doulos's project write

8/3/2019 Doulos's Project Write

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Bachelor of Medical Science (Hons.)

Third Year Research Project

Developing a Mathematical Model of

Agonist Action at Ligand Gated Ion

Channels


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Doulos Tam 932073

Supervisor: M. Keen


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Abstract:

Efficacy and affinity are terms used to describe the effects of agonist on receptors. By using

mathematical models of ligand gated ion channels, the effects of altering efficacy and affinity of

agonists on the system are observed. This contributes towards the understand of the meaning of

efficacy and affinity of drugs. Therefore, mathematical models are very useful for researchers to test

hypothesis on interactions between receptors and ligands. There are two criteria determining the

appropriateness of the model. Firstly, the model has to be reflecting the biological system as closely

as possible. Secondly, the model should be as simple as possible. The two models used in this study

are both for modeling ligand gated ion channels. Model 1 is more simple than Model 2, but Model 1

doesn't allow binding of allosteric modulators onto receptors. Therefore, in situations where

allostersic modulators are involved in the system, Model 1 is useless, but Model 2 can be used.

When, however, researchers want to model a system with only agonist and receptors, Model 1 is

preferred as it is simpler.

The results produced is suggesting that Model 1 is useful in modeling the effects of changing

agonist efficacy, changing agonist affinity and changing initial receptor number on a ligand gated

ion channel system without allosteric modulation. Model 2 is useful in modeling the effect of

changing positive modulator strength, changing positive modulator affinity and changing receptor

desensitization on a ligand gated ion channel system with allosteric modulations. The findings

suggest many possible future experiments that are useful to be carried out, including future

development on the two models and also experiments on different LGICs.

Introduction:

Mathematical models describe systems by using different equations to define terms that build up the

systems [15]. With appropriate softwares, those equations can be calculated to produce graphs that

predicts the behavior of the system modeled [16]. Comparison between real experimental data and


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data produced by the model is often made to test how good (i.e. how close to the real condition)

the model is [30]. A good mathematical model is useful in predicting changes of the system caused

by different conditions (e.g. binding of agonist or allosteric modulators on receptors) [2, 15]. And

the better the model is, the more reliable is the prediction made [15, 30]. Therefore, developing a

good mathematical model is helpful in expanding our knowledge in pharmacology, and thus have

the potential to facilitate rational drug design (Wolters, 2006).

In this particular study, the final model (Model 2) describes the behavior of ligand gated ion

channels (LGICs), especially 5HT3 receptors, in response to ligand binding under the influence of

allosteric modulator. In order to develop a good mathematical model for LGICs, we must have good

understanding of their biology.

Different types of LGICs:

LGICs are membrane proteins that have important roles in fast neural signaling and are the target of

several neuro-active drugs (Reeves et al., 2003), e.g. serotonin on 5HT3 receptors [4] and glutamate

on glutamate receptors (Dingledine et al., 1999). There are three superfamilies of LGICs: the cys-

loop receptors, ionotropic glutamate receptors and ATP-gated channels. All cys-loop receptors have

a loop, which is resulted by a disulfide bond between two cysteine residues (Connolly and

Wafford, 2004). Also, cys-loop receptors can be further subdivided into vertebrate anionic cys-loop

receptors and vertebrate cationic cys-loop receptors, depending on the charge of the ion that the

channels conduct. Vertebrate anionic cys-loop receptors include GABAA receptors and glycine

receptors. Examples of vertebrate cationic cys-loop receptors are 5-Hydroxytryptamine type 3

receptors (5HT3/serotonin receptor), nicotinic acetylcholine receptors (nAChR) and zinc-activated

ion channels (ZAC). Ionotropic glutamate receptors, including AMPA, kainate NMDA and 'Orphan'

(GluD), are activated by binding of the neurotransmitter glutamate. ATP-gated channels (P2X) are

activated by binding of ATP (Hodges et al., 2011).


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Structures of LGICs:

Although there are many different types of LGICs, they have high degrees of structural similarities

within their superfamily. Each LGIC subunits has an hydrophilic N-terminal region, which is

located extracellularly, containing many N-glycosylation sites. This N-terminal domain has been

proven to be the principal ligand binding region. Apart from the N-terminal domain, each LGIC

subunit also have four transmembrane domains, M1 to M4. It is believed that the walls of the

conducting channel are made up predominantly by M2 domains in most types of LGICs (Karlin and

Akabas, 1995; Unwin, 2000). There are extramembranous loops connecting the transmembrane

domains. M1-M2 and M2-M3 are joined by short peptide segments, usually 4 or 5 amino acids

long, much shorter than the loop joining M3-M4. The M3-M4 loops can interact with cytoskeletal

proteins and have important roles in localization of LGICs at the postsynaptic membrane and also in

some functional modulation. Fig 1 (taken from Keramidas, 2004) shows some of the charged

residues in different LGIC subunits. These charged residue located in the pore of channels affect

conductance and ion selectivity. So, Fig. 1 helps us to see the reason why different types of LGICs

can sometimes conduct the same ions (e.g. both nicotinic acetylcholine receptors and 5HT3

receptors can conduct Ca2+ ions (Haghighi and Cooper, 1998), and this fact was used in the

Flexstation experiments I explained in later sections). Other charged residues in the ligand binding

region affects the binding of agonists.

The structure of LGICs allow binding of agonists onto their binding domains. Binding of agonists

can cause LGICs to adopt a conformation with an opened channel, allowing ions to pass through.

This open or active state of LGICs is further defined by some selectivity filter that render

specificity for the protein (Beyl et al., 2007). When LGICs adopt a closed or inactive

conformation, the flow of ions is blocked. The channel proteins can spontaneously switch between

the two conformational states, and the dynamics of such switches are very important for studies of


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LGICs (Zhu and Hummer, 2010).

For cys-loop receptors, the negatively charged aspartate residue at position 11of the loop is an

anionic site that interacts with positively-charged amine group of agonists (Connolly and Wafford,

2004). The aspartate is invariant, meaning that the -electron system of agonists with a local dipole

can be oriented in the electrostatic field of the aspartate. Also, the turn of the cys-loop has a

conserved aromatic residue, which has a ring-proton that can interact with the -electron density of

agonists. Selective recognition of agonists is partly determined by the type of amino acid residue at

position 6 of the loop. Also, high affinity agonists often have electronegative atom in their -

electron system, allowing them to form hydrogen bonds with the cys-loop receptors (Jansen et al.,

2008).

The 5HT3 receptors:

The 5HT3 receptors can have two types of subunits, A and B, and can exist homo-oligomericaly

(with A subunits only) or hetero-oligomericaly (with both A and B subunits). 5HT3 receptors have

significant structural and functional homology to other cys-loop LGICs [17], and this, together with

the fact that these receptors function as homo-oligomers, suggests that 5HT3 receptor is a good

model system for understanding features of all cys-loop receptors (Reeves et al., 2003). The

opening of 5HT3 receptors allow passive transport of both Na+ and Ca2+ ions [17] (Fig . 1 gives

some ideas why these 2 types of ions get conducted) and these ion movement can lead to

depolarisation of the synaptic membrane. Central and peripheral 5HT3 receptors have some

structural (Morales and Wang, 2002) and functional differences [2]. Central 5HT3 receptors are

important in cognition, anxiety and depression (Greenshaw and Silverstone, 1997). This means that

5HT3 agonists, when used clinically, can cause a side effect of enhanced anxiety and have proemetic

effects. 5HT3 antagonists, however, are much more important therapeutic agents, because they

block perherial 5HT3 receptors and thus are effective in treating the nausea caused by cancer


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chemotherapy (Tyers et al., 1989). 5HT3 modulators have also shown therapeutic uses for treating

schizophrenia, anxiety and cognition (Thompson and Lummis, 2007).

