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Role of Thyroxin in Mammalian Brain Development

Mathematical Modeling of the Role of Thyroxin in Mammalian Brain Development
Afzal Sara, Ahmad Muhammad, Shahid Faryal
Abstract: it has been known that tri-iodothronine (T3) plays a vital role in fetal brain development however despite its importance no mathematical model has been made for it thus far. Here we present a mathematical model for metabolic pathway of T4 to T3 conversion in brain development and gene regulatory pathway of recently characterized thyroid hormone receptor response genes. Our results show that low transcription of these thyroid hormone receptor response genes is sufficient for fetal brain development. On the other hand, high concentrations of metabolites are required in fetal brain development.
It has been well-established that thyroid hormone plays an essential role in the mammalian brain development. More specifically, Thyroxin (T4) is partially de-iodinized to tri-iodothronine (T3) in brain cells. The T3 acting through the nuclear receptors, Thyroid Receptor Hormone, serve as activating factors for certain downstream genes like Ser3 and hairless that play vital roles in the proper brain development in the mammalian fetus including having involvement in cell differentiation and migration, myelination and signalling.
Synaptotagmin-related gene 1 (Srg1) is one such novel thyroid hormone-responsive gene, which might possibly have a role in synaptic structure maintenance and/or activity[2].
Hairless, on the other hand is a transcriptional cofactor that may possibly influence the expression of other genes that respond to thyroid hormone[1].
Ser3 catalyzes the first step in serine biosynthesis, amongst having other roles[3]. This particular gene has been chosen for inclusion in our system because of the recently identified role of L-serine in proper functioning of central nervous system (CNS)[4].
Thyrotropin releasing hormone (TRH) is a functional neurotramsmitter in the CNS of mammals and can also modify the tasks that the CNS performs.
The entire pathway we are observing can be broken down into the following two parts:
Metabolic pathway: which involves deiodinized Thyroxin (T4) and its subsequent conversion to tri-iodothronine (T3) catalysed by enzyme iodothreoninedeiodinase2 (D2)
Gene regulatory pathway: which involves the activation of Thyroid hormone receptor and three of its downstream targets; hairless, synaptotagmin-related gene 1(srg1), 3-phosphoglycerate dehydrogenase (ser3) and thyrotropin releasing hormone (TRH).
This has been clearly depicted in the wiring diagram in Figure 1.

Figure 1: Wiring diagram of Thyroxin activation and interaction with downstream targets
Despite the simplicity of the pathway it has never been modeled in its entirety before, which was partly the inspiration behind choosing to model using a Systems’ approach. Moreover, the steps of this thyroid hormone pathway can be dissected and analyzed using a broad range of topics studied in the Systems’ Biology course, including Michaelis Menton Kinetics and Boolean Networks. Hence, the project will serve as a platform to demonstrate our all-inclusive understanding of the concepts learnt in the course by practically applying combinations of these techniques to the system chosen.
At a more macroscopic level, modeling of this system can unveil possibilities of developing a deeper understanding of the system dynamics of this thyroid hormone pathway, and an insight into its various potential targets. Analyzing these targets can thus help uncover potential drugs or treatments for various diseases or disorders resulting from improper brain development such as the Pendred’s Syndrome, the Grave’s disease and other psychiatric disorders like Cerebral Palsy, related to hyperthyroidism and hypothyroidism.
Methods and results: Michaelis Menton Kinetics:

Figure 2: Wiring diagram of conversion of T4 to T3 under competitive inhibition
Having found parameters (ki’s and km’s) from literature using experimentally derived values(8-11), we plotted the trajectories of substrate (T4), enzyme (D2), ES complex, inhibitor (rT3D2) and the IE complex using ODE’s. The ODE system for the dynamics of this reaction reads:
= k-1[T4D2] k-i[rT3D2]- k1[T4 ][D2]
= k-1[T4D2] k-i[rT3D2]- ki[rT3][D2]- k1[T4][D2] k2[T4D2]
= k1[T4 ][D2]- k-1[T4D2]- k2[T4D2]
-k-i[rT3D2] ki[rT3][D2]
= k2[T4D2]- kd[T3]
Following are the trajectories obtained:

Figure 3: Michaelis Menten Kinetics
T3 interaction with Thyroid Hormone Receptor (THR)
We took a closer look at the T3’s interaction with its receptor. The mechanism is shown below in figure 4:

Figure 4: T3 interaction with THR
Using the following ODE’s in ODE45 we modeled this interaction and obtained figure 5 shown below:

