A mathematical model of aging-related and cortisol induced hippocampal dysfunction
© McAuley et al; licensee BioMed Central Ltd. 2009
Received: 23 January 2008
Accepted: 25 March 2009
Published: 25 March 2009
The hippocampus is essential for declarative memory synthesis and is a core pathological substrate for Alzheimer's disease (AD), the most common aging-related dementing disease. Acute increases in plasma cortisol are associated with transient hippocampal inhibition and retrograde amnesia, while chronic cortisol elevation is associated with hippocampal atrophy. Thus, cortisol levels could be monitored and managed in older people, to decrease their risk of AD type hippocampal dysfunction. We generated an in silicomodel of the chronic effects of elevated plasma cortisol on hippocampal activity and atrophy, using the systems biology mark-up language (SBML). We further challenged the model with biologically based interventions to ascertain if cortisol associated hippocampal dysfunction could be abrogated.
The in silicoSBML model reflected the in vivoaging of the hippocampus and increased plasma cortisol and negative feedback to the hypothalamic pituitary axis. Aging induced a 12% decrease in hippocampus activity (HA), increased to 30% by acute and 40% by chronic elevations in cortisol. The biological intervention attenuated the cortisol associated decrease in HA by 2% in the acute cortisol simulation and by 8% in the chronic simulation.
Both acute and chronic elevations in cortisol secretion increased aging-associated hippocampal atrophy and a loss of HA in the model. We suggest that this first SMBL model, in tandem with in vitroand in vivostudies, may provide a backbone to further frame computational cortisol and brain aging models, which may help predict aging-related brain changes in vulnerable older people.
Aging-related neurodegenerative diseases are ever increasing thanks to global demographic changes. Alzheimer's disease (AD) is the most common aging-related neurodegenerative disease; the incidence of which doubles yearly after one's seventh decade. Key symptoms of AD are the loss of declarative memory and decreased cognition which are associated with amyloid plaques and tau neurofibrillary tangle deposition and the depletion of hippocampal neurons [1, 2]. The loss of hippocampal CA1 neurons is particularly associated with hippocampal atrophy and memory deficits in AD . As yet, the exact pathological mechanism underscoring hippocampal degeneration in AD remains elusive; however aging-related factors such as diabetes, vascular disease and stress (elevated cortisol levels) are common risk factors for AD [4–6]. In the elderly, elevated plasma cortisol levels are associated with hippocampal atrophy, suggesting cortisol is involved in hippocampal dysfunction. Furthermore, the negative effects of elevated plasma cortisol levels on cognition in the elderly can be abrogated by blocking plasma cortisol release [7, 8]. This suggests that better plasma cortisol regulation may yield improved hippocampal activity in older people.
Plasma cortisol levels are regulated by the hypothalamic-pituitary-adrenal (HPA) axis and the hippocampus, which interact to form a negative feedback circuit to regulate cortisol release. Cortisol's effect on the hippocampus is mediated through interactions with mineralocorticoid receptors (MR) which increase the firing rate of CA1 neurons. A rise in cortisol levels sufficient to fully saturate MR receptors induces the transcription of inhibitory glucocorticoid receptors (GR) which decrease CA1 neuronal firing in tandem with augmenting negative feedback to the HPA to decrease cortisol secretion .
Cortisol provides tonic activation of hippocampal neurons, which can be useful during stressful situations which require alertness and increased neuronal activity. However, a short term overshoot of normal cortisol plasma levels may induce GR transcription, the inhibition of CA1 neuronal activity, and transient amnesia; the "tip of the tongue" phenomenon some experience during stressful situations. Plasma cortisol thus has a "U" shaped dose dependent effect on the firing potential of hippocampal neurons . In the long term elevated cortisol levels are associated with hippocampal atrophy [11–13]. This has led to suggestions that the chronic pathological effects of elevated cortisol levels may be treated in older people by physiological or pharmacological interventions. For example, plasma cortisol levels can be decreased by simple activities of daily living such as exercise .
Effects of chronic and acute changes in cortisol levels on Hippocampal Activity and Atrophy
B) Sensitivity of plasma cortisol to negative feedback at Hypothalamus, Pituitary and CRH levels
The effect of a change in the rate of negative feedback at the level of the pituitary was examined by decreasing kdc in the range of 10–50%. An alteration in cortisol feedback at the pituitary produced a rise in plasma cortisol in tandem with each increase in kdc, followed by a decrease in plasma cortisol until levels reached a steady state akin to that observed with the default value (Figure 4, graph B).