Complexity of mathematical models:

Mathematical models can be very simple or very complex. The models that include more known

biological facts are usually more complex and closer to real conditions. Fig 2 is one of the simplest

mathematical model considered by Colquhoun (1998) [1], which only considers four basic receptor

states. This basic model assumes that channels have only two conformations, shut or open. Agonist

(A) can bind to unoccupied, closed receptor (R) forming a closed receptor-agonist complex (AR),

and the receptor can then change conformation to open state with agonist still bound (AR*).Also,

the model allows closed receptor to open without the binding of agonist (R to R*), as observed in a

few experiments with native receptors (Jackson 1994). Binding of agonist directly to the opened

receptor is also possible in the model. This simple model is easy to understand, but it doesn't take

into account of many known characteristics of LGICs and therefore is not a very accurate

simulation. Colquhoun (1998) [1] also considers the Monod-Wyman-Changeux scheme (Fig 3),

which uses all the assumptions made in the above model, but also takes into account that most

LGICs (e.g. muscle type nicotinic acetylcholine receptor) have two binding sites [1] and, therefore,

describes the system with 6 different receptor states. This particular scheme allows a second agonst

molecule to bind to both the closed receptor-agonist complex (AR) and the opened receptor-

agonist complex (AR*), forming a new closed or opened receptor-agonist complex with two

agonist molecules bound (A2R or A2R*).

In contrast to those simple models described above, more complex models often can involve over

20 equations. Examples include: (i) the cubic ternary complex receptor-occupancy model (Weiss et

al., 1996) that considers G protein coupled receptors with eight states and involves 26 equations;

and (ii) the ligand-receptor-G-protein ternary complex (Broadley et al.,2000) that involves 29


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equations.

Binding of allosteric modulators:

Apart from binding of agonists, binding of allosteric modulators can also cause conformational

change on LGICs. Allosteric modulators bind to allosteric binding sites and allosteric binding alone,

(without agonist) seldom causes opening of LGICs (Chang et al., 2010). However, they causes

conformational change of the channels that can facilitate (positive modulator) or inhibit (negative

modulator) binding of agonists, and also can have effects on channel opening and receptor

desensitization. For 5HT3 receptors, examples of positive allosteric modulators include

trichloroethanol [4] and 5-hydroxylindole [5, 10]. In contrast, verapamil is an example of negative

modulator on 5HT3 receptors [2]. One important allosteric binding model was a ternary complex

model of allosteric action on muscarinic acetylcholine receptor (Lazareno and Birdsall, 1995),

which is a G-protein coupled receptor (GPCR). The model simulates the allosteric action of two

competitive ligands (agonists) and one allosteric modulator, and the receptor was considered to

have one binding site for agonist and another for allosteric agents. It was assumed that the agonist

and allosteric modulator can bind stimultaneously. This model allows a ligand to change in its

affinity when the receptor is bound to another type of ligand. Later, the model was used to

bidirectional allosteric binding to glycine receptors (Biro and Maksay, 2004), which are LGICs, and

then, Maksay et al., 2005 (Fig. 11) described the first application of allosteric model to 5HT3

LGICs. The particular model assumes that a radiolabelled antagonist, an allosteric modulator and

agonists can bind simutaneouly to 5HT3 receptors. It was found out that the model can simulate not

just the effects of a positive allosteric modulator on the 5HT response on 5HT3 receptor, but also

the effects of negative allosteric modulators. This was an important development as it was great

potential in helping in vitro development of allosteric modulators for 5HT3 receptors (Maksay et al,

2005) and also later development of allosteric models. Fig. 11 shows that the Maksay model is an

equilibrium model, which is different from the 2 models I used (they are both steady state models).


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Also, the Maksay model was used mainly to look at binding (Maksay et al, 2005), while I used

my models to look at function.

Desensitization of LGICs:

It is now known that LGICs can have three main states. The closed state, the opened state and

the desensitized state [18, 19]. As mentioned before, LGICs are usually in the closed state without

the binding of agonists, and can turn into opened state in ~20s after agonist binding, and then can

turn back to closed state again when the agonist dissociates [18]. When LGICs are continually

exposed to a reasonably high concentration of agonist, they can change to the desensitized state

with agonist still bound. In the desensitized state, the channels are non-conducting and are unable to

be re-activated (i.e. cannot turn directly from desensitized state to opened state). It is thought that

only after the dissociation of the bound agonist, the channels can turn back to the inactive, closed

state [18, 19]. Many allosteric modulators of LGICs can affect desensitization of the channels, e.g.

5-hydroxyl indole that slows desensitization of 5HT3 receptors [5, 10, 17], trichloroethanol that

increases desensitization of 5HT3 receptors (Lovinger and Zhou, 1993) and aniracetam that slows

densensitization of glutamate (AMPA) receptors [37]. The Maksay model shown in Fig. 11 does

not consider desensitization so cannot be used to simulate the effects of modulators slowing

receptor desensitization.

Trichloroethanol and 5HT3 receptors:

Trichloroethanol can interact with 5HT3 receptors as a positive allosteric modulator (Hu and

Peoples, 2007; Lovinger and Zhou, 1993). It has been suggested that loops 2, 7 and 9 and also the

transmembrane domain 2-3 loop are the structures in 5HT3 receptors that have important roles in

allosteric modulation with trichloroethanol (Hu and Peoples, 2007). It is believed that

trichloroethanol is inducing the positive modulation by increasing the efficacy of 5HT on 5HT3

receptors (Lovinger and Zhou, 1993), i.e. the binding of trichloroethanol facilitate the transition of


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5HT3 receptors from closed to open states. Researchers have tried adding trichloroethanol with a

range of different concentrations of 5HT into cells expressing 5HT3 receptors(Lovinger and Zhou,

1993) and then measuring the inward currents induced. It was found that trichloroethanol increase

the peak current amplitude significantly with 1M of 5HT, but have a lower percentage increase

with 5M of 5HT. This may be because that the rate of transition from closed to open state of 5HT3

receptors are reaching maximal, so the effects of trichloroethanol is less significant. However, it

seems that a high concentration of trichloroethanol (>5mM) is also increasing the rate of

desensitization of 5HT3 receptors (Lovinger and White, 1991; Lovinger and Zhou, 1993). As

desensitized 5HT3 receptors are much less sensitive to trichloroethanol, using high conentrations of

trichloroethanol can result in a complete loss of trichloroethanol action within seconds (Lovinger

and Zhou, 1993).

Advantages and disadvantages of mathematical models:

With increasing computational power and improved data collection methods, there is an increasing

use of mathematical models in recent years (Batzel J. et al., 2009; Glaser and Bridges, 2007). Good

mathematical models are very useful in exploring new experimental possibilities (Batzel J. et al.,

2009; Satulovsky et al., 2008). This is because editing a model is much quicker and easier than

changing experimental settings for real experiments that does not work as expected. The situation is

similar with identifying errors and errors correction. When doing real experiments, human errors

can often happen. Therefore, when expected results are not observed, researchers often have to

repeat the experiment many times before even noticing the errors. This also means that any attempts

to improve chosen method and to reduce human errors would take much time. In the case of

mathematical model, modern software has allowed graphical data to be produced quickly and,

therefore, any errors can usually be noticed and corrected within a short period of time. These are

some advantages of mathematical models, but not their main use. The main use of models is for

researchers to test hypotheses about how ligands and modulators affect receptors.


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It is important to note that more complex models may not always be better models, and they can, in

some cases, involve more inaccurate assumptions. In order to make models closer to real

experiments, we often need to increase the complexity of the model. However, this action of

adjusting models to perfect (having exactly the same conditions with real experiments), often

causes the models to loss the advantage of easy use. Complex models involve large number of

equations and terms, meaning that checking for errors can take lots of time and effort. Also,

complex models often have intermediate states that may not exist. Although they are added for

making the models more realistic, those intermediate states sometimes make the parameters

difficult to identify, and thus increases estimation error.

