Lecture11 • Introduction to signaling pathways • Glycolytic Oscillation • Reverse Engineering of biological networks
Introduction to signaling pathways Signaling networks involves the transduction of “signal” usually from outside to the inside of the cell On molecular level signaling involves the same type of processes as metabolism such as production and degradation of substances, molecular modifications (mainly phosphorylation but also methylation and acetylation) and activation or inhibition of reactions. But signaling pathways serve for information processing or transfer of information while metabolism provide mainly mass transfer
Introduction to signaling pathways • Signal transduction often involves: • The binding of a ligand to an extracellular receptor • The subsequent phosphorylation of an intra cellular enzyme • Amplification and transfer of the signal • The resultant change in the cellular function e.g. increase /decrease in the expression of a gene
Signaling paradiam Usually a signaling network has three principal parts: Events around the membrane Reactions that link sub-membrane events to the nucleus Events that leads to transcription Source: Systems biology in practice by E. klipp et. al.
Schematic representation of receptor activation Source: Systems biology in practice by E. klipp et. al.
Steroids Not always a receptor exists at the membrane for example the steroid receptors. Sterol lipids include hormones such as cortisol, estrogen, testosteron and calcitriol. These steroids simply cross the membrane of the target cell and then bound the intracellular receptor which results in the release of the inhibitory molecule from the receptor. The receptor then traverses the nuclear membrane and binds to its site on the DNA to trigger the transcription of the target gene. Source: Systems biology by Bernhard O. Palsson
G-protein coupled receptor (GPCR) represents important components of signal transduction network This class of receptor comprises 5% of the genes in C. elegans The G-protein complex consists of three subunits (α, β and λ) and in its inactive state bound to guanosinediphosphate(GDP) When a ligand binds to the GPCR, the G-protein exchanges its GDP for a guanosinetrihosphate(GTP) This exchange leads to the dissociation of the G-protein from the receptor and its split into a βλ complex and a GTP-bound α subunit which is its active state initiating other downstream processes G-protein signaling Source: Systems biology by Bernhard O. Palsson
G-protein signaling model Source: Systems biology in practice by E. klipp et. al.
G-protein signaling model Time course of G protein activation. The total number of molecules is 10000. The concentration of GDP-bound Gα is low for the whole period due to its fast complex formation with the heterodimerGβλ Source: Systems biology in practice by E. klipp et. al.
The JAK-STAT network The JAK-STAT signaling system is an important two-step process that is involved in multiple cellular functions including cell growth and inflammatory response A cell surface receptor often dimerizes upon binding to a cytokine The monomeric form of the receptor is associated with a kinase called JAK When the receptor dimerizes the JAKs induce phosphorylation of themselves and the receptor which is the active state of the receptor. The active complex phosphorylates the STAT(signal transducer and activator of transcription) molecules STAT molecules then dimerizes, go to nucleus and trigger transcription Source: Systems biology in practice by E. klipp et. al.
Schematic representation of the MAP kinase cascade. An upstream signal causes phosphorylation of the MAPKKK. The phosphorylation of the MAPKKK in turn phosphorylates the protein at the next level. Dephosphorylation is assumed to occur continuously by phosphatases or autodephosphorylation Source: Systems biology in practice by E. klipp et. al.
Signaling pathways in Baker’s yeast HOG pathway activated by osmotic shock, pheromone pathway activated by pheromones from cells of opposite mating type and pseudohyphal growth pathway stimulated by starvation condition A MAP kinase cascade is a particular part of many signalling pathways . In this figure its components are indicated by bold border Source: Systems biology in practice by E. klipp et. al.
Glycolytic Oscillation In living organism we see many periodic changes or oscillations: Pulse of the heart Respiration Ovulation in mammals Annual flowering of the plants Sleeping at night Lifecycle of cells Actually after starting or being affected by some perturbation many systems go through oscillations before becoming stable or unstable (collapsing)
Glycolytic Oscillation Phosphofructokinase-1 (PFK-1) catalyzes the important step of glycolysis, the conversion of fructose 6-phosphate and ATP to fructose 1,6-bisphosphate and ADP. The ADP then exert a positive feedback on PFK-1 This system can be represented as follows: For a large range of parameter values the system moves to a stable steady state but beyond a critical parameter value the system becomes unstable.