The next parameter investigated was kcrh,; the rate constant for the secretion of CRH. kcrh was decreased in the range 10–50%, each of which produced significant decreases in basal plasma cortisol levels (Figure 4, graph C). When kcrh decreased by 30, 40 and 50%, the basal plasma cortisol level eventually dropped to zero, reflecting the key role CRH has in the synthesis of cortisol. Conversely when kcrh was increased in the range of 10–50%, gradual increases in basal plasma cortisol levels were observed. Again plasma cortisol levels reached a steady state instantaneously with each parameter change, but plasma cortisol did not continue to rise further after kcrh was increased by 40% (Figure 4, graph D).
Altogether these results suggest the in silicosystem responds to negative feedback in a similar fashion to that reported in biological in vivosystems; ie the hypothalamus, pituitary and CRH hormone production were all reflexive to negative feedback via sensitivity to plasma cortisol levels.
C) Response of the system to decreased negative feedback from the hippocampus
D) Sensitivity of HPA axis to altered cortisol synthesis
These observations suggest that the mechanisms in place to deal with elevations in plasma cortisol (e.g. feedback at the level of the pituitary and hypothalamus) ensured that plasma cortisol did not stay elevated for long, thus showing that the simple in silicosystem reflects the biological HPA regulation of cortisol in vivo.
E) Response of System to Somatic Cortisol Demands
F) Parameter changes to examine daily cortisol rhythm
The physiological mechanisms underpinning the association between elevated plasma cortisol and hippocampal atrophy in the elderly are not fully understood. However, it is accepted that the expression and activation of cortisol receptors influences hippocampal neuronal activity, and that elevated plasma cortisol is associated with hippocampal dysfunction and memory loss [10, 18]. The neurotoxic effects of elevated cortisol on the hippocampus most likely involves "allostatic" loading of hippocampal cortisol receptors, accelerated by an aging-related loss of neurons and trophic factors [12, 13]. To help further understand the association between stress and hippocampal function, we used information on aging, the HPA axis, plasma cortisol and hippocampal activity, to simulate the effect of chronic and acute cortisol elevations on the hippocampus.
We recognise that cortisol receptors are present throughout the brain, in limbic, brainstem, and cortical regions, all of which are sensitive to aging-related dysfunction. For example, prefrontal cortical (PFC) neurons contribute to cognitive function, particularly executive function; a decrease in which is found in patients with advanced AD, Parkinson's disease and vascular dementia [19, 20]. Rodent studies have also demonstrated dystrophy of PFC neurons after exposure to elevated cortisol levels . This suggests that the PFC may be an interesting component to add to the current model in other to expand its utility in terms of understanding the relationship between cortisol and cognitive function. However in this first paper, we wished to model the clinically documented, but ill-understood link between elevated plasma cortisol levels and AD type hippocampal dysfunction. Therefore we focused on the atrophy of the hippocampus and activity of CA1 neurons therein, because the hippocampus regulates semantic memory and verbal fluency- cognitive domains which are lost at early stages of AD.
The simulations produced by the model suggest that chronic elevations in cortisol are more detrimental to the hippocampus than a series of acute bursts in cortisol. This may be important for clinicians, in terms of the need to take a continuous series of cortisol measurements from patients rather than a snapshot of their plasma cortisol levels in order to calculate their potential risk of cortisol associated hippocampal dysfunction. We further suggest that it could also be useful to study if the cortisol values which decreased hippocampal output and volume in this simulation mirror ageing-related processes in vivo. The model could also be expanded to include gender differences in chronic stress , which may augment neurotoxic effects of elevated plasma cortisol on hippocampal function in females.
Although SBML modelling is in its embryonic stages, skeletal models of physiological systems which share a common computational platform , may be useful in the future to test a variety of hypothesis not only in relation to aging but also disease processes. A natural limitation of SBML modelling lies not only in the translation of biophysical interactions into biomathematical equations, but also in the availability of clinical data to use to inform the values of parameters in the model. However, despite these limitations it is possible to generate useful systems models of aging-related neurodegenerative processes, which may be expanded and potentially used by clinicians as prognostic aides.
We used a variety of Michaelis-Menten and Hill type rate equations to generate a simple steady state model linking resting cortisol levels with hippocampal output. The effects of aging were simulated using a variety of parameters including neuronal loss, a decrease in growth factors, and simulated producing a gradual decrease in HA and HV, at levels not reported to produce cognitive impairment or dementia.
A simulation of the effects of acute increases in plasma cortisol over time produced a decrease in hippocampal activity of 30% and atrophy of 20% by age 90 years. While a chronic elevation of cortisol levels produced a greater decline in hippocampal activity; 40% and greater loss in hippocampal volume 25% – suggesting a chronic elevation in cortisol may be more detrimental in this system rather than an acute elevation. Interestingly the effects of a biological intervention were found to attenuate the effects of chronic cortisol on the hippocampus more greatly than for acute cortisol elevations. Whether or not this in silicointervention is reflecting a real biological process remains to be tested. In theory cognitive impairment associated with a chronic elevation in plasma cortisol may be as a result of structural tissue damage, or transient receptor activation and up-regulation, remodelling of GC associated synapses or simply reflecting a heightened multi-systemic ageing-processes in susceptible older individuals involving a general decrease in health.
