We quantified the statistical energy landscapes for binding, from which we can characterize the distributions of the binding free energy (affinity), the equilibrium constants, the kinetics and the specificity by exploring the different ligands binding with a particular receptor.

Our study provides new insights into the statistical nature of thermodynamics, kinetics and function from different ligands binding with a specific receptor or equivalently specific ligand binding with different receptors.

Therefore by exploring the sequences of ligands (typically 106 ~ 109 sequences, a large number which is perfect for the statistical description) or small molecule databases (the number of small molecules can be on the order of 1060), one can explore the biological specificity and function by mimicking the natural evolution selection process with the fittest surviving from the ensemble of ligands .

The combinatorial library or virtual screening of small molecule database therefore provides a natural laboratory for uncovering the fundamental principles in biomolecular binding and design through the study of the statistical features of the ensembles of the ligands or small molecules with different sequences binding to a specific receptor.

The experimental features on binding indicate that the appropriate physical variable is the free energy of binding of ligands to the receptor, not the energy.

When we discuss about the distribution of the free energies, we mean the sampling of different free binding energies from the different ligands with different sequences binding to the same receptor.

Collecting the free energies from different ligands binding to the same receptor, we can find the distributions of the free energy.

Moreover, the proposed approach does not require the use of known ligands for the target protein since it can leverage recent multi-target machine learning predictors where ligands for similar targets can serve as initial training data.

Combined with a multi-target model, it can be used to predict binding motifs for targets with no known ligands .

Moreover, the proposed approach can be employed without known ligands for the target protein because it can leverage recent multi-target machine learning predictors [10, 14] where ligands for similar targets can serve as an initial training set.

Split and pool combinatorial peptide synthesis is a simple but efficient way to synthesize a very Wide spectrum of peptide ligands .

It has been used for the discovery of ligands for receptors [30, 31], for proteins [32—35] and for transcription factors [36, 37].

Cell lines were treated (or left untreated, control) with ligands or the ALK inhibitor TAE684 as indicated in Table 1.

For organelle fractionation phosphoproteomics, cell lines were treated with ligands (LAN-6 and TrkA-CFP-expressing SK-N-BE(2): NGF, SMS-KCNzBDNF) for 10 min at 37°C.

Ligands were bound to cells at 4°C for 1 hr, then cells were warmed to 37°C for 10 min or 1 hr.

LYN and FYN also increased in fractions 16—22 in response to both ligands (Fig 7A—7D).

The main difference between these theories rests in how conformational transitions proceed upon binding of ligands .

Where L0 is the allosteric constant between the R and T states in the absence of ligands , xFJ-J-represent effector concentrations binding to specific allosteric sites, KRM and KTJ-J- denote the effectors dissociation constants for each state, éRO and em are the free enzyme fractions in both conformational states as function of the respective rate parameters (kR,kT) and reactant concentrations (x), 111 represents the number of allosteric sites, and finally, r and tare the number of positive and negative effectors binding to the allosteric sites in the R and T states, respectively.

[34] have derived a simple expression to determine the allosteric constant in the absence of ligands assuming symmetric binding for the two states (Equation 24).