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  • ssb_toolkit.md 18.04 KiB

    SSBColab Documentation



    The SSB toolkit

    The SSB computational toolkit was developed to easily predict classical pharmacodynamic models of drug-GPCR (class A) interactions given just as input structural information of the receptor and the ligand. The toolkit doesn’t use any novel or untested methods. Instead, it brings together free and/or open source bioinformatic tools into a user-friendly pipeline to be used by experts and non-experts. The pipeline was built, as a first instance, in a jupyter notebook – an interactive computational environment for replication and exploration of scientific code and analysis. Nowadays, jupyter notebooks are being extensively used by the computational biology community, making them the preferred choice to share and rerun computational protocols (Rule, A et al., 2019).



    SSB_img



    All the code under the toolkit was developed as a python module - a python file containing python classes, functions and statements. This helped us to modularize the code granting its readability, reusability, and deployment. Although the code will not be detailed in this thesis, many libraries were used for its development, such as SciPy, Numpy, Matplotlib, Pandas, scikit-learn, PySB and Biopython.



    equation

    Fig. 1 - Structure Systems Biology toolkit’s pipeline.



    Drug-receptor binding affinities

    The concept of drug-receptor binding constitutes the baseline of pharmacodynamics’ studies. When a drug or an endogenous ligand such as a neurotransmitter or a hormone binds though complementary to protein conformations, a cellular effect may result from that binding interaction (such as biochemical metabolic effects of second messengers or modulation of basal activity), which is typically described in quantitative terms. This complementary binding depends mainly on the affinity and efficacy of the ligand – parameters unique to its chemical structure (Golan et al.,3rd. ed, 2012). While the affinity of a ligand can be defined as a measure of how strong the ligand binds to the receptor, the efficacy is the measure of the maximum biological effect that results from the binding.

    The affinity of a ligand to a receptor can be calculated according to the law of mass action, from which the equilibrium constant for bound versus unbound ligand is defined as the dissociation constant (Kd), as follows:

    equation (eq. 1)


    equation (eq. 2)

    being [L], [R] and [LR] the ligand, receptor and the ligand-receptor complex’s concentration, respectively, and K d the equilibrium dissociation constant. If one assumes that the concentration of the receptor is constant: = [LR] + [R] [Rtotal] ; it comes that:

    equation (eq. 3)

    being [LR]/[Rtotal] the fraction of all available receptors that are bound to the ligand at equilibrium. That is to say that if the ligand acts as an agonist, according to the occupancy theory, this fraction represents the concentration of active receptors at equilibrium (Golan et al.,3rd. ed, 2012). From this equation, is possible then, to plot the fraction of bound receptors in the equilibrium over a range of ligand’s concentration, rendering the so-called drug-receptor binding curve (Fig.3).



    equation

    Fig. 2 - Drug-binding curve. Since ligands can occur in a wide range of concentration values, if the ligand’s concentration is plotted semi-logarithmically, the hyperbolic shape of the curve becomes sigmoid. When the curve is presented in this way, a straight line can be obtained between 20% and 80% of the curve, being easy to calculate the concentration of ligand needed to activate specific a fraction of receptors. Moreover, it also makes easier to compare affinities between ligands.



    Givin as input the experimental/computational Kd values for a ligand, with the SSBtoolkit it is then possible to obtain a drug-receptor binding curve for each ligand by calculating eq.3 in function of a range of ligand concentrations. In the SSBtoolkit, by default, the range of ligand concentration is defined as a geometric progression of 20 concentration values between a minimum value (close to zero) and a maximum value defined by the user (normally, 3 orders of magnitude higher). In the end, a binding curve for each ligand is obtained by fitting a logistic regression to the discrete data:

    equation (eq. 4)

    where Y is the response (the response of a drug-binding curve is the fraction of receptors occupied in the equilibrium); X, is the arithmetic ligand concentration; a , the response when X = 0; d , the response when X is equal to the maximum ligand’s concentration; c (for drug-repsonse curve, the c value corrresponds to the Kd value) ; is the concentration value corresponding to the halfway between a and d ; and b is the “slope” value that describes the steepness of the curve (DeLean, A. et al., 1978). The reason why a geometric progression is used to obtain the range of ligand concentrations, is due to the impact of the dilution factor on the accuracy of Kd and EC50/IC50, values experimentally estimated. This factor, that defines the spacing between the adjacent concentration values, has an impact on the concentration values that are on the linear portion of the curve. Using a geometric progression we can mimic the experimental conditions where each concentration equals the power of 2 of the previous lowest concentration (Sebaugh, J.L., 2011)*. Obtaining then the drug-receptor binding curve for each ligand, allows us to compare the potencies between them. Considering the assumption that Kd can be defined as the concentration of ligand at which 50% of the available receptors are occupied, the more the Kd shifts to right in the plot, the more ligand concentration is needed to achieve the 50% of available occupied receptors (see Fig. 2). In other words, the more the Kd goes to right in the plot the less potent the drug is.

    However, this analysis is just valid if we are dealing with agonists. If antagonists come into play the scenario is different. By definition, an antagonist is a drug that inhibits the action of an agonist, having no effect in the absence of the agonist (Neubig, R.R. et al., 2003). Therefore, to incorporate the effect of a competitive antagonist, a modified version of eq.3 must be applied:

    equation (eq. 5)

    The only difference is the increase in the Kd of the effective ligand by a factor of: 1 + [L2] / Kd L2 (Golan et al.,3rd. ed, 2012).