Vdi=kdi* Ri

Figure 5: Receptor ligand interaction of T3
In this graph, the blue line indicates the inactivated receptor while the green line indicates the activated receptor.
Boolean Network:
A Boolean network of gene regulatory network was constructed and analyzed. The genes in the gene regulatory pathway were assigned symbols for simplicity as follows:

Figure 6: Boolean Graph
Using the formula 2N, with N indicating the number of involved genes/nodes, we generated 25=32 possible states at time ‘t’ using a method of recursion in MatLAB.
The rules used for generating successive states were devised as follows:
A(t 1)= not B(t)
B(t 1)= A(t)
C(t 1)= A(t)
D(t 1)= A(t)
E(t 1)= not C(t)
The rules were applied 20 times to observe patterns in successive states and analyze the states where the system might have converged. However instead of forming a few stable states, our system in fact formed a basin of absorption including the following states:
[1, 1, 1, 1, 1][0, 1, 1, 1, 0][0, 0, 0, 0, 0]
(For detailed results refer to supplementary material 1).
Directed Graph:
A directed graph for the gene regulation pathway was constructed as follows:

Figure 7: Directed Graph
Edges/interactions= {(A, B, ve), (A, C, ve), (A, D, ve), (B, A, -ve), (C, E, -ve)}
Baysian Network:
Next, a Baysian network was constructed for the gene regulatory pathway.

Figure 8: Baysian Network
The dependencies of genes are indicated for by the following conditional probabilities:
Transcription of thyroid hormone response genes:
We proceeded to study the transcription of the thyroid hormone response genes, the activator and the repressor.

Figure 9: Microscopic binding and conformations of promoterref.
From figure blah we inferred the basal level mRNA synthesis of T3 responsive genes is approximately 25au, the level of repressor expression is around 2-3a.u. and level of activator expression is 35a.u.

Figure 10: mRNA synthesis of T3 response genes in frog[7]
Since we free could not find free energy values for thyroid hormone receptor we instead used the free energy value for the oestrogen hormone receptor whose dynamics resembles those of other members of the nuclear receptor family including the thyroid hormone receptor.

Next, in order to calculate the rate of transcription we used the following equation:

Stochastic modeling:
T4 D2 T4D2 T3 D2
Individual Reaction: T4 D2 T4D2
Rate constant = k1
T4 T4 -1
D2 D2 -1
T4D2 T4D2 1
Individual Reaction: T4 D2 T4 D2
Rate constant = k-1
T4 T4 1
D2 D2 1
T4D2 T4D2 – 1
Individual Reaction: T4 D2 T3 D2
Rate constant = k2
D2 D2 1
T4D2 T4D2 – 1
T3 T3 1
Individual Reaction: D2 rT3 D2rT3
Rate constant = k3
D2 D2 -1
Rt3 rT3 – 1
Rt3D2 rT3D2 1
Individual Reaction: D2 rT3 D2 rT3
Rate constant = k-3
D2 D2 1
Rt3 rT3 1
Rt3D2 rT3D2 – 1
We could not, however calculate the propensities due to time constraints on this project, and also because having research on neural cells, we discovered that the volume of neurons has been expriementally measured to be 5964µm3 [6] , and therefore we cannot approximate deterministic rate constants to stochastic propensities because volume is not equal to 1.

Figure 11: Stochastic modeling under Gillespie algorithm
Analysis: Applying michaelis menton to our metabolic pathway indicated that our system was consistent with an ideal Michaelis menton model.
Due to lack of parameters for the production and degradation of thyroid hormone receptor in active and inactive states, our model did not obey conservation principle of number of receptor molecules as indicated in figure 5.
Our Boolean network results indicate that our gene regulatory pathway forms a basin of absorption which includes the following states:
[1, 1, 1, 1, 1][0, 1, 1, 1, 0][0, 0, 0, 0, 0]
These states can be potential targets of further studies in this field.
Our calculation of gene regulation function depicts that the level of transcription of thyroid hormone receptor response genes is which indicates the brain development occurs at low transcript levels of thyroid hormone receptor response genes. However, it can be interesting to experiment various expression levels of these genes and compare them to the effect on fetal brain development.
Implementation of stochastic modeling using Gillespie revealed that the trend was similar to that of an ideal stochastic model. We also observed that the graph obtained for stochastic simulation was similar to that obtained for deterministic model. This shows that our metabolic pathway involves high number of molecules.
Sources Used [1]
[2] Thompson CC (1996) Thyroid hormone-responsive genes in developing cerebellum include a novel synaptotagmin and a hairless homolog. J Neurosci 16:7832–7840.

