Biopolymers, such as proteins and DNA, are polymers whose three-dimensional

conformations dene their biological functions. Current emphasis on structures has

greatly advanced our understanding of the functions of biopolymers. However, there

is a need to understand the deeper link between biopolymer dynamics and function,

because in water and under cellular conditions, everything that biopolymers do can

be understood in terms of "the jigglings and wigglings of atoms". These motions

arise from thermal noise in the solvent and due to intrinsic motion of the enzymes. In

biological systems, the motions are often highly regulated to ensure that cellular processes are executed over the required time scales. For enzymes, which are essentially

proteins that catalyze chemical reactions or generate mechanical work, conformational

fuctuations are coupled at various stages through interactions with ligands

during the catalytic cycle. We have studied two dierent enzymes, dihydrofolate

reductase (DHFR), which catalyzes reduction of dihydrofolate to tetrahydrofolate,

and RNA polymerase (RNAP from bacteria and Pol II from yeast), which is responsible for RNA synthesis using DNA as a template. In order to study the link between

dynamics and function we have developed new methods and extended a variety of

computational techniques. For DHFR, we use both evolutionary imprints (SCA)

and structure-based perturbation method (SPM) to extract a network of residues

that facilitate the transitions between two distinct conformational states (closed and

occluded states). The transition kinetics and pathways connecting the closed and

occluded states are described using Brownian dynamics (BD) simulation. We found

the sliding motion of Met20 loop across helix 2 is involved in the forward and reverse

transitions between the closed and occluded states. We also found that cross-linking

M16-G121 inhibits both the forward and the reverse transitions. In addition, we

showed the transition states of these transitions are broad and resemble high energy

states.

For RNAP, we focus on the conformational changes of RNAP and DNA in

promoter melting process. Using BD, we show that DNA conformation changes

in promoter melting occur in three steps. We also show that internal dynamics

of RNAP is relevant to facilitate the bending of DNA. For Pol II, the structural

transitions between two initiation conformational states and between initiation state

and elongation state are studied using SPM and BD. We determine the structural

units that regulate structural transitions and describe the transition kinetics. The

combination of three dierent methods, SCA, SPM and BD, provide results that

are in accord with many experiments. Moreover, our description of the detailed

structural transitions in these enzymes lead to new insights and testable predictions

in these extraordinarily important enzyme functions.