Methods and apparatuses for stretching polymers

Details Methods and apparatuses for stretching polymers Methods and apparatuses for stretching polymers

2000-08-11

2004-02-24

Ludlow, Jan (Department: 1743)

Chemical apparatus and process disinfecting, deodorizing, preser

Analyzer, structured indicator, or manipulative laboratory...

Means for analyzing gas sample

C422S082050, C422S105000, C422S105000, C422S068100, C436S086000, C436S094000

Reexamination Certificate

active

06696022

ABSTRACT:

1. FIELD OF THE INVENTION
The present invention relates to the general field of polymer characterization. More particularly, the invention relates to the use of structures to stretch a polymer or to select a polymer on the basis of length in a chip.
2. BACKGROUND OF THE INVENTION
Macromolecules are involved in diverse and essential functions in living systems. The ability to decipher the functions, dynamics, and interactions of macromolecules is dependent upon an understanding of their chemical and three-dimensional structures. These three aspects—chemical and three-dimensional structures and dynamics—are interrelated. For example, the chemical composition of a protein, and more particularly the linear arrangement of amino acids, explicitly determines the three-dimensional structure into which the polypeptide chain folds after biosynthesis (Kim & Baldwin (1990) Ann. Rev. Biochem