Osmoregulation in Different Environments

Write an essay on the topic “patterns of Osmoregulation in aquatic and terrestrial environments”.
Introduction Osmoregulation refers to the process by which living organisms maintain the constant osmotic conditions in the body. It involves the regulation of water and solute concentration of the body fluids such as potassium, sodium and chlorides so that their body fluids are maintained within homeostatic limits. In order for the cells in the body of an organism to function effectively the body fluids such as the cell contents as well as fluids outside cells such as tissue fluids, lymph and blood plasma must remain constant. Freshwater, marine and terrestrial organisms consists of varying modes adaptations for Osmoregulation that meet the challenges of these diverse environments. Therefore, this essay will disclose the patterns of Osmoregulation in aquatic and terrestrial environments.
The environment of an organism influences the process of Osmoregulation and the nature of excretion because Osmoregulation involves the same body structures with nitrogenous wastes. This is attributed to the fact that the elimination of nitrogen wastes is usually associated the problem of losing and gaining water. Different organisms live in different environments such as aquatic which includes fresh water and marine environment, and terrestrial environment. In all these environments, organisms employ specific patterns of controlling the concentration of water and salt so that their body fluids do not become too dilute or too concentrated through their environment as a media, (Solomon, P.E et-al 1069).
Aquatic environment As earlier alluded to, aquatic organisms include those which live in fresh water and also those which live in marine water.
Osmoregulation in freshwater organisms Organisms which live in fresh water are able to regulate the concentration of water and salts in their bodies through the pattern of gaining water and losing salts. This is because fresh water organisms in hypotonic medium. This is attributed to the fact that these organisms have a lower water potential than the surrounding environment, (Taylor D.J et-al 2011). As a result, there a constant tendency for water to enter the cells by osmosis through the cell surface membrane which poses a constant threat of organisms becoming water logged. To overcome this challenge, different organisms employ particular mechanisms; for example, species protozoans such Amoeba uses the organelles known as contractile vacuoles which eliminates the water entering the cell by osmosis, thereby osmoregulating the internal environment of an organism.
Certain species such as Paramecium have vesicles in the cytoplasm which fills with fluid from the cytoplasm and then most of the ions are pumped out of the fluid by active transport with energy from the surrounding mitochondria. Then the vesicles loads the remaining watery fluid into the contractile vacuole whose membrane cannot allow water to escape back into the cytoplasm by osmosis and suddenly the water is reduced hence osmoregulating its content.
Furthermore, in fresh water organisms such as fishes undertake Osmoregulation through the release of excess water through the gills and through the excreting of large amounts of dilute urine. Solomon, P.E et-al (2011: 1072) adds that “these organisms tend to lose salts by diffusion through the gills into the water”. In this way such organisms control the concentration of body water and salts. In addition to this, some amphibians such as frogs have their pattern of osmoregulating the body environment which is through producing large amounts of dilute urine and also active transport of salts into the body by specialised cells in the skin compensates for the loss of salt through the skin and urine.
Osmoregulation in marine environments Another pattern of Osmoregulation in aquatic organisms occurs in marine species which involves the losing of water and gaining of salts to maintain a favourable and constant internal environment. To this, aquatic organisms adapt successfully. These organisms live in a hypertonic environment meaning that their inner water content is higher than the surrounding environment, hence they lose water by osmosis and then they gain salts from the seawater they drink by diffusion. Solomon, P.E et-al (2011:1073) adds that, “to compensate for fluid loss marine fishes drink a lot of sea water, excrete the salts through the gills and also produce a small volume of urine thereby osmoregulating their body fluids.
Then also, other marine species such as those of marine cartilaginous fishes i.e. sharks and rays have their own pattern of carrying out Osmoregulation. They have different osmoregulatory adaptations that allow them to tolerate the salt concentration of their environment. These organisms are able to accumulate and tolerate urea because their kidneys undertake the reabsorption of urea in high concentration such that their body tissues become hypertonic to their surrounding medium resulting in a net inflow of water by osmosis. Then also they excrete quantities of dilute urine and excess salt is excreted also by the kidneys and in most species by a rectal gland, hence osmoregulating the body fluids.
And for marine snakes they carry out Osmoregulation by using salivary sublingual gland to get rid of excess leaving a normal blood concentration. Additionally, some reptiles, snakes and marine birds ingest sea water and take in a lot of salt in their food. To control the concentration of salts and water they posses glands in their heads which undertake the excretion of excess salts from their blood plasma.