Having meaningful presentation of the data produced from models:

By using appropriate software to visualize models, graphical outputs can be produced showing any

variable plotted against another (the x-axis usually is time, or concentration of ligand). For example,

having percentage response on y-axis and ligand concentration on x-axis would create a dose

response curve. This allows meaningful presentation of the model, which is easy to interpret and

also allows direct comparison to real experimental data. Dose response curves are often fitted with

the Hill equation, which can be used to give the Hill coefficient when plotted as a Hill plot. (Hill

plot is log[(y-ymin)/(ymax-y)] plotted against log[A] [1], and the slope of the straight line it produces

is Hill coefficient.) The Hill equation cannot be used to describe any physical mechanism. It is an

empirical description (JN Weiss). This means that the fits and Hill coefficient does not give direct

information about binding or gating of receptors. However, it is still useful to work out Hill slope,

because the number of agonists required to induce a response are usually higher than the Hill slope

(Wyman and Gill, 1990) at the midpoint (e.g. Haemoglobin, with four binding sites, has Hill slope

of about 2.4). Therefore, the Hill slope gives an idea of the number of binding sites of each receptor.

Unfortunately, it is often not accurate to estimate the number of receptors' binding sites by Hill


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coefficient. Hill coefficient can estimate the number of binding sites accurately only in specific

conditions of strong positive cooperativity. Hill slope for 5HT binding to 5HT3 receptors was found

to be near 1, but never more than 2 as 5HT3 receptors have only two binding sites for 5HT. Dose

response curves for 5HT, however have Hill coeffient ~2.7 [17], suggesting

The Hill coefficient is affected by the binding cooperativity and change in receptor conformation. If

the binding of agonists shows cooperativity, (which means that the binding of first agonist increases

the binding affinity of second agonist), the Hill coefficient will be higher (steeper slope). Binding of

5HT is believed to increase binding affinity of second molecule of 5HT, so will have a relatively

high Hill coefficient. If, conversely, the binding of first agonist reduces the binding affinity of

second agonist, the Hill coefficient will be reduced. Concerted change in receptor conformation also

increases the Hill coefficient (assume no cooperativity, i.e. first binding affinity = second binding

affinity).

Aims:

The main aim of this project is to develop a mathematical model that simulates the behavior of

5HT3 receptors in response to agonist binding with or without the presence of allosteric modulators.

Hopefully, a better understanding of LGICs can be developed from the model. Also, a further aim is

to see how realistic the model is at describing changes (e.g. changing modulator strength, affinity

and receptor desensitization) made to the system.

A better understanding of how modulators affect LGICs may have clinical implications. One ideal

example is to find ways to inhibit 5HT3 receptors by binding of allosteric modulators, and thus to

reduce schizophrenia and anxiety.


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Methods:

Model 1:

The Monod-Wyman-Changeux scheme (Fig. 3) mentioned by D. Colquhoun, 1998 [1], gives the

original base for model 1. Model 1 uses all the terms in Fig 3, and includes also the desensitized

state of LGICs. In model 1, Rc represents closed LGICs; Ro represents opened LGICs; Ri

represents desensitized LGICs; A represents one molecule of agonist and A2 represents two

molecules of agonist. Threrefore, ARi represents a desensitized channel bound to a first agonist.

Similarly, A2Ro represents a closed channel bound to two agonists. Same as Fig. 3, both the closed

channel (Rc) and the opened channel (Ro) can bind to agonist, and the agonist bound can dissociate

from the channels. The channels with one agonist bound (ARo and ARc) can have a second agonist

binding to them and also, the second agonist can disassociates from the channel. All channels at

closed state can change to open state, and also the reverse.

Different to the original scheme, Model 1 assumes that all opened LGICs, bound or unbound to

agonists (Ro, ARo and A2Ro), can become desensitized. However, the desensitized channels (Ri,

ARi and A2Ri) cannot be re-activated [18, 19]), so there are arrows pointing from the opened

channels to the desensitized channels, but not the reverse. This characteristic of receptor

desensitization in LGICs are supported by the fact that there are no evidence of channels opening as

they recover in single channel recording (Sivilotti, 2010) . Also, the desensitized channels (Ri, ARi

and A2Ri) can change to the normal closed channels (Rc, ARc and A2Rc), but not the reverse.

Therefore, Model 1 considers the system to have 9 receptor states, bit more complex then the

scheme in Fig. 3.

Model 2:

Model 2 is developed from Model 1. Model 2 uses all the assumptions and terms of Model 1, and


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has a new assumption that all of the 9 receptor states in Model 1 can have allosteric modulators

binding to them. M represents allosteric modulator. Therefore, MA2Ro represents opened LGICs

with two molecules of agonist bound to the ligand binding region, and also a molecule of allosteric

modulator bound to the allosteric binding site.

Model 2 is quite complex, involving 18 differential equations and many parameters (see appendix).

In order to see whether Model 2 can be used to mimic the effects of modulators in real experiment,

a few Flexstation experiments were done.

Performing a Flexstation experiment:

The first step of all my Flexstation experiments is to culture cells that express 5HT3 receptors and to

get the correct concentration of cells in each well of the 96well plate (each well contains ~1x10^5

HEK3A cells). These cells were prepared for me by Lawrence Wooley, a student in the University

of Birmingham. The cells were then incubated for ~20 hours in an incubator at 37oC. After the

incubation, the supernatant in the cell plate were all removed. This is to remove all the serum in

culture medium that can bind to drugs and thus affects results. 200l of HBSS was then added to

each well and removed again. Hank's Balance Salt Solution (HBSS) is a salt solution containing

Kcl, NaCl and other salts. The HBSS used was prepared before the washes, having the conditions of

1x concentration with pH~7.4. This step was to make sure that all culture medium were washed

away and was repeated 2 times. After the 2 washes, 100l of HBSS containing ~0.1M of a special

compound, Fluo4-Ag, is pipetted into each well. The Fluo4-Ag has an ester, so it can diffuse into

cells through membranes. Inside cells, the Ag is cut off from the compound and Fluo4 can't diffuse

out of cells. When Ca2+ ions enter cells, they bind to the Fluo4 and changes the fluorescent

wavelength. This fluorescent signal can be detected by the Flexstation machine. The fluorescent

level should be proportional to Ca2+ influx, which is proportional to channel opening and so it is

showing the level of response. As the process is pH dependent, it is important to make sure that the


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pH of HBSS is ~7.4 (add NaOH to increase pH; add HCl to decrease pH). After adding the Fluo4-

Ag to the cells, the cell plate was covered with aluminum foil (Because exposure to light would

reduces the florescent signal) and was then left for 1 hour. After the hour, a reasonable amount of

fluo4-Ag should have diffused into cells. Therefore, 200l of HBSS was then added to each well

and removed again to remove all the excess Fluo4-Ag. This washing step was repeated for 2 times.

After the two washes, 100l of HBSS was then added to each well to keep cells alive, and then the

cell plate was left for 30 mins (remain covered in foil). After the 30mins wait, the cell plate was

ready for Flexstation. Apart from the cell plate, a drug plate was also essential for a successful

Flexstation (see appendix for the drug plate plan). The Flexstation machine can add the drug from

the drug plate to the cells automatically and then monitor the response in each well for 6 mins.

Therefore, the correct concentrations of drugs need to be worked out and put into the drug plate.

When both plates were ready, they were put into the Flexstation machine. By using the computer

software, SoftMax Pro, the Flexstation machine can be set to put in the drugs into correct wells

automatically. Plate plan 1 (Fig. 4) and plate plan 2 (Fig. 5) shows the final concentrations of drugs

acting on the cells, drug plate plan 1 (Fig.6) +drug plate plan 2 (Fig. 7) shows the working

concentrations of drugs that is prepared in the drug plates.