Glycolytic Oscillation The Temporal behavior of the concentration of substrate and product can be described as follows: Here the supply rate of S is v0 and k1 and k2 are mass action rate constants. The function R(p) represents the autocatalytic effect of the product P on its own production
Glycolytic Oscillation Glycolytic Oscillation Assuming r(P) = P2,The Temporal behavior of the concentration of substrate and product can be described as follows:
Glycolytic Oscillation The dynamic behavior of the above system with a particular set of parameter values is represented as follows: The above solution corresponds to v0 = 1, and k1 =1, and k2 = 1.00001 S(0)=2, P(0)=1 in arbitrary unit
Glycolytic Oscillation By using dS/dt =0 and dP/dt = 0, The steady state solutions for the above system can be determined as follows: However the steady state is achievable or not depends on the parameter values
Glycolytic Oscillation The stability of the steady state can be analyzed by inspection of the Jacobian matrix J. The character of the steady state is determined by the value and signs (positive, negative , zero etc.) of trace and the determinant of the Jacobian matrix
Glycolytic Oscillation The stability analysis of the above system for fixed value of k1=1 and variable values of V0 and k2
Glycolytic Oscillation The stability analysis of the above system for fixed value of k1=1 and variable value of vo and k2 With v0 = 1, k1 =1, and k2 = 1.00001 the system is in the stable focus region which means it gradually goes to steady state through decaying oscillation
Reverse Engineering of biological networks The task of reverse engineering of a genetic network is the reconstruction of the interactions among biological entities ( genes, proteins, metabolites etc.) in a qualitative way from experimental data using algorithm that weight the nature of the possible interactions with numerical values. In forward modeling network is constructed with known interactions and subsequently its topological and other properties are analyzed In reverse engineering the network is estimated from experimental data and then it is used for other predictions
Reverse Engineering of gene regulatory network By clustering the gene expression data, we can determine co-expressed genes. Co-expressed genes might have similar regulatory characteristics but it is not possible to get the information about the nature of the regulation. Here we discuss a reverse engineering method of estimating regulatory relation between genes based on gene expression data from the following paper: Reverse engineering gene networks using singular value decomposition and robust regression M. K. Stephen Yeung, JesperTegne´ r†, and James J. Collins‡ Proc. Natl. Acad. Sci. USA 99:6163-6168
Reverse Engineering of gene regulatory network It is assumed that the dynamics i.e. the rate of change of a gene-product’s abundance is a function of the abundance of all other genes in the network. For all N genes the system of equations are as follows: In Vector notation Where f(X) is a vector valued function
Reverse Engineering of gene regulatory network Under linear assumption i.e. has linear relation with Xi s we can write Here Aij is the coupling parameter that represents the influence of Xj on the expression rate of Xi . In other words Aij represents a network showing the regulatory relation among the genes. Target of reverse engineering is to determine A. Solving A requires a large number of measurements of and X
Reverse Engineering of gene regulatory network Measurement of is difficult and hence can be estimated in several ways. First, if time series data can be obtained then can be approximated by using the profiles of the expression values for fixed time intervals Alternatively a cellular system at steady state can be perturbed by external stimulation and then can be determined by comparing the gene expression in the perturbed cellular population and the unperturbed reference population.
Reverse Engineering of gene regulatory network Now using any method if we can produce matrices and then we can write Or, (if external perturbation is used) Here BNxMis the matrix representing the effect of perturbation The goal of reverse engineering is to use the measured data B, X, and to deduce A i.e. the connectivity matrix of the regulatory relation among the genes.
Reverse Engineering of gene regulatory network By taking transpose the system can be rewritten as A is the unknown. If M =N and X is full-ranked, we can simply invert the matrix X to find A. However, typically M<<N mainly because of the high cost of perturbations and measurements. We therefore have an underdetermined problem. Underdetermined problem means the number of linearly independent equations is less than the number of unknown variables. Therefore there is no unique solution One way to get around this is to use SVD to decompose XTinto
Reverse Engineering of gene regulatory network where U and V are each orthogonal which means: with I being the identity matrix, and W is diagonal: Without loss of generality, we may assume that all nonzero elements of wkare listed at the end, i.e., w1, w2, . . . , wL=0 and wL+1, wL+2,. . . , wN≠0, where L :=dim(ker(XT)). Then one particular solution for A is:
Reverse Engineering of gene regulatory network the general solution is given by the affine space with C = (cij)N×N, where cijis zero if j >L and is otherwise an arbitrary scalar coefficient. This family of solutions in Eq. 3 represents all the possible networks that are consistent with the microarray data. Among these solutions, the particular solution A0 is the one with the smallest L2 norm. Now, the question is which one of the solutions of equation 3 is the best.
Reverse Engineering of gene regulatory network In such cases, we may rely on insights provided by earlier works on gene regulatory networks and bioinformatics databases, which suggest that naturally occurring gene networks are sparse, i.e., generally each gene interacts with only a small percentage of all the genes in the entire genome. Imposing sparseness on the family of solutions given by Eq. 3 means that we need to choose the coefficients cijto maximize the number of zero entries in A. This is a nontrivial problem.
Reverse Engineering of gene regulatory network The task is equivalent to the problem of finding the exact-fit plane in robust statistics, where we try to fit a hyperplane to a set of points containing a few outliers. Here they have chosen L1 regression where the figure of merit is the minimization of the sum of the absolute values of the errors, for its efficiency. In short, this method of reverse engineering can produce multiple solutions (gene networks) that are consistent with a given microarray data. This paper says among them the sparsest one is the best solution and used L1 regression to detect the best solution.