Modelo XGT y Master-K120S

A major contributor to preterm labour is dysfunction of the myometrium, the smooth

muscle layer of the uterine wall. Globally, 15 million babies are born preterm each year

and at least 1 million of these babies will not survive as a consequence of their prematurity.

E↵ective management of preterm labour remains a huge challenge because of limitations in our knowledge of the mechanisms that govern uterine excitability and contraction. Throughout most of gestation, the uterus maintains a quiescent environment under the

influence of the hormones progesterone and relaxin. The uterus undergoes a period of

activation towards the end of pregnancy to provide the powerful contractions needed to

deliver the baby. Gap junctions, which connect neighbouring myocytes, are one of the

most important proteins involved in this activation process. While the uterus is quies-

cent, gap junction density is almost negligible and activity is not propagated through the

network. By the end of pregnancy, gap junction density is high and the myometrium is

well-connected. There is a paucity of quantitative data on the impact of gap junction regulation on the propagation of electrical excitation.

The overall aim of this thesis is to understand how intercellular communications mediated by gap junctions shape the dynamics of the myometrial smooth muscle network in its

transition to an excitable state. The specific objectives are:

• to construct a mathematical model of signal propagation within the myometrium with parameters influenced by experimental data;

• to use the model to investigate the hypothesis that spatial heterogeneity is crucial in generating global activity in the myometrium; and

• to develop the model to incorporate voltage-dependent gap junctions and investigate the e↵ect of the type of connexin that makes up the gap junction.

1.11.1 Construction of the mathematical model and spatial heterogene- ity

Chapter 2 (Sheldonet al., 2013) introduces the FitzHugh-Nagumo model and the construc-

tion of the model network. A mathematical model is developed consisting of an array of

25_⇥25 nodes representing the smooth muscle cells connected by resistors which represent the gap junctions. Each node in the network obeys FitzHugh-Nagumo dynamics. Initially,

each cell is considered to be at rest. An exciting stimulus is given to the central cell in

the network; the stimulus can take the form of a current input or a pacemaker cell. The

strength and presence of inter-cell connections within the network are modified stochas-

tically; that is, the couplings are drawn from statistical distributions and are considered to be non-deterministic. In addition, experimental data from human, mouse, and rat my-

ometrial samples are used to inform the cell parameters and to draw more biologically

relevant conclusions.

Chapter 2 (Sheldon et al., 2013) next addresses the role of spatial heterogeneity in an

excitable network. Heterogeneity is first introduced through the strength and presence of

inter-cell connections. It is shown that in quiescent networks introducing even a modest

degree of heterogeneity is sufficient to globally excite a network. In networks with a pacemaker cell as an exciting stimulus, it is demonstrated that a fully connected or strongly

coupled network reduces the frequency of pacemaker oscillations. The correlation between

the activity of the stimulus cell and its neighbours, as a function of their`1 separation, is also examined. It is shown that when the stimulus is strongly correlated with its immediate

neighbours, excitation is not able to propagate any further. A less well-connected network

1.11.2 Voltage-dependent gap junctions

Chapter 3 (Sheldon et al., 2014) extends the mathematical model of the myometrium to incorporate voltage-dependent gap junctions. It was demonstrated by Miyoshiet al.(1996)

that the conductance of a gap junction was dependent on the transjunctional voltage of

two neighbouring rat myocytes. Two distinct conductance relationships were reported

in the Miyoshi paper, which were shown to correspond to gap junctions with either a

predominantly connexin-43 (Cx43) composition or a predominantly connexin-45 (Cx45)

composition. The Boltzmann distribution fits proposed by Miyoshi are used in the model

to calculate the conductance of the gap junction from a given transjunctional voltage.

The models constructed in this paper suggest that networks with exclusively Cx45 are not

able to propagate activity, whereas Cx43 networks exhibit global excitability. Analysis of human and rat RNA expression in myometrial samples from pregnancy and in labour

suggests a down-regulation of Cx45 at term. A hypothesis is proposed in which Cx45 halts

the spread of activity in the pregnant uterus, and is removed at the end of pregnancy to

Spatial heterogeneity enhances

and modulates excitability in a

mathematical model of the

myometrium

This chapter is the published manuscript of our paper demonstrating the importance of

spatial heterogeneity in generating excitability in the myometrium. Herein, the construc-

tion of the two-dimensional model is described. The model has nodes assembled into a

25_⇥25 grid with connections between each cell and its four neighbours. Closed boundary conditions are used; that is, the cells at the edge of the lattice are considered to have three

neighbours (or two in the case of cells at a corner). Cells at one edge are not directly

connected to cells at the other edges. Each node is modelled by the FitzHugh-Nagumo

di↵erential equations, and at the start of the simulations both equations are set to be zero, i.e. the rate of change of both the excitation and recovery variables is zero. A stimulus

is applied to the central cell in the grid, and by changing parameters and the strengths of

inter-node connections, the way in which the stimulus spreads throughout the network is

investigated.

Master’s degree (awarded in 2012). During the project, I observed that the proportion of

cells in the network that become excited after a stimulus to the central cell is dependent on the strength of the inter-cell connections. The bounds on the coupling strength are a

function of the size of the applied stimulus.

The work was continued by Marc Baghdadi in a second eight-week mini-project as part of

his Master’s degree; the assessment method for the project was to write the manuscript for

a publication. Marc noted that in networks with a coupling strength outside the excitable

range, removing around 20 % of the connections between cells was enough to generate

global activity. He also set up the network in which the magnitude of each connection is

drawn from a uniform distribution. With uniformly distributed couplings strengths, the

standard deviation is shown to be more important in predicting the level of activity than

the total coupling magnitude.

I returned to the project in my doctoral studies. I increased the size of the lattices used in

all simulations, examined spatial correlation as a function of distance from the stimulated cell, incorporated real-life cell capacitance and resting membrane potential (RMP) values

into the cell parameters by fitting distributions to the raw data values, and investigated the

e↵ect of replacing the stimulated cell with a pacemaker cell. The rat myocyte capacitance values and RMP values were produced from patch-clamp experiments carried out by Dr

Conor McCloskey. Using Marc’s manuscript as a basis and incorporating my new results,

in a mathematical model of the myometrium

Rachel E. Sheldon1,3_{, Marc Baghdadi}1_{, Conor McCloskey}3_{, Andrew M. Blanks}3_,

Anatoly Shmygol3_{, and Hugo A. van den Berg}2 1 _{MOAC Doctoral Training Centre, University of Warwick}

2 _{Systems Biology, University of Warwick}

3 _{Division of Reproductive Health, Warwick Medical School}

J. R. Soc. Interface, 2013,10(86), 20130458.