The 4 drugs that I used were: Carbachol, 5HT, trichloroethanol and 5-hydroxyl indole. Carbachol is

a selective agonist that affects both muscuranic (Yuan et al., 1998) and nicotinic (DeLorme and

McGee, 1988) acetylcholine receptor. The opened nAChR conducts Na+, K+ and also Ca2+ ions

(Haghighi and Cooper, 1998). Therefore, carbachol can induce a response (because response in this

experiment is determined by the increase in intracellular Ca2+ concentration) that is not caused by

opening 5HT3 receptors, and thus is an important control. 5HT is an agonist for 5HT3 receptors.

The adding of 5HT into the cells expressing 5HT3 receptors would be expected to cause channel

opening and influx of Ca2+ ions into cells. Both trichloroethanol and 5-hydroxyl indole are positive

modulators for 5HT3 receptors. Therefore, the adding of these two drugs into cells before adding


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5HT should cause the maximal response induced by binding of 5HT to increase. 5-hydroxyl indole

alone doesn't really induce any response, but trichloroethanol at concentration of ~10mM can cause

a small response [4].

Flexstation experiment 1:

In my first Flexstation experiment, all of the four drugs mentioned above were used (see Fig. 4 for

the final concentration of each drugs in each well). The aim of this experiment is to plot dose-

response curves showing the effects of the two different positive modulators on 5HT response. Two

different concentrations of 5HT (300nM and 3M) were used in combination with the two

modulators of a ranged of concentrations. In the first 3 columns of the 96well plate, there is 300nM

of 5HT in the prescence of trichloroethanol in each well. Column 4-6 contain 300nM of 5HT in the

presence of 5-hydroxyl indole. Column 7-9 contains 3M of 5HT with trichloroethanol. Column

10-12 contains 3M of 5HT with 5-hydroxyl indole. The effective dose of trichloroethanol is

roughly from 0.3mM to 30mM [4]. Therefore, the concentrations used are ranged from 30M to

30mM, which should show the minimal response and also the maximal. The effective dose of 5-

hydroxyl indole is roughly around 1mM. Therefore, the range of concentrations of 5-hydroxyl

indole used in this experiment were also from 30M to 30mM. Both modulators, trichloroethanol

and 5-hydroxyl indole, were added to cells at 20s after the Flexstation starts recording the response.

5HT was added at 80s, and carbachol was added at 320s. In drug plate 1 (Fig. 6), it is showing that

the working concentration of the modulators are three times more than the final concentration aimed

in plate plan 1. This is because the Flexstation machine was set to pick up 50l of modulators from

drug plate at 20s and pipette into each appropriate well in the cell plate. At that moment of time

(20s), all the wells should contain 100l of HBSS already (as mentioned above in the preparation of

cell plate). So, the 3x concentration of modulators in drug plate will become the final concentration

when mixed with the 100l HBSS in cell plate. Similarly, before 50l of 5HT was added, the wells

already contain 150l, so working concentration of 5HT in drug plate has to be 4 times the final


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concentrations. The 50l carbachol was added last, so its working concentration has to be 5 times

the final concentration. This Flexstation was repeated 4 times and the average result was used to

plot a dose response curve.

Flexstation experiment 2:

Also, I did another Flexstation with just 5HT, 5-hydroxy indole and carbachol (See Fig. 5). The aim

of this Flexstation is to see the effect of 5-hydroxyl indole on 5HT3 receptor desensitization.

Therefore, I used two different concentrations of 5-hydroxyl indole (3M and 3mM) with one

concentration (3M) of 5HT for the entire plate. The carbicol (concentration = 5mM) response

again act as a control. Column 1-6 have 3mM of 5-hydroxyl indole with 5HT in each well; Column

7-12 have 3M of 5-hydroxyl indole with 5HT. Again, 5-hydroxyl indole was added to the cells

first at 20s, 5HT was then added at 80s, and carbachol is added last at 320s (See Fig. 7, which

shows drug plate 2).

Using Berkeley Madonna:

Berkeley Madonna, shareware version, was the software used to visualize Model 1+2. This software

is able to solve systems of ordinary differential equations. The first step of performing any

experiment with those models was to derive differential equations from the model. The second step

is to type in a value for all the terms involved in the equations (must make sure that the equations

are balanced). Also, to define some of the terms in more biological meaningful ways, additional

equations that doesn't alter the model were added to state the relationship of different terms. (Please

see appendix for all the terms and equations typed into the software) Then, by clicking run,

graphical results were produced (The software automatically uses time as the x-axis, but y-axis can

be set to show any parameter in the equations).

Simulations using Model 1:


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The aim of the first simulation using Model 1 was to see the effect of changing agonist efficacy on

the LGICs system. The range of efficacy value (E2) used was from 10^-2 to 10^4. With each efficacy

value, the system was run with ligand concentrations ranging from 2x10^-5M to 2x10^5M. Each run

was performed for 10seconds and I recorded the maximum response of each ligand concentrations.

Therefore, a dose-response curve can then be plotted for each efficacy value.

The second simulation is to model the effect of changing agonist binding affinity on the system.

Therefore, the original affinity values were set as the starting binding affinity of agonist. This was

then increased by 10x in every curve, up to 10000x.

The third simulation of Model 1 involves changing the initial number of receptors to see the effect

of it on the LGICs system. Dose-response curves were produced from this experiment.

Simulations using Model 2:

Model 2 allows simulation of the effects of modulators on LGICs. The first simulation of Model 2

was changing the characteristic of modulators into positive modulators with increasing power. In

the starting values of Model 2, the binding of modulator was set to increase the response induced by

agonist. A low value of positive modulator strength is set to be the 1x positive modulator strength.

By increasing the positive modulator strength step by step until 500x positive modulator strength,

dose-response curves for different modulator strength were then constructed using a range of

modulator concentrations from 10M to 100mM (Agonists concentration is kept constant).

The second experiment of Model 2 was done by changing the modulator binding affinity. A range of

different modulator binding affinity was used, from 1x modulator binding affinity to 10000x

modulator binding affinity. The agonist concentration is again kept constant. By recording the

maximum response of each modulator concentrations (10M to 100mM), dose-response curves


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were constructed.

I also tried using two different concentrations of modulators (3mM and 30mM) with a range of

agonist concentration to construct dose-response curves. The agonist concentrations used were

ranged from 1M to 0.3M.

KaleidaGraph4.0 was used to work out the Hill coefficient of the dose-response curve. This allows

comparison of output to experimental data.

Results

Fig. 12 shows the effect of changing agonist efficacy on the system simulated by Model 1 (Fig. 8).

In this Model, response is assumed to be a function of stimulus. It is assumed that the total number

of opened channels, S, equates to stimulus. This is because only opened LGICs can conducts ions,

but not closed and desensitized ones.

In Fig. 12, it is clear that with higher efficacy values (E2 is the main efficacy term that is defined by

E2=ko2/kc2. Increasing the efficacy in here means increasing the ko2 value and keeping the kc2

value constant, thus causes E2 to increase), the agonists are inducing higher response. This

correlates with the fact that, in real experiment, full agonists (with higher efficacy) produces higher

response than partial agonists (lower efficacy). Fig. 12 shows that increasing the efficacy value in

this model is reducing the effective dose of the agonist (i.e. causing the curve to shift left). This

means that agonists with different efficacy values are all having slightly different EC50 values. The

EC50 of the curve showing highest efficacy (E2=10^4) is 20mM, lower than all the others.

Therefore, it can be concluded that, in Model 1, increasing efficacy values is causing upward shift

of the dose-response curve, and also decreases the EC50 (causing curves to shift left). When the

system produces maximal response (with 20M of agonist), it is having the highest number of


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opened channels but not necessarily all the channels are opened (some maybe desensitized). The

amplitude of the maximal response is affected by many factors, including the concentration of

agonist, the initial number of receptors and the rate of transition from opened to desensitized

channels (desensitization). Therefore, increasing the agonist concentration further doesn't further

increase the response after reaching maximal is because of the other limiting factors: (i) maybe

because no more LGICs are present to be opened to increase response; or (ii) it maybe because

channels are turning into desensitized state. With low number of initial, closed channels, even with

excess agonist, no closed channels are available to be opened by agonist binding, so response is

limited. The amplitude of maximal response can be decreased by increasing the desensitization

terms (kds0, kds1 and kds2). This is because desensitized channels cannot change directly into

opened channels, instead have to change to the closed state first. So, increasing the rate of

desensitization can reduce response.