Osmoregulation in terrestrial environments Organisms which live on land have a common challenge of regulating water in the body due to their contact with the atmosphere. However, each species has a particular pattern and adaptation to life on land for example insects. These, they contain an almost impermeable waxy layer which covers their exoskeletons to reduce loss of water from the body surface. Then also insects have wave-like structures in their spiracles which reduce the loss of water from tubes which connect spiracles to cells, (Taylor D.J et-al 2011).
In addition to this, water loss through excretion is prevented through the help of the malpighian tubules whose lower segment absorbs water and various salts and then the nitrogenous wastes precipitates out of the solution as solid crystals of uric acid. Thereafter, concentrated fluids of the tubules enter the rectum in which they mix with digestive wastes. From there the rectal gland absorb water again from uric acid and faeces suspension and then the dry waste is eliminated from the body as pellets. All the above adaptations form a suitable pattern for controlling and maintaining a constant osmotic condition of the insect’s body.
Other terrestrial organisms i.e. invertebrates such as flateworms consists of nephridial organs with branching tubes called nephridiopores excess fluid leaves the body thereby osmoregulating the internal fluid content, and also protonephridia composed of tubes with flame cells. They also have complex nephridial organs known as metanephridia whose end opens into a coelom and the fluid from the coelom passes into the tubule bringing with it whatever it contains i.e. glucose, salts or even wastes. As the fluid moves through the tubule, needed substances like water and glucose are removed from the fluid by tubules are reabsorbed back in blood capillaries, hence carrying out Osmoregulation.
Organisms such as a Kangaroo rat carry out Osmoregulation by using its fur to prevent the loss of water to the air and also during the day it remains in a cool burrow. Mader, S.M (2010) adds that a Kangaroo rat carries out Osmoregulation by using its nasal passage which has a highly convoluted mucous membrane surface capture condensed water from exhaled air and also conserves water by producing very concentrated urine and almost dry fecal matter.
Solomon, P.E (2010:1070) states that “to animals moved on the land, natural selection favoured the evolution of structures and processes that conserve water”. Thus this, facilitates Osmoregulation. The excretory system in terrestrial organisms such as birds, reptiles and mammals gives them a pattern by which they maintain fluid and electrolyte homeostasis by selectively adjusting the concentrations of salts and other blood substances and body fluids. Because this system is adapted to collect fluids from the interstitial fluids and blood it is able to control the fluid’s composition by selectively returning those required by the body into the body fluids. For example; birds undertake the process of Osmoregulation by excreting nitrogen as uric acid which only releases a little water and also by efficiently reabsorbing water through their cloaca and interstine. In addition to this, birds osmoregulate by excreting salt solution from the salt-excreting glands through their nostrils thereby maintaining a normal body fluid content. Then also, large terrestrial organisms are able to control their body fluid content because their skins are adapted to minimze the loss of water through evaporation and also by drinking water to compensate the water lost through the skin, respiratory passages and through urination, hence Osmoregulation their body fluid content. .
Furthermore, terrestrial organisms consists of a very effective and efficient kidneys enables them osmoregulate the body fluids and conserve water though a series of processes i.e. filtration, reabsorption of the needed substances by the body in the body fluids and the tubular secretion in the nephron. For example; Water passes out of the descending limb of the loop of Henle, leaving a more concentrated filtrate inside. The heavy outline along the ascending limb indicates that this region is relatively impermeable to water. NaCl diffuses out from the lower and thin part of the ascending limb. In the upper and thick part of the ascending limb, NaCl is actively transported into the interstitial fluid. The saltier the interstitial fluid becomes, the more water moves out of the descending limb. This process leaves a concentrated filtrate inside, so more salt passes out. Water from the collecting ducts moves out osmotically into this hypertonic interstitial fluid and is carried away by capillaries, hence osmoregulation is carried out,( Eckert, R et-al 2005).
Conclusion As indicated above Osmoregulation is the process by which organisms control the concentration of water and salts in the body so that their body fluids are maintained within homeostatic limits. This process occurs in organisms depending on the environment in which an organism live i.e. aquatic which include fresh water and marine water, and also terrestrial environment.
BIBLIOGRAPHY Eckert Roger and Ranall David (2005), Animal Phsysiology; mechanisms and adaptations, New York, CBS Publishers