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Unformatted text preview: Principles of protein-protein interactions
Biophysical Chemistry 1, Fall 2010 Fundamentals of biological thermodynamics Basics of protein-protein recognition and interactions Reading assignment: Slater, Chap. 3 (handout) What does a force field look like? U = bonds Kb (b - beq )2 + angles K ( - eq )2 + 4 impropers Kw w 2
12 + torsions K cos(n ) + nonbonded pairs r - r 6 + qi qj r H H O O C H1 formamide N H2 water H3 Lightening intro to biological thermdynamics
System and Surroundings Biological Thermodynamics A system is defined as the matter within a defined region of space (i.e., reactants, products, solvent) The matter in the rest of the universe is called the surroundings The first law of thermodynamics The First Law of thermodynamics
The Energy is conserved The total energy of a system and its surroundings is constant In any physical or chemical change, the total amount of energy in the universe remains constant, although the form of the energy may change. What is "U" (internal energy)?
The internal energy of a system is the total kinetic energy due to the motion of molecules (translational, rotational, vibrational) and the total potential energy associated with the vibrational and electric energy of atoms within molecules or crystals. U is a state function, that is, its value depends only on the current state of the system Energy is heat + work Work (W) and Heat (Q)
U= W + Q Work involves the non-random movement of particles Heat involves the random movement of particles Entropy and probability (qualitative!)
p(H) = w exp(H/RT) The Boltzmann entropy Entropy (S) - a measure of the order of the system S = k lnN Energy & entropy: the math
(good reading: J.C. Slater, "Introduction to Chemical Physics"; Dover, Chapter III) First law of thermodynamics: dU = dQ - dW or U = Second law of thermodynamics: dS dQ /T or TdS dU + dW (2) dU = dQ - dW (1) Connections to microscopic properties
Let pi be the probability (fraction) of micro-state i. Then we can postulate a connection to the entropy: S = -k pi ln pi
i (3) This is large when the system is "random". For example, if pi = 1/W (same for all i), then S = k ln W . This entropy is also additive (or "extensive"). Consider two uncorrelated systems that have a total number of states W1 and W2 . The total number of possibilities for the combined system is W1 W2 . Then: S = k ln(W1 W2 ) = k ln W1 + k ln W2 = S1 + S2 (4) The canonical ensemble: temperature
Now consider dividing an isolated system (whose total energy U is therefore fixed) into a number of subsystems, each of which could have its own internal energy Ei , but where there is thermal contact between the subsystems, so that energy can be transferred among them. The fixed total energy is U = Ei pi
i where pi is the probability that subsystem i will have energy Ei . Let us find the most probable configuration by maximizing the entropy, subject to the constraint of constant total energy and that pi = 1: dS = 0 = -k dpi (ln pi ) + k Ei dpi - ka dpi Here a and are undetermined multipliers. The only general solution is when the coefficients of the dpi terms add to zero: ln pi = a - Ei exp(- Ei ) exp(- Ei ) (5) pi = (6) Connections to clasical thermodynamics
The Lagrange multiplier a is just the denominator of Eq. 6. To figure out what is, we connect this back to thermodynamics: dS = k dpi Ei = k dQ
i = 1/kT The denominator of Eq. 6 is called the partition function, and all thermodynamic quantities can be determined from it and its derivatives: Z exp(- Ei ) A S = U - TS = -kT ln Z = -( A/ T )V = k ln Z + kT ( ln Z / T )V 2 (kT ln Z ) U = -( ln Z / ); CV = T T2 Connections to classical mechanics
We have implicitly been considered a discrete set of (quantum) states, Ei , and the dimensionless partition function that sums over all states: ZQ = e- E
i i How does this relate to what must be the classical quantity, integrating over all phase space: ZC = e- H (p,q ) dpdq Zc has units of (energy time)3N for N atoms. The Heisenberg principle states (roughly): pq h, and it turns out that we should "count" classical phase space in units of h: ZQ Zc /h3N For M indistinguishable particles, we also need to divide by M !. This leads to a discussion of Fermi, Bose and Boltzmann statistics.... The second law of thermodynamics The Second Law of thermodynamics
The total entropy of a system and its surroundings always increases for a spontaneous process The concept of free energy Biological Thermodynamics
The Gibbs free energy (G)
!Stotal = !Ssystem + !Ssurroundings !Ssurroundings = -!Hsystem/T !Stotal = !Ssystem - !Hsystem/T -T!Stotal = !Hsystem - T!Ssystem !G = !Hsystem - T!Ssystem
For a reaction to be spontaneous, the entropy of the universe, Stotal, must increase
!Ssystem > !Hsystem/T or !G = !Hsystem T!Ssystem < 0 The free energy must be negative for a reaction to be spontaneous! Free energy is enthalpy minus entropy Biological Thermodynamics
G = H TS The Enthalpic term
Changes in bonding van der Waals Hydrogen bonding Charge interactions The Entropic term
Changes the arrangement of the solvent or counterions Reflects the degrees of freedom Rotational & Translational changes G = H TS How to think about protein/ligand interactions Protein folding vs. protein-protein Protein folding Protein binding and interactions
Very similar processes! Hydrophilic and hydrophobic residues Protein folding Amino acid distribution space-filling cross-section nonpolar polar The hydrophobic effect do proteins fold? Why Back to structural biology: protein-protein interactions