Figure 13 shows the effects of altering the agonist binding affinity on the system. The terms for

agonist binding affinity are Ka for the binding of the first agonist on LGICs and Ka2 for the binding

of a sencond agonist. The starting Ka value is 2*10^-3; and Ka2 is 5*10^-4. It is observed that the

increase in binding affinity causes a decrease in EC50 in the dose-response curves, but the maximal

response induced is kept roughly constant (at ~50%). When 10000x binding affinity was used, the

dose-response curve has EC50 of about 2M, much lower than the 2M with the starting binding

affinity.

Figure 14 is showing the effects of changing initial receptor number on the system. The highest

number of receptor number used was 10^8, and the lowest was 10^2. By increasing the number of

initial receptor number, the dose-response curves shift left and have maximal response with higher

amplitude. The leftward shift of curves means a decrease in EC50. Therefore, this model tends to

give maximal response earlier in higher initial receptor number. With 10^6 receptors, EC50 was


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~10^-2M, much lower than the ~1M with 10^2 receptors. The parameters in Model 1 assumes that a

small amount of closed receptors can change to opened state without binding of agonist. Therefore,

an increase in initial receptor number would allow more opening of receptors without agonist

binding. The opened receptors can conduct ions and induce response. This increase in response is

unrelated to agonist concentration, but depends on the rate of transition from unbound, closed

receptors to unbound, opened receptors and also initial receptor number. This explains the leftward

shift. The increase in the maximal response is an expected result, because increasing the initial

receptor number provide more closed receptors for agonist binding, so more agonists can bind

receptors, and more receptors can be in opened state to conduct ions and thus, maximal response is

increased.

Figure 15 has dose-response curves showing the effect of increasing positive modulator strength in

Model 2. In this section, I chose to increase Emo1 and Emo2 to increase modulator strength.

Emo1=kom1/kcm1 and Emo2=kom2/kcm2. Therefore, by increasing kom1 and kom2, and at the

same time keeping kcm1 and kcm2 constant, would increase Emo1 and Emo2. This increases the

rate of channel opening for channels that are bound to both MA(one modulator, one agonist) and

MA2 (one modulator, two agonists). The agonist concentration in this part of the experiment was

kept constant at 10mM. When no modulator was involved, the % response was constant at ~40%.

40% response, therefore, must be the basal response caused by agonist alone binding to LGICs.

With a weak positive modulator (1x modulator strength), there is only a very small increase in %

response at high modulator concentrations (over 1mM). Increasing the strength of positive

modulator causes the increase in % response to start at lower concentrations and the peak of ~99%

response was reached at lower concentrations of modulator with the higher positive modulator

power. With the 500x modulator strength (strong positive modulator), the % response start to

increase before 10M of modulator concentration. This increase starts much lower than the 1mM in

the case of 1x positive modulator strength (weak positive modulator). Also, with 500x modulator


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strength, the maximal response was reached at ~10mM modulator concentration, lower than the the

ones with lower modulator strength. This means that the increase in modulator strength cause not

just increase in maximal response, but also shift curves to the left (i.e. decreases the EC50).

Figure 16 is showing dose-response curves that show the effect of changing modulator binding

affinity, Kmc0, Kmc1 and Kmc2, in Model 2. Kmc0=kmcr/kmcf, Kmc1=kmcra/kmcfa and

Kmc2=kmcra2/kmcfa2. Therefore, increasing modulator affinity means increasing kmcra and

kmcra2, but keeping kmcfa and kmcfa2 unchanged. This increases the rate of modulator binding to

closed receptors (with or without agonists). Again, the agonist concentration was kept constant at

10mM, giving a basal 40% response. The curves all have similar shape and slope. The increase in

modulator binding affinity shifts curves to the left. This means that the higher the affinity of

positive modulator, the lower the concentration needed to cause an increase in % response. Also,

with higher affinity, just maximal response is reached at lower modulator concentrations.

Figure 17 shows dose-response curves obtained from the first Flexstation experiment. With the

higher agonist concentration (3M of 5HT), the basal response is higher than that with lower

agonist concentration (300nM of 5HT). Also, the trichloroethanol seems to be more potent than 5-

hydroxy indole as trichloroethanol starts to increase the 5HT response at lower concentration

(Trichloroethanol starts to increase the 3M 5HT response at a concentration of 30M, much lower

than the 1mM with 5hydroxylindole). The Hill coefficient for trichloroethanol and 5-hydroxyl

indole is quite similar (~1.5 and ~1.6), suggesting that the cooperativity of the two modulators is

almost the same. At lower concentration of agonist (300nM of 5HT), both modulators show some

increase of response, but is a much lower compare to the 3M of 5HT. This suggests that both

modulators, especially 5-hydroxyl indole, when alone, has tiny effect on increasing a response. It is

when agonists bind to channels, the modulator can help increasing the amplitude of response

induced by agonist binding.


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Figure 18 shows results from the second Flexstation experiment. With 3M of 5-hydroxyl indole,

3M of 5HT causes the fluorescent level in cells to increase from ~11000 to ~20000 in ~7s. This

response is caused by binding of 5HT to 5HT3 receptors, leading to opening of 5HT3 receptors and

the influx of Ca2+. The Ca2+ ions interacts with the Fluo4 inside cells (see method) causing the

fluorescent level to increase. The fluorescent level then stays at maximal (~20000) for ~3s. The

fluorescent level than decreases back to the basal value of ~11000. This decrease is believed to be

caused by the desensitization of 5HT3 receptors. When the receptors changed from its opened state

into the desensitized state, they become non-conducting, and the Ca2+ ions inside cells are then

transported out of cells. Therefore, the desensitization of 5HT3 receptors cause the intracellular

Ca2+ concentration to decrease back to normal level and thus the fluorescent level drops back to the

basal value. With the higher concentration of 5-hydroxyl indole, the basal value is still ~11000, but

the maximal response is ~31000, much higher than before. This suggests that 5-hydroxyl indole

(when used with 5HT) is a positive modulator of 5HT3 receptors and its effective dose is around 1

mM. Also, the desensitization of 5HT3 receptors seem to be slower when a higher concentration of

5-hydroxyl indole is present. This is shown by the slower decrease of fluorescent level (The slope

less steep when higher concentration of 5-hydroxyl indole used). The higher concentration of 5-

hydroxyl indole (3mM) causes the fluorescent level to take ~100s to return to basal level, bit longer

than the ~60s with 3M of 5-hydroxyl indole.

Figure 19 was produced from Model 2. By increasing the desensitization terms, (kdsm0, kdsm1 and

kdsm2), the rate of changing from opened LGICs to desensitized LGICs in the model is reduced in

the presence of modulator. The increase in desensitization causes the maximal response to decrease.

The maximal response with highest desensitization (all kdsm values are 1000) is ~4%, much lower

than the >75% when kdsm values are 0.001. Also, increasing the desensitization causes the

maximal response to be reached quicker. When the kdsm values are all 1000, maximal response was


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achieve at ~2 seconds, quicker than the ~27 seconds with kdsm values=10. After reaching the

maximal, the desensitization causes the response to slowly decrease (because opened receptors are

turned to desensitized receptors, so less ion conductivity). Increasing the desensitization also

reduces the time that response stays at maximal. In this simulation, Kdsm0, kdsm1 and kdsm2 were

set to be equal. Meaning that the rate of changing from opened receptor to desensitized receptor is

assumed to be unaffected by agonist binding, i.e. an opened channel unbound to agonist can become

desensitized as easily as a channel with bound agonist.

