Chap4. Trainable Gene Regulation Networks

4.1 Introduction

Gene regulation : a combination of cis-acting regulation by the extended promoter of a gene (including all regulatory sequences) by way of the transcription complex, and of trans-acting regulation by the transcription factor products of other genes.

Larger network : need to have recurrent (feedback) NeuralNetwork connections

Gene circuits = gene regulation networks = genetic regulatory networks : A network model set with recurrent NeuralNetworks : can be used as a modeling language for multiple developmental processes, including gene regulation within a cell, cell-cell communication, and cell division

Trainable gene regulation networks formed with dynamic equations : ODEs(Ordinary differential equations)

(4.1) equation : Chap1의 recurrent NeuralNetwork 설명 부분에 있는 (1.18) Equation과도 같은 공식이었습니다.

vi : continuous-valued state variable for gene product i Tij : the matrix of positive (zero) or negative connetions g() : nonlinear monotonic sigmoidal activation function

if, Tij <> 0 then regulatory connection from gene product j to gene i if, Tij > 0 then enhancing if, Tij < 0 then repressing if, Tij = 0 then no connection

(Figure 4.1) Gene : open circle ; Nonzero connection : arrow

4.2 Three examples

Three applications to Drosophila gene expression pattern formation

1. a model of gap gene expression patterns along the A-P

2. the extension of this model to incorporate the important pair-rule gene even-skipped (eve) and an number of other improvements

3. a gene circuit model of neurogenesis incorporating nonlinear signaling between nearby cells through th Notch receptor and the Delta ligand

4.2.1 Gap gene expression

Aim : to understand the network of gap genes expressed in bands (domains) along the A-P axis of the very early embryo (the syncytial blastoderm) of Drosophila.

Advantage of this experimental system : no cell membranes between adjacent cell nuclei, so no need of elaborate cell-cell signaling mechanisms. : Drosophila is easy to manipulate genetically because “saturation muagenesis” is possible.

Encoding of positional information along the A-P axis during development First main encoding : exponential gradient of Bicoid (bcd) protein and Hunchback (hb) expression input to the gap genes : bcc, hb other input : kruppel (Kr), knirps (kni), giant (gt), tailess (tll), hunchback (hb) input to the pair-rule genes : eve and fushi tarazu (ftz)

(Figure 4.2) The spatial gene expression pattern along the A-P axis of triple-stained embryo. (Figure 4.3) Model-fitted curves for gap gene expression. (Figure 4.4) Positional information for the gap gene system is specified cooperatively by maternal bcd and hb.

4.2.2 ''eve'' stripe expression

The gap gene circuit as extended to include the first of the pair-rule genes, eve (Figure 4.5) qualitative and reproducible circuit parameter signs gap gene 만으로 만들어진 pair-rule expression 에서는 알 수 없었던 periodic spatial pattern의 phase를 이해할 수 있게 되었다.

4.2.3 neurogenesis and cell-cell signaling

syncytial blastoderm은 morphognetic system으로 자주 애용되고, 특이하기는 하지만, genetic model로 발전하려면, gene regulation network에 함께하는 signaling이 필요하다.

selection of particular cell for modeling : cells in epthilial sheet to become neuroblasts adding of essential molecule : Notch receptor - a membrane bound receptor protein responsible for receiving the intercellular signals that mediate this selection process binding ligand on neighboring cells : Delta

(Figure 4.6)

4.3 Extending the modeling framework ot include promotor substructure

What’s the influence of promoter substructure on eve stripe formation? Eve promotor has many transcription binding sites. e.g. : MSE2(minimal strip element), MSE3 and 7

만약 hb 가 MES2에 대해서는 enhancer로, MSE3에 대해서는 inhibitor로 작용한다면 net effect는 어떠 할 것이고 silencer element 의 역할은 무었인가? 답을 얻기 위해서는 Promotor의 substructure에 대해 좀더 알아야 한다. : binding site, interaction, promotor element …

Suggested model for activation of MSE2 : activated by bcd and hb “in concert”

• repressed by gt anteriorly and kr posteriorly

μMSE2 = (bcd + γ x hb)(1 - gt)(1 - kr) νMSE2 = g( μMSE2),

γ : weight on the relative contribution of hb compared with bcd

Formula for MSE3 :

μMSE3 = Dstat(1 - gt)(1 - kr) νMSE3 = g( μMSE3).

Validation or invalidation of this formula and interpretation in terms of more detailed models will required a quantitative treatment of the relevant expression data.

4.3.1 Hierarchical Cooperative Activation (HCA)

A kind of gene network model incorporating a promotor-level substructure Basic idea of the model : equilibrium statistical mechanics model [complete with partition functions valid for dilute solutions] of “cooperatie activation” in activating a protein complex.

Monof-Wyman-Changeux (MWC) model

(4.2) equation Z = К Π (1 + Кb νj(b)) + Π (1 + Ќb νj(b)),

This formula is determined by relative binding constants for each component b of the complex in the active and inactie states, but there are no other interaction vj : concentration of gene product j of a gene circuit j : function of b à so each binding site is specialized to receive only one particular transcription factor

To remove this assumption,

(4.3) equation Z = К Π (1 + ΣAbj Кbj νj) + Π (1 + ΣAbj Ќbj νj),

A = 0 or 1 specifies which transcription factors may bind to which sites by its sparse nonzero elements. К : relevant binding constant for a binding site when the complex is in its “active state” Ќ : is “inactive state”

For this partition function, all binding sites are independent of one another. This conditional independence leads to the products over the binding sites in the expression for Z.

(4.4) equation : The probability of activation of the complex (4.5) equation : the product is taken over enhancer elements α which regulate gene i (4.6) equation

• n(b) = 1 for monomers and 2 for homodimers

(4.7) equation (4.8) equation (4.9) equation : Michaelis-Menton kinetics in steady state for phosphorylation and dephosphorylation, and one-site dimeric partition functions (4.10) equation : overall partition function for promotor element (4.11 - 13) equation : The full hierarchical cooperative activation (HCA) dynamics

The resulting HCA (equation 4.8) can describe promotor elements, silencer regions, dimeric and competitive binding, and constituitve transcription factor binding, among other mechanisms.

4.4 Conclusion