Identification of protein assemblies is at the heart of functional genomics and drug discovery. Figure 1. Examples of different types of proteinprotein interactions : (A) obligate homodimer, P22 Arc repressor; (B) obligate heterodimer, human cathepsin D that consists of a non-homologous light (red) and heavy (green) chain; (C) non-obligate homodimer, sperm lysin; (D) non-obligate heterodimer, RhoA (green) and RhoGAP (red) signalling complex; (E) non-obligate permanent heterodimer, thrombin (red) and rodniin inhibitor (green); (F) non-obligate transient heterotrimer, bovine G protein, i.e., the interaction between Ga (green) and Gb (red, orange) is transient. The proteins in an obligate interaction are not found as stable structures on their own in vivo. . Published in: Irene M.A. Nooren; Janet M. Thornton. EMBO J. (2003) 22, 3486-3492. Multi-protein complexes are very common
Prediction of protein assemblies is crucial for understanding cellular organization. Figure 3. Putative structure through modeling and low-resolution EM. (a) Exosome subunits. The top of the panel shows the domain organization of two subunits present in the complex, but lacking any detectable similarity to known three-dimensional structures. The model for the nine other subunits (bottom) was constructed by predicting binary interactions using InterPReTS and building models based on a homologous complex structure using comparative modeling. (b) EM density map (green mesh) with the best fit of the model shown as a gray surface and the predicted locations of the subunits labeled. The question marks indicate those subunits for which no structures could be modeled .
Published in: Robert B. Russell et al. Curr Opin Struct Biol. 2004, 14, 313-324.. Instrisincally disordered proteins Proteins are flexible. A large fraction of cellular proteins are thought to be natively disordered, or unstable in solution. The structures of disordered proteins are not necessarily random. Rather, the disordered state has a significant residual structure. In the disordered state, a protein exists in an ensemble of conformers. In many cases, these regions constitute only certain parts or domains of the whole protein. While disordered on their own, their native conformation is stabilized upon binding. The global fold of disordered proteins does not necessarily change upon binding to different partners; however, local conformational variability can be observed, thereby complicating predictions of protein interactions. Published in: Ozlem Keskin; Attila Gursoy; Buyong Ma; Ruth Nussinov; Chem. Rev. 2008, 108, 1225-1244. Proteins are flexible
Proteins are flexible. Figure 2 (A) The free energy landscape of a protein may change upon binding to another protein. Binding may induce a shift in the distribution of the populations of the conformational states of the protein; consequently, the relative population of the conformer with an altered binding site shape at another location on the protein surface may increase. The solid black line refers to the free energy landscape, and the dashed red line refers to the relative populations. (I) Distribution of the substates of the protein conformations, presenting several binding possibilities. (II) When a ligand binds at the first binding site, it shifts the conformational energy landscape and the distribution of the populations to favor selective binding at a second, allosteric site. (III) The final dominant conformer recognizes both ligands. Allosteric structural changes
Proteins are flexible. Figure 3 Comparisons of proteins in bound, complexed states versus in the free (apo) states. (A) The conformational changes undertaken by the K-binding protein (PDB IDs: 2lao (yellow) and 1lst (cyan)). The free structure (yellow) closes up and becomes stabilized when it is bound (cyan structure) to its ligand. The ligand, shown in red, belongs to the cyan structure. This is a domain motion example. (B) Glutathione S-transferase-I in free and bound forms (PDB IDs: 1aw9 (shown in cyan) and 1axd (yellow), respectively). The ligand introduces a conformational change in the loop. The idea of "hot spots"
Protein binding sites are clusters of "hot spots". Figure 5 Crystal structure of a complex displaying the hot regions between two M chains of the human muscle L-lactate dehydrogenase (PDB ID: 1i10). Two interacting chains are shown in yellow and cyan. The hot spots (red), shown in ball and stick representation, are residues whose substitution by Ala leads to a significant (G 2 kcal/mol) drop in the binding free energy (Clackson & Wells; Science 1995 267, 383). There are two hot regions in this interface of the homodimer. The figure illustrates that hot spots are in contact with each other and form a network of interactions forming hot regions. Sequences differ, structures are the same
Different protein partners may have similar binding motifs. Figure 9 Example of multiple proteins binding at the same site on the protein surface, dimerization cofactor of hepatocyte nuclear factor (DCoH). DCoH serves as an enzyme and a transcription coactivator. The left figure is the crystal structure of hepatocyte nuclear factor dimerization domain, HNF-1, bound to a DCoH dimer (PDB ID: 1F93, Chains A, B of DCoH, and Chains E, F of HNF-1). In order to act as a coactivator, DCoH binds to HNF 1. The figure on the right displays the enzymatic form of the protein DCoH forming dimers of dimers (shown Chains A, B, C, and D, PDB ID: 1DCH). Published in: Ozlem Keskin; Attila Gursoy; Buyong Ma; Ruth Nussinov; Chem. Rev. 2008, 108, 1225-1244. ...
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