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Cilj ove doktorske disertacije je razvoj direktnih inhibitora interakcija u kompleksu CDK9 / ciklin T1. Ciklin zavisna kinaza 9 u kompleksu sa ciklinom T1 čini katalitičko jezgro P-TEFb kompleksa. Inhibicija funkcije P-TEFb kompleksa je od značaja u terapiji više patoloških stanja kod ljudi: nekih tipova maligniteta, HIV-1 infekcije, hipertrofije miokarda, hroničnih inflamatornih bolesti. Postojeći inhibitori P-TEFb funkcije imaju ograničenu selektivnost dejstva, koju je moguće poboljšati primenom direktnih inhibitora CDK9 / ciklin T1 interakcije. U ovom istraživanju urađena je in silico studija P-TEFb kompleksa. Ispitana je struktura, hidratisanost i dinamika vezivnih površina kompleksa. Utvrđene su energetski najznačajnije hot spot aminokiseline u strukturi kompleksa i upotrebljene za dalji dizajn inhibitora. Struktura slobodne CDK9, neophodna za dizajn liganada je, u nedostatku eksperimentalno utvrđene strukture, simulirana klasičnom i ubrzanom molekularnom dinamikom. Ispitana je sposobnost vezivne površine kompleksa da interaguje sa ligandima, kao i postojanje, otvaranje i postojanost privremenih hidrofobnih džepova na vezivnoj površini CDK9, pogodnih za vezivanje liganada. Dobijene informacije o vezivnim površinama kompleksa CDK9 / ciklin T1, upotrebljene su za dizajn peptidnih i nepeptidnih inhibitora interakcije. Peptidni inhibitori su dizajnirani po ugledu na strukturu ciklina T1, ali i de novo dizajnom iz aminokiselina. Peptidne strukture sa najpovoljnijom energijom vezivanja za CDK9, iskorišćene su u razvoju nepeptidnih inhibitora. Predložene su strukture potencijalnih nepeptidnih inhibitora interakcije CDK9 / ciklin T1. U okviru ovog istraživanja urađeno je i ab initio ispitivanje prelaznih stanja intramolekulske Heck-ove ciklizacije alilnih alkohola i predloženo je objašnjenje za eksperimentalno zapaženu regioselektivnost procesa. The goal of this doctoral dissertation is the development of direct inhibitors of CDK9 / cyclin T1 protein-protein interaction. Cyclin dependent kinase 9 in complex with cyclin T1 forms the catalytic core of P-TEFb protein complex. Inhibition of P-TEFb function is of significance in the therapy of several pathological states in humans: some malignancies, HIV-1 infection, cardiac hypertrophy, chronic inflammatory diseases. Existing inhibitors of P-TEFb function have a limited selectivity of action, which could be improved with the direct inhibitors of CDK9 / cyclin T1 interaction. An in silico study of the P-TEFb complex was conducted in this research. The structure, hydration and dynamics of the complex binding surfaces were examined. Energetically most significant amino acids, hot spots, were determined and used in the design of inhibitors. The structure of the free CDK9, needed for the ligand design, was, in absence of an experimentally determined structure, simulated using classical and accelerated molecular dynamics. The ability of complex binding surfaces to interact with ligands was examined, as was the existence, opening and persistence of transient hydrophobic pockets on CDK9 interface surface, suitable for ligand binding. Information obtained of the CDK9 / cyclin T1 complex binding surfaces was used in the design of peptide and small molecule inhibitors of this interaction. Peptide ligands were designed using cyclin T1 as a template structure, as well as using de novo design from amino acids. Peptide structures with the most favourable binding energy to CDK9 were utilised in the design of small molecule inhibitors. Structures of potential small molecule inhibitors of CDK9 / cyclin T1 interaction were proposed. An ab initio study of transition states in an intramolecular Heck cyclisation of allyl alcohols was also conducted in this research. An explanation for the experimentally observed regioselectivity of the process was proposed.