Figure 20 shows a dose-response curve produced from Model 2. This figure shows the effect of

increasing the positive modulator concentration on dose-response curves of agonist. 3 different

concentrations of modulator were used (300M, 3mM and 30mM). The lowest concentrations of

modulator used (300M) was causing a response of ~30% when there is no agonist. Such response,

produced in the absence of agonist, becomes higher when higher modulator concentrations were

used (~42% with 3mM of modulator and ~72% with 30mM of modulator). This is suggesting that,

in Model 2, modulator itself is opening LGICs and causing a response. This maybe an unwanted

result, a mistake occurring with bad starting values, because allosteric modulator seldom induces

response on its own. Also, it was then found out that Model 2, with the values shown in appendix, is

inducing a response of ~5% without any modulators or agonists. This is unexpected in real

situations. With the lowest modulator concentration (300M), the agonist starts producing a

response at agonist concentration of ~1mM and then gives the maximal response at ~0.5M. With

higher concentrations of modulator, the agonist produce the initial response at slightly higher

concentrations, but they all reaches maximal response at same agonist concentration. This is

suggesting that the modulator (with the starting values used) is not affecting the binding affinity of

agonist (This is expected because the modulator was set to effect only the efficacy of agonist (Emo1

and Emo2), but not the affinity (Ka and Ka2)). There is only tiny increase in the maximal response

when the concentration of modulator increases. This is because the efficacy of agonist was set to be


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quite high, so it almost reaches 100% response even with the lowest modulator concentrations used.

By decreasing the modulator concentrations further, the maximal response should continue to

decrease. Also, it may be important to note that the positive modulator strength in this experiment

was set to be quite low (1x). i.e. the Model was simulating the effects of a weak positive modulator.

Using a stronger positive modulator may caused bigger difference in the amplitude of maximal

response. Also, increasing the concentration of modulator has also decreases the Hill slope of dose-

response curves. When 30mM of positive modulator was involved, the Hill slope is ~1.1, much

lower then the ~3.1 when 300M of positive modulator was used.

Fig. 21 shows the basal response caused by closed receptors changing to opened state without

binding of agonist or modulators in Model 1+2. These values were exactly the same for both

models. The higher the number of initial receptor, the higher the % response. This explains the

increase of basal response that occurred in Fig. 14 with increasing initial receptor number. Also, this

suggests that using a lower value of initial receptor agonist would reduce the basal response in Fig.

20.

Fig. 10 is showing dose-response curves resulted from a Flexstation experiment done by Lawrence

Wooley (a student studying in the University of Birmingham). The experiment tested the effect of

three different agonists (5HT, DDP733 and SR57227A) on 5HT3 receptors. The three drugs were

given separately to cells expressing 5HT3 receptors, and the response observed were fluorescent

response that is assumed to be proportional to the opening of 5HT3 receptor channels. Fig.10 is

showing that the maximal response induced by SR57227A is only slightly lower than that of 5HT,

while that of DDP733 is much lower than 5HT. Suggesting that DDP733 is the weakest partial

agonist, however, DDP733 has an EC50 value of ~10nM, lower than that of 5HT (~200nM) and

SR57227A (~500nM), so seems to be the most potent among the three drugs.


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Discussion:

Model 1 and 2 are developed to model different functions and characteristics of LGICs, especially

5HT3 receptors. Model 1 can be used to model receptor desensitization and agonist binding of the

5HT3 receptor system. Model 2 can model all that Model 1 can model and also the effects of

modulator binding onto 5HT3 receptors. In order to test how well these two models describe the

system, the results produced from the two models have to be compared to data produced by other

researchers.

Comparing Model 1, Model 2 and the Maksay allosteric model:

The allosteric model developed by Maksay et al.(2005), has got an antagonist involved in the

system, which can completes with the agonists for the binding site on 5HT3 receptors. This is what

Model 1+2 doesn't have, so they lack the ability to simulate a situation with binding of antagonists.

It might be a very interesting study to include an antagonists into Model 1+2, but would also makes

the models very complex. Comparing Model 1, Model 2 and the Maksay allosteric model, Model

1 is the simplest, therefore, the most useful in simple situations where only one type of agonist is

involved (so it is not an allosteric model). Both Model 2 and the Maksay allosteric model

involves binding of allosteric modulators. However, the allosteric modulators in the Maksay

model were set only to affect binding of other ligands, while Model 2 had set the modulators to

affect also receptor desensitization and efficacy terms apart from binding affinity.

Effects of different agonists on 5HT3 receptors:

The effects of 5HT, DDP733 and SR57227A on 5HT3 receptors have been studied intensively.

There are strong evidences suggesting that 5HT is a full agonist of 5HT3 receptors [21], while

DDP733 [22] and SR57227A [23, 24] are partial agonists of 5HT3 receptors. This correlates with

the results shown in Fig. 10.


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By comparing Fig. 10 and Fig. 12, how well Model 1 describes the real data can be seen. Fig. 12

shows that increasing agonist efficacy, in Model 1, also increases the amplitude of the maximal

response. This correlates with Fig. 10, where 5HT (full agonist, believed to have the highest

efficacy) has the highest maximal response. Fig. 12 has also suggested that increasing efficacy of

agonist, in Model 1, slightly decreases EC50. This is similar to other studies, e.g. Alder et al.,

(2003) [26] and Strange (2008) [25], on how increasing agonist efficacy affects dose-response

curves.

The curves of the three drugs in Fig. 10 differs not just in the amplitude of their maximal response,

but also in their EC50 values. Compare to 5HT, DPP733 has lower maximal response and also

lower EC50. This suggests that the three agonists are differ not only in their efficacy value but also

in their potency. EC50 of a dose-response curve is the concentration at which the agonist produces

50% of its maximal response. It gives an idea about the agonist's potency and is determined partly

by agonist binding affinity. Fig. 13 has shown that increasing agonist binding affinity shifts curves

to the left, i.e. decreases EC50. This correlates with other studies, e.g. Alder et al. (2003) [26] and

PG Strange (2008) [25] on how increasing agonist affinity affects dose-response curves. Therefore,

Model 1 is working well in showing the effects of increasing agonist efficacy and affinity in the

system.

Effects of changing receptor number:

Increasing initial receptor number has huge effects on the total response, an increase in the

amplitude of the maximal response and also a decrease in the EC50. This is because the response

measured in Model 1 is proportional to the opening of channels. Increasing the initial receptor

number provided more receptors for agonist binding, so more channels can be turn into opened

state. This increase in numbers of channel opening then increases the response.

In theory, the maximal response should always be increased by increasing the initial receptor


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number, but in Fig. 14, it is not (there is no obvious increase in the maximum response when

changing Rc from 10^5 to 10^6). This is because the response was calculated in percentage, so the

highest maximal response was limited to 100%, but the increase is clearly observed when

increasing the initial receptor number from 10^2 to 10^5. It is also important to note that the

equation relating number of opened channels to response involves a transducer function (Trans). In

Model 1, the Trans value was set to be 1000, and its function is to allow maximal response to be

produced when less than 100% of channels are opened. This is essential as this allows the system to

have spare receptors. A pharmacological system can have spare receptors in at least two conditions

[29]: (i) When receptors can stay in the activated state after dissociation of agonist, allowing a

single molecule of agonist to activate more than one receptors, and also (ii) when the agonist has

efficacy high enough to induce maximal response without occupying all the receptors present

(Agneter et al., 1997; [30].

