Welcome to my Research Web Page:

My research work is mainly in two fields:

  1. Analytical Continuum Electrostatics (ACE):

ACE is a continuum electrostatic model (Schaefer & Karplus, Journal of Physical Chemistry, 1996, 100).

Continuum electrostatics methods describes the effect of water on the system (typically a protein) while the water is treated implicitly. This is particularly useful when one performs Molecular Dynamics simulations or finding minimum energy pathways using methods like CPR (Conjugate Peak refinement) (
S. Fischer & M. Karplus. Conjugate Peak Refinement : An algorithm for finding reaction paths and accurate transition states in systems with many degrees of freedom. Chemical Physics Letters 194, 252-261 (1992)) between two conformations of a protein.

I wrote a small introduction to Continuum Electrostatics. Here I describe the most common methods used describing the electrostatics component of solvation free energy for huge macromolecules and specifically elaborate on ACE (a generalized born model).

If you are interested to know more about continuum models, please download my
Introduction to Continuum Electrostatics.

My aim to use continuum methods is to study the Conformational transitions in Myosin II and thus understand the energetics involved when Myosin II goes from one conformation to another

 2. 
Conformational Transitions and Energetics in Myosin II:

 I. Research on muscle contraction goes back to the Greeks:
           Understanding muscle contraction answers one of the fundamental questions posed in classical times, namely the nature of the spiritus animalis. The spiritus animalis was an intrinsic property of living things. Erasistratus (3rd century B.C.) of the Alexandrian school associated the spiritus animalis with the muscles. The pneuma was thought to course along the nerves and make the muscles swell and shorten. In the beginning of the 2nd. century A.D. Galen, the last classical physiologist took over and expanded these ideas introducing a primitive metabolism involving the four humours. Furthermore, Galen made a detailed anatomical examination of muscles and understood that they worked in antagonistic pairs, and that the heart was a muscle for pushing blood into the arteries. In the ensuing millennium nothing much happened and even Galen's insight that muscles pull rather than push seems to have been forgotten, since at the beginning of the ¢16, on the basis of his own anatomical examinations Leonardo da Vinci wrote: "perchè l'ufizio del musculo è di tirare e non di spingere ".

            A few years later Vesalius used the phrase Machina Carnis to underline the fact that the production of force resided in the flesh (muscle) itself, and in the early ¢16 Descartes proposed a neuromuscular machine not unlike that of Erasistratus: the nerves carry a fluid from the pineal gland (the seat of the soul) to the muscles which makes them swell and shorten. A little later, Swammerdam was to show that muscles contract at constant volume which invalidated this whole class of pneumatic theories. However, other mechanical models were soon proposed. Alongside such mechanical thinking, however, vitalism survived into the ¢19th., and one needed the whole fabric of metabolic biochemistry and thermodynamics to support the concept that muscle is a chemical machine driven by isothermal combustion which was first articulated by von Helmholtz.
 

II. Myosin II :

            In vertebrates several myosin-types can be found. Not all of them are involved in muscle contraction as the Myosin II. (Myosin I for example is necessary for vesicle transport along actin-filaments in the cell.) The muscle, Myosin II is a Hexamer with 2 identical heavy chains which are connected to each other via a coiled coil-structure in the tail-region and both of them harbor 2 light chains ("regulatory" and "essential")

 
           

            Looking closer at the S1-structure you can see that it is subdivided in domains. The head is elongated and consists of a seven stranded beta sheet and a C-terminal a-helical tail which carries the two calmodulin-like light chains (magenta and yellow). S1 can be proteolytically broken into 3 fragments named after their apparent molecular weight:
a) 25K (N-terminal)
b) 50K (middle)
c) 20K C-terminal)
The 50K fragment spans two domains called the 50K upper domain and the 50K lower domain (actin binding domain).
The ATP-binding site lies near the 25K-50K boundary and contains a P-loop which can be found in many ATPases and G-proteins. The 20K domain contains a broken helix with two reactive thiols (SH1 and SH2). The converter domain follows the SH1 helix which functions as a socket for the C-terminal helical tail.
The C-terminal tail which is associated with the light chains is called the regulatory domain or neck and has the main function as a lever arm to amplify rotational movements by the converter domain.


III. The cross bridge cycle

In muscle contraction Myosin II undergoes a continuously conformational changes which involves consuming a molecule of ATP, hydrolyzing it and then performing "A Power Stroke". This cycle of events is  called the Lymn-Taylor cycle which was postulated in 1971.

After a Ca signal from the outside the troponin-complex enables Myosin to bind to Actin which then leds to the release of Orthophosphate and then ADP. After that the power stroke moves Myosin about 10nm along the Actin-filament by changing the structure from the open to the closed form which changes the orientationn of the S1-head. This is the cause of muscle contraction. After binding of ATP the affinity of Myosin for Actin is rapidly decreased and the Myosin looses the contact with Actin. Upon ATP-hydrolyzation the S1-domain rearranges and a new cycle can begin.

The conformational changes between OPEN and CLOSED are limited to the switch region (switch 2 and switch helix) and the SH2-SH1 hinge region.
After closing of the gamma-phosphate-binding pocket the switch-2-helix is twisted about 60 degrees which causes a 60 degree rotation of the
To close the g-phosphate-binding site there is a rotation of the actin-binding domain with respect to the 50 K upper domain about the helix 648-666. This pushes the SH1 helix into the switch 2 helix. The switch 2 helix responds by breaking and twisting at residue 497. As this happens, the end of the switch 2 helix rotates through about 60 degrees and carries the converter domain with it.

 

IV The Myosin Cross Bridge has two Conformations:

            According to the Lymn-Taylor scheme (fig. 2) the myosin cross bridge would be expected to have two discernible conformations: (1) when it first attaches to actin with the products of hydrolysis still bound with the lever at the beginning of the working stroke called the CLOSED conformation and
(2) at the end of the working stroke when the phosphate and ADP are released. A new ATP molecule binds into Myosin and Myosin dissociates from Actin and we have the OPEN conformation. This is the conformation before the hydrolysis of ATP to ADP and gamma-phosphate occurs

Fig 3 & 4

This sequence is often referred to as the "power stroke". The end state is referred to as "rigor", since it is the state muscle enters on ATP depletion. It is also called "strong" because it binds to actin quite tightly. The initial state is called the "weak binding state" because of its low affinity for actin (see (Geeves and Conibear 1995) ). We might anticipate that these two states of the myosin cross bridge might exist independently from actin and indeed protein crystallography shows this to be the case.
The chicken S1 structure was solved without bound nucleotide. Furthermore, the chicken S1 crystal structure fits excellently into the electron micrograph reconstruction's of the strong actin-myosin nucleotide-free interaction (decorated actin) . Therefore the crystal structure of chicken S1 would appear to represent the end of the power stroke or rigor state. In addition, Rayment et al have studied a crystalline fragment of the dictyostelium myosin II cross-bridge which has been truncated after residue 761 (equivalent to gg781). The truncation eliminates the lever arm and the associated light chains (which aids crystallization). However, the converter domain is still present. The crystal structures of the 761 construct have been determined with a number of ATP analogs, particularly ADP.BeFx (Fisher et al. 1995) and ADP.vanadate (Smith and Rayment 1996). ADP.vanadate complexes are used as analogs of the transition state or possibly of the ADP.Pi state. While the ADP.BeFx state looks similar to rigor, the ADP.vanadate structure shows, compared to the chicken rigor structure dramatic changes in shape of the S1 structure, There is a closing of the 50K upper/lower domain cleft, particularly around the [gamma]-phosphate binding pocket, and large movements in the C-terminal region. The 50K upper/lower domains rotate a few degrees w.r.t. each other around the helix gg648-666 in a way which closes the nucleotide binding pocket (Fig 5) - a movement of some 5Å. At the same time the outer end of the long helix (the so called switch 2 helix, residues gg475-507) bends out 24° at residue V497. This is coupled to a rotation of the converter domain (gg711-781) by 70°. The fulcrum is provided by the mutual rotation of the distal part of the SH1-SH2 helix around the distal part of the switch 2 helix.

V. References :

1. Geeves, M. A. & Holmes, K. C. (1999). Structural mechanism of muscle contraction. Ann. Rev. Biochemistry 68, 687-727.

2. Cooke, R. (1986). The Mechanism of Muscle Contraction. CRC Crit Rev. Biochem 21, 53-118.

3. Holmes, K. C. (1997). The swinging lever arm hypothesis of muscle contraction. Current Biology 7(2), R112-R118.

 

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