We suggest it would be interesting to clinically assess the circulating levels of cortisol at regular intervals in non-cognitively impaired older people who may be at risk of AD. A prospective study should more fully consolidate the link between plasma cortisol levels and cognitive function in older people, in tandem with the use of models such as this, to ascertain if the extrapolated hypothetical effects of increased cortisol level in the elderly are mirrored by clinical changes in cognition. Furthermore, we realise that this paper is framed on the concept that cortisol may induce hippocampal dysfunction. However, hippocampal dysfunction induced by disease processes may uncouple negative feedback by the hippocampus to HPA and alter regulation of cortisol. Hippocampal lesions in Rhesus monkeys alter circulating plasma cortisol levels [3, 24]. Therefore it may be interesting to study patients with familial AD, which should not be associated with cortisol as a risk factor, so as to understand if hippocampal related disease processes may be the a priori event, which subsequently causes deregulation of cortisol synthesis by the HPA, initiating a self-propelling degenerative process involving ever increasing cortisol levels and increasingly dysfunctional hippocampal neurons.
The physiological system modelled is delineated in a simple physiological diagram and flow chart designed to show the relationship between cortisol and hippocampal function (Fig 1a and 1b). SBML was then used to tie together the physiological variables in the model using biochemistry based mathematical questions relating to enzyme substrate reactions (Michaelis-Menten) and receptor ligand interactions (Hill).
The HPA-axis is one of the most studied biological systems and based on available knowledge, a large number of mathematical models of the HPA-axis have been generated [25, 29]. Such models have focused on recreating the circadian and ultradian rhythms associated with cortisol secretion over 24 hour oscillations. In this paper we were interested in modelling the effects of elevated cortisol levels on hippocampal function over a forty year period. As people age, while it recognised that the circadian rhythms of cortisol secretion are flattened with altered phase and amplitude in older people [30, 31]. In older people with chronic stress disorders, such as post traumatic stress disorders, and in older people with cognitive impairment, cortisol levels are found to be elevated above the normal diurnal or circadian levels . Thus the natural rhythms in cortisol secretion were not focussed on in this first model, rather the impact of age, negative feedback and stress were the main features of the model.
There were two principal model outcomes which we were interested in and which relate to clinically described end points in patients with elevated cortisol levels. The first parameter was hippocampal volume (HV)- indexed to hippocampal atrophy, which was a gross measure of decreased neuronal density and dendritic arborisation. The second parameter as hippocampal output (HO); defined as the combined interaction of CA1 excitatory, inhibitory and aging related signals. The CA1 neuron layer is the major output neuronal subfield in the hippocampus. This parameter does not represent hippocampal output in general; rather a simple measure of its temporal activity particularly in relation to AD and declarative memory.
Parameter changes to simulate stress and ageing
Ageing Parameter Changes
1.6 × 10-6
8.1 × 10-6 at 60 years
5.3 × 10-5 at 80 years
2.5 × 10-6
9 × 10-6 at 60 years
3.4 × 10-6 at 80 years
Acute Stress Intervention
Hippocampus Output Chronic Stress Intervention
2.4 × 10-3
Increased default value every year by 5.0 × 10-5 from 60–80 years then reduced parameter by 3.24 × 10-5 to mark cessation of chronic stress
Hippocampus output Acute Stress Intervention
2.4 × 10-3
Increased default value every year by 3.0 × 10-5 from 60–80 years then reduced parameter by 2.50 × 10-5 to mark cessation of chronic stress
Hippocampus Output Acute Stress Intervention
2.4 × 10-3
Increased default value every year by 1.55 × 10-5 from 60–80 years then reduced parameter by 2.50 × 10-5 to mark cessation of acute stress
Hippocampus output chronic stress intervention
2.4 × 10-3
Increased default value every year by 2.05 × 10-5 from 60–80 years then reduced parameter by 1.5 × 10-5 to mark cessation of chronic stress
Hippocampus output with PA intervention for acute stress
2.4 × 10-3
Decreased value used for acute stress intervention by 2.8 × 10-5 on 60 years 3.0 × 10-6
Hippocampus Output with PA intervention for chronic stress
2.4 × 10-3
Decreased value used for acute stress intervention by 1.0 × 10-5 on 60 years and 80 2.5 × 10-6
Hippocampus Volume With PA intervention for chronic stress
2.4 × 10-3
Decreased value used for acute stress intervention by 5 × 10-8 on 60 years and 80 years 5 × 10-5
Hippocampus Volume With PA intervention for acute stress
2.4 × 10-3
Decreased value used for acute stress intervention by 3.0 × 10-6 on 60 years and 80 8.0 × 10-8
Model Species and Initial Values
Adrenal cells sink
35 pg/mL (Jacobi, Titze et al. 2001)
15 μg/dL (Jacobi, Titze et al. 2001)
Denditic Growth Factors
Denditic Growth Factors Sink
Active GR receptors
Active GR receptors sink
1.4 × 104 (Goncharuk, Van Heerikhuize et al. 2002)
Hypothalamus secretory cells sink
Hypothalamus secretory cells
Hippocampus Tissue Area
Hippocampus output sink
Active MR receptors
Sink for MR active receptors
Neuronal branching; Dendrites
Neuronal branching dendrites sink
Neuronal Growth factors
Loss of neuronal growth factors
Population of neurons in the CA1
4.85 × 107 (Simic, Kostovic et al. 1997).
Decline in neuronal population of cells
Pituitary secretory cells
1.0*107 (Trouillas, Guigard et al. 1996)
Pituitary secretory cell sink
Synaptic inhibitory spikes sink
Trophic Factors Sink
Model Kinetics and Rate Constant Values.
Rate constant for generation of CRH
3.8 × 10-1
Rate constant for generation of ACTH
1.085 × 10-1
Rate constant for generation of cortisol
2.4 × 10-3
Rate constant for the degradation of cortisol.
8.5 × 10-3
Saturation level of inhibition for hypothalamic cells
Saturation level of inhibition for pituitary secretory cells
Dissociation constant for cortisol in the hypothalamus
Dissociation constant for cortisol in the pituitary
Concentration of cortisol at which GR receptors are 50% saturated.
1 × 108
Concentration of cortisol at which MR is 50% of its max
2.5 × 103
Rate constant for the deactivation of MR receptors
Rate constant for the inhibition of CA1 neurons by MR receptors.
4.99 × 10-2
Rate constant for degradation of GR activity
4.45 × 10-1
Rate constant for stimulation of CA1 neurons by growth factors.
10 × 10-8
Rate constant for death of neurons.
4.5 × 10-2
Rate constant for neuronal growth factor decline.
Rate constant for stimulation of NBD
5 × 10-2
Rate constant for stimulation of synaptic excitatory signals.
Rate constant for stimulation of synaptic firing
Rate constant for stimulation of synaptic output.
Rate constant for stimulation of hippocampal output.
Rate constant for degradation of synaptic output
5.5 × 104
Rate constant for inhibition of synaptic firing by synaptic inhibitory signals.
2.2 × 10-1
Rate constant for production of synaptic inhibitory signals.
4.45 × 10-1
Rate constant for stimulation of synaptic firing.
Rate constant for decline in synaptic inhibitory signals
3.8 × 10-1
Saturation level of inhibition for hypothalamic cells
Saturation level of inhibition for pituitary cells
Maximum rate of activity of MR receptors
1 × 102
Maximum rate of activity of GR receptors
1 × 102
Hill coefficient for GR receptor Activity
Hill coefficient for MR receptor activity
Volume of Hippocampus
1 HPA Regulation of Cortisol Secretion
2 Cortisol's Interaction with MR and GR Receptors
3 Aging of CA1 neurons and cortisol stimulation
4 Excitatory Input Synapses
5 Inhibitory Input Synapses
6 Aging related changes in Synaptic Current [Is]
7 Synaptic Output
8 Hippocampal Atrophy
9 Hippocampal Tissue Output
Firstly the system model was brought into a steady state, and the initial hippocampus output was set at 100% which is a mathematical representation of activity, and does not refer to the cognitive ability of the in silicoindividual modelled in this paper.
The response to stress was examined by using events in SBML designed to mirror physiological responses to stress. The first event triggered an increase in the reaction rate kcrh, which raised the secretion of CRH. This in turn precipitated an increase in ACTH, followed by an increase in plasma cortisol. The second event returned kcrh to its original value after a short period of time which produced a yearly increase in cortisol. kcr was not returned to its original value after each event in order so as to represent stress and ageing altering the ability of the HPA-axis to recover from repeated challenges which reflects the clinical hypothesis that ageing impairs homeostatic adaptations of cortisol secretion to stress.(31).
We acknowledge Daryl Shanley, Carole Proctor and Arthur E Oakley for their technical and neuro-anatomical expertise and advice. MT Mc Auley was funded by an EPSRC CASE studentship with Unilever. VM Miller was funded by the Alzheimer's Research Trust UK.
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