There were many evidences of spare receptors occurring in pharmacological studies, including

Feuerstein et al., (1994) [31] and Limberger et al., (1989) [32], where 2-autoreceptor agonist

clonidine was able to produce a same maximal response as a full agonist, noradrenaline. The

situation is similar in Fig. 14 where Rc=10^5 is able to produce same maximal response as that of

Rc=10^6 (Difference between the two curves is that curve of Rc=10^5 has a higher EC50 value

than the curve of Rc=10^6). Therefore, it can be interpreted that when Rc is increased to 10^6, there

are spare receptors (unbound to agonist) present in the system.

It is also quite clear that the increase in initial receptor number also increases the basal response.

This is because Model 1 allows a small percentage of closed LGICs to change into opened LGICs

without binding of any agonists or modulators. In Model 1, this percentage is determined by the ko0

value, which was set to be 0.001. Increasing the ko0 value makes opening of unbound channels

more likely; while decreasing it cause the reverse. Although 0.001 is a low value, when higher


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numbers of receptor were involved, higher number of unbound channels could be opened, and

eventually causes a very high basal results that the standard sigmoidal shape of dose-response

curves are not longer seen. With 10^8 receptors in the system, ~98% response was produced

without modulators or agonist, which completely covers the actual response. By putting no agonist

and no modulator into the system, the basal response at each receptor number was worked out (Fig.

21), but it can also be seen in Fig. 14 as the basal response with no agonist and no modulator is

roughly the same as the response with very low agonist concentrations.

Effects of modulator strength and binding affinity on 5HT3 receptors:

Langmead, C.J. (2007) [33] has attempted to look at the differences in dose-response curves of

positive allosteric modulators. The result produced were very similar to Fig. 15, which was

produced using Model 2, suggesting that increasing the positive modulator strength decreases the

EC50 and increases the maximal response in dose-response curves. Although the result produced by

Langmead (2007) [33] is only showing the general effects of increasing positive modulator strength

on maximal agonist response, it suggests that Model 2 is working well in describing the effects of

increasing positive modulator strength in the 5HT induced response (as its result correlates with

Fig. 15).

McMahon et al., (2007) has found evidence that a positive modulator can sometimes have different

potency to same type of receptor at different sites. This change in potency also means a change in

the effective dose, so the findings are of significant importance clinically. Fig. 16 is produced from

Model 2, showing the effects of changing modulator binding affinity on dose-response curves. Fig.

16 suggests that increasing modulator binding affinity decreases the EC50, so makes the modulator

more potent. (It is important to note that potency is only partly determined by binding affinity) This

suggests that Model 2 is useful in modeling the effects of modulators with different potency on

5HT3 receptors.


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Fig. 17 is the result of the first Flexstation experiment. It can be compared to Fig. 15 and 16 to see

how well Model 2 describe the effects of modulator on 5HT3 receptors. The trichloroethanol

(+5HT) curves in Fig. 17 has lower EC50 than the 5-hydroxyl indole (+5HT) curves, suggesting

that trichloroethanol is slightly more potent than 5-hydroxylindole. This correlates with previous

studies that trichloroethanol [4] has a slightly lower effective dose than 5-hydroxylindole [5]. (Also,

correlates with Fig. 16, therefore, suggests, again, that Model 2 works as expected in modeling the

effects of modulators with different affinity on 5HT3 receptors.) Unfortunately, the shape of the

trichloroethanol (with 3M 5HT)curve is not very sigmoidal. This may be due to random human

errors in performing the Flexstation (e.g. calculation errors or pipetting errors in working out

dilutions and concentrations [35], or may be systemic errors that happens because of an inaccuracy

in measurement [34]. (More likely to be random errors occurring in Fig. 17 as the error seems

unpredictable.) Also, in the concentrations used, the 5-hydroxyl indole curve might not have

reached maximal yet. Other studies have used 5-hydroxyl indole in concentrations of 5mM, so with

the 3mM used in Fig. 17 might not be causing maximal response. Therefore, because of the

uncertainties present in Fig. 17, a firm conclusion about how well Model 2 works in modeling

different positive modulator strength cannot be drawn just by comparing Fig. 15 with 17. However,

Fig. 17 is still useful in showing the positive modulator effects of trichloroethanol and 5-hydroxyl

indole on 5HT3 receptors. Fig. 17 also shows that with a low concentration of 5HT, the increase in

response is significantly reduced for both modulators, suggesting that both modulators, especially

5-hydroxyl indole, doesn't produce much response without agonists binding to receptors.

Desensitization of 5HT3 receptors:

The effects of 5-hydroxylindole on 5HT3 receptors have been studied by many researchers.

Kooyman et al., 1993, [5] found that 1mM 5-hydroxylindole enhances the response induced by 5HT

binding to 5HT3 receptors, and significantly slows down the receptor desensitization of 5HT3


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receptor. My results from the second Flexstation experiment (Fig. 18) supports this findings. When

a higher concentration of 5-hydroxyl indole was used, the 5HT-induced response achieve a greater

maximal value. This is consistent with the nature of 5-hydroxyl indole as a positive modulator [5,

10]. Also, in the presence of the higher concentration of 5-hydroxyl indole, the maximal response

persists for longer. This is consistent with the effect of slowing desensitization of 5-hydroxyl indole

[5].

Shankaran et al., (2007) has used mathematical model to model the effects of changing receptor

desensitization rate to EGFR and GPCR. The results were quite similar to Fig. 19, which were

produced using Model 2, in an attempt to model the effect of slowing desensitization of 5-Hydroxyl

indole. This figure successfully shows that decreasing the desensitization terms (kdsm0, kdsm1 and

kdsm2) in Model 2 causes a slower decrease in response.

Effects of positive modulators on 5HT responses:

Downie et al., (1995) [4], showed that trichloroethanol decreases the Hill slope of the dose-response

curves of 5HT. This matches with the result in Fig. 20, where the increase of trichloroethanol

concentration decreases the Hill slope of the dose-response curve produced by Model 2. Also,

Downie et al, 1995 [4], has shown that by increasing the concentration of trichloroethanol (from

500M to 5mM) added to 5HT3 receptors, the basal response is increased. This is similar to the

result shown in Fig. 20, where increasing the modulator concentration also increases the basal

responses. However, Downie et al, 1995 [4], also shows that trichloroethanol reduces the EC50 of

the dose-response curve of 5HT. This reduction in EC50 was not observed in Fig. 20, where the

EC50 were the same for three curves. As shown in Fig. 12,13 and 14, increasing efficacy, affinity

and initial receptor number all causes decrease in EC50. Therefore, if modulator binding in Model 2

can be set to increase the agonist efficacy more, the decrease in EC50 might be observed.

Unfortunately, the chosen method to increase the modulator strength in Fig. 20 is by increasing the


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Emo0, Emo1 and Emo2 value. Increasing Emo0 allows binding of modulator to induce opening of

channels, this is modeling the effect of trichloroethanol alone on 5HT3 receptors [4]. If the Emo0,

Emo1 and Emo2 values are increased further then 100x as used in Fig. 20, the basal response

caused by modulator binding alone will be too high, and will mask the response produced by

agonist.

Also, in Downie et al., (1995) [4], the response induced by trichloroethanol increases when its

concentration was increased from 0.5mM (response ~5%) to 10mM (response ~58%), but drops

back to ~40% when in 50mM. The reason for this drop is unclear. 2 possible explanations of this

drop includes: (i)the high concentration of trichloroethanol kills cells; (ii)the high concentration of

trichloroethanol induces 5HT3 receptors to become desensitized. Death of cells causes a decrease in

total receptor number. As shown by Figure 14, drop in receptor number causes decrease in response.

Therefore, killing of cells would cause the response to drop and is quite likely to be what happened

in real experiment. All desensitized LGICs are non-conducting, including 5HT3 receptor. As shown

by Fig. 18 and 19, increasing the rate of desensitization of LGICs increases the rate of drop of

response. If the high concentration of trichloroethanol increases the desensitization largely that the

rate of desensitization becomes larger than the rate of receptor opening, than the response would

drop. This second possibility is however highly unlikely to happen in real experiment.

