diseases of ageing, cardiovascular disease (CVD) has by far the highest prevalence. It is regarded that a finely tuned lipid profile may help to prevent CVD as there is a long established relationship between alterations to lipid metabolism and CVD risk. In fact elevated plasma cholesterol, particularly Low Density Lipoprotein Cholesterol (LDL-C) has consistently stood out as a risk factor for having a cardiovascular event. Moreover it is widely acknowledged that LDL-C may rise with age in both sexes in a wide variety of groups. The aim of this work was to use a whole-body mathematical model to investigate why LDL-C rises with age, and to test the hypothesis that mechanistic changes to cholesterol absorption and LDL-C removal from the plasma are responsible for the rise. The whole-body mechanistic nature of the model differs from previous models of cholesterol metabolism which have either focused on intracellular cholesterol homeostasis or have concentrated on an isolated area of lipoprotein dynamics. The model integrates both current and previously published data relating to molecular biology, physiology, ageing and nutrition in an integrated fashion.

RESULTS

The model was used to test the hypothesis that alterations to the rate of cholesterol absorption and changes to the rate of removal of LDL-C from the plasma are integral to understanding why LDL-C rises with age. The model demonstrates that increasing the rate of intestinal cholesterol absorption from 50% to 80% by age 65 years can result in an increase of LDL-C by as much as 34 mg/dL in a hypothetical male subject. The model also shows that decreasing the rate of hepatic clearance of LDL-C gradually to 50% by age 65 years can result in an increase of LDL-C by as much as 116 mg/dL.

CONCLUSIONS

Our model clearly demonstrates that of the two putative mechanisms that have been implicated in the dysregulation of cholesterol metabolism with age, alterations to the removal rate of plasma LDL-C has the most significant impact on cholesterol metabolism and small changes to the number of hepatic LDL receptors can result in a significant rise in LDL-C. This first whole-body systems based model of cholesterol balance could potentially be used as a tool to further improve our understanding of whole-body cholesterol metabolism and its dysregulation with age. Furthermore, given further fine tuning the model may help to investigate potential dietary and lifestyle regimes that have the potential to mitigate the effects aging has on cholesterol metabolism.

Modelling approach to simulate reductions in LDL cholesterol levels after combined intake of statins and phytosterols/-stanols in humans

BACKGROUND

To examine the effects on LDL cholesterol of the combined use of statins and phytosterols/-stanols, in vivo studies and clinical trials are necessary. However, for a better interpretation of the experimental data as well as to possibly predict cholesterol levels given a certain dosing regimen of statins and phytosterols/-stanols a more theoretically based approach is helpful. This study aims to construct a mathematical model to simulate reductions in low-density lipoprotein (LDL) cholesterol in persons who combine the use of statins with a high intake of phytosterols/-stanols, e.g. by the use of functional foods.

METHODS AND RESULTS

The proposed model includes the cholesterol pool size in the liver and serum levels of very low-density lipoprotein (VLDL) cholesterol. Both an additional and a multiplicative effect of phytosterol/-stanol intake on LDL cholesterol reduction were predicted from the model. The additional effect relates to the decrease of dietary cholesterol uptake reduction, the multiplicative effect relates to the decrease in enterohepatic recycling efficiency, causing increased cholesterol elimination through bile. From the model, it was demonstrated that a daily intake of 2 g phytosterols/-stanols reduces LDL cholesterol level by about 8% to 9% on top of the reduction resulting from statin use. The additional decrease in LDL cholesterol caused by phytosterol/-stanol use at the recommended level of 2 g/d appeared to be similar or even greater than the decrease achieved by doubling the statin dose.

CONCLUSION

We proposed a simplified mathematical model to simulate the reduction in LDL cholesterol after separate and combined intake of statins and functional foods acting on intestinal (re)absorption of cholesterol or bile acids in humans. In future work, this model can be extended to include more complex (regulatory) mechanisms.

Endocytosis and signalling: a meeting with mathematics

Although endocytosis has traditionally been understood as a signal attenuation mechanism, an emerging view considers endocytosis as an integral part of signal propagation and processing. On the short time scale, trafficking of endocytic vesicles contributes to signal propagation from the surface to distant targets, with bi-directional communication between signalling and trafficking. Mathematical modelling helps combine the mechanistic, molecular knowledge with rigorous analysis of the complex output dynamics of endocytosis in time and space. Simulations reveal novel roles for endocytosis, including the control of cell polarity, enhancing the spatial signal propagation, and controlling the signal magnitudes, kinetics, and synchronization with stimulus dynamics.

Mathematical modelling of competitive LDL/VLDL binding and uptake by hepatocytes

Elevated levels of low-density-lipoprotein cholesterol (LDL-C) in the plasma are a well-established risk factor for the development of coronary heart disease. Plasma LDL-C levels are in part determined by the rate at which LDL particles are removed from the bloodstream by hepatic uptake. The uptake of LDL by mammalian liver cells occurs mainly via receptor-mediated endocytosis, a process which entails the binding of these particles to specific receptors in specialised areas of the cell surface, the subsequent internalization of the receptor-lipoprotein complex, and ultimately the degradation and release of the ingested lipoproteins' constituent parts. We formulate a mathematical model to study the binding and internalization (endocytosis) of LDL and VLDL particles by hepatocytes in culture. The system of ordinary differential equations, which includes a cholesterol-dependent pit production term representing feedback regulation of surface receptors in response to intracellular cholesterol levels, is analysed using numerical simulations and steady-state analysis. Our numerical results show good agreement with in vitro experimental data describing LDL uptake by cultured hepatocytes following delivery of a single bolus of lipoprotein. Our model is adapted in order to reflect the in vivo situation, in which lipoproteins are continuously delivered to the hepatocyte. In this case, our model suggests that the competition between the LDL and VLDL particles for binding to the pits on the cell surface affects the intracellular cholesterol concentration. In particular, we predict that when there is continuous delivery of low levels of lipoproteins to the cell surface, more VLDL than LDL occupies the pit, since VLDL are better competitors for receptor binding. VLDL have a cholesterol content comparable to LDL particles; however, due to the larger size of VLDL, one pit-bound VLDL particle blocks binding of several LDLs, and there is a resultant drop in the intracellular cholesterol level. When there is continuous delivery of lipoprotein at high levels to the hepatocytes, VLDL particles still out-compete LDL particles for receptor binding, and consequently more VLDL than LDL particles occupy the pit. Although the maximum intracellular cholesterol level is similar for high and low levels of lipoprotein delivery, the maximum is reached more rapidly when the lipoprotein delivery rates are high. The implications of these results for the design of in vitro experiments is discussed.