Basal response caused by opening of unbound channels:

Both Model 1+2, at the moment, is having basal response without any agonist or modulator in the

system. This is because both models allow closed LGICs (Rc)to change conformation into opened

channels (Ro)without binding of any agonists or modulators, which is something that can happen in

theory but proven to be highly unlikely in real experiments. To reduced the chance of unbound

channels inducing response, the rate of changing from Rc to Ro (Eo)was set to be a very low value

(0.001). However, because high numbers of initial receptors (10^5) were involved, there is still a


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~5% basal response. Reducing the initial number of receptors can reduce the basal response, but

would also have huge effects on other parts of the system, e.g. lowered the maximal response.

Fortunately, the basal response is not causing much problem (unless it is too high and covers the

real response) because the real result can be worked out simply by subtracting the basal response

(~5%) by the response produced by the Models. Also, low values of basal response doesn't affect

the shape of the curves. In Fig. 21, it can be seen that the values of basal response for both Models

are the same. This is because Model 1 and 2 differ only in the binding of modulators. When

modulator number is set to be 0, Model 1 is exactly the same as Model 2.

Future experiments:

From the above, it can be conclude that Model 1 + 2 generally works okay, but is far from perfect.

One of the most obvious improvement would be to reduce the basal response. Although I have

suggested above that reducing the Eo value would reduce the basal response, real situation is not as

simple as it seems. Especially in more complex model e.g. Model 2, changing one value in a Model

can often have huge effects on the system, because many terms in the model are linked to one

another. Therefore, when changing parameters, it is important to make sure the equations are

balanced. Another simple way to remove the basal response is to assume that closed receptors

without agonist binding would never be activated (So, won't not have arrow pointing from Rc to

Ro). Because it real experiment conditions, closed receptors seldom get activated without agonist

binding. Therefore, this way of simplifying the model should not cause any big difference on

showing the agonist induced response and at the same time largely reducing the problem with basal

response. Although simplifying a model often means to rule out some possible interactions that can

happen in the system, it makes the model easier to understand and at the same time reduces

estimation errors. So, it is important to have in mind that simplified models can sometimes be more

useful then the original, full model. This is, however, not recommend when using low values of

initial receptor number (Rc>10^6), because the basal response is insignificant unless the initial


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receptor number gets over 10^6. Therefore, in most situations, it is okay to leave the basal response

as I did.

In both Model 1+2, especially Model 2, there were some parameters that were difficult to give

estimation on their normal values (But of course some can be obtained experimentally). Some of

these parameters I didn't have any clues on their normal values and I simply made up those numbers

to balance equations. These terms include: kor1, kor2, kir1, kir2, kmora, kmora1, kmora2, kmira,

kmira2, komr1,komr2, kimr1,kimr2. These uncertainties in the estimation of values increase errors

of the models. Therefore, any future experiments that can give us more knowledge on LGICs would

help us in the estimation of those values and thus would reduce the estimation error of the two

models.

The experiment data I used to test Model 1 and 2 were mainly with 5HT3 receptors. Although

5HT3 receptors were believed to be a good representative of LGICs, it is also important to test how

this model fits with other types of LGICs. Therefore, it may be worth doing some experiments with

other LGICs, e.g. nicotinic acetylcholine receptors, and compare the model-produced results with

the real experiment results.

Another experiment that can be done would be to set the modulators as negative modulators and see

its affect on the system. Negative modulators of LGICs should be expected to have reverse effects

of positive modulators. Therefore, they might decrease the binding affinity and efficacy of agonists,

and also increase receptor desensitization. In the Maksay allosteric model mentioned before,

effects of negative modulators were modeled. It would be interesting to try that with Model 2 to see

if similar conclusions can be drawn.

Furthermore, It would also be useful to model binding data (like Maksay did with the allosteric


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model) and then compare to published data. This can, again, helps in improving the models.

Conclusion:

In conclusion, both Model 1 and Model 2 have many improvements to be made. However, Model 1

works well (results consistent to published data) in modeling the effect of changing efficacy of

agonist on the system, and also in modeling the effects of changing initial receptor numbers. Model

2 works okay in modeling the effect of changing modulator strength, binding affinity and also in

receptor desensitization. As models are never perfect, so it is not surprising that the models need

refining. I have also suggested many potentially beneficial future experiments that would enhance

our understanding on the effects of allosteric binding on LGICs. Therefore, I conclude that Model 1

and Model 2 are both useful in testing hypothesis on how agonists affects the function of LGICs,

and Model 2 can also be used to test hypothesis on how allosteric modulators affect LGICs.


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Figure 1: The charged residues in different LGIC subunits

Figure 2: A simple mathematical model (D. Colquhoun, 1998 [1])


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Figure 3: The Monod-Wyman-Changeux scheme (D. Colquhoun, 1998. [1])


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Figure 4: Plate plan 1


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Figure 5: Plate plan 2

Figure 6: drug plate 1


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Figure 7: drug plate 2


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Figure 8: Model 1

Figure 9: Model 2


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Figure 10: Lawrence's Flexstation result showing dose-response curves for three 5HT3 receptor

agonist.


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Figure 12: The effect of changing efficacy in Model 1

The x-axis of the graph is ligand concentration in log scale. The y-axis is the percentage response,

which is defined by this equation: response=100x[S/(S+Trans)], where S is the total number of

channel opened channels and Trans=1000. S is calculated by adding Ro(opened channels with no

agonist bound), ARo(opened channels with one molecule of agonist bound) and A2Ro(opened

channels with 2 molecules of agonist bound).


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Figure 13: The effects of increasing agonist binding affinity

-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

0

10

20

30

40

50

60

1x Affinity

10x Starting Affinity

100x StartingAffinity



-6.0 -4.0 -2.0 0.0 2.0 4.0 6.0

0.00000

20.00000

40.00000

60.00000

80.00000

100.00000

120.00000

Efficacy=0.01

Efficacy=0.1

Efficacy=1

Efficacy = 10

Efficacy = 100

Efficacy = 1000

Efficacy = 10^4


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Figure 14: The effect of changing initial receptor number in Model 1

Figure 15: The effect of changing modulator strength in Model 2

-6 -4 -2 0 2 4 6

0

20

40

60

80

100

120

Rc=10^2

Rc=10^3

Rc=10^4

Rc=10^5

Rc=^6

Rc=^7

Rc=10^8


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The x-axis is concentration of modulators in log scale. The y-axis is the percentage response. In

Model 2, response is calculated by the equation: response = 100*S/(S+Trans), in which S=total

number of opened channels (Ro+ARo+A2Ro+MRo+MARo+MA2Ro) and Trans = 1000.

Figure 16: The effect of changing modulator binding affinity in Model 2

The x-axis is modulator concentration in log scale and the y-axis is % response.


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Figure 17: Results of first Flexstation experiment (Effects of trichloroethanol and 5-hydroxyl indole

on 5HT response)

The x-axis is modulator concentration in log scale and the y-axis is the level of fluorescent, which

is representing response.

Figure 18: Results of second Flexstation experiment (The effects of 5-hydroxyl indole on 5HT

response)


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The x-axis is time, the y-axis is fluorescent level. Each line is result observed in one well. The two

wells had the same concentration of agonist (3M of 5HT), but different concentrations of allosteric

modulator, 3mM and 3M of 5-hydroxyl indole.

Figure 19: Effects of changing desensitization term (kdsm0,1+2) in Model 2

0 10 20 30 40 50 60

0

10

20

30

40

50

60

70

80

90

Kdsm=0.001

Kdsm=0.1

Kdsm=10

Kdsm=100

Kdsm=1000


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Figure 20: Effects of modulator on receptor in Model 2

The x-axis is agonist concentration in log scale and the y-axis is percentage response.

Figure 21: basal responses at different initial receptor number

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Basal response 4.74 33.22 83.26 98.03

-7.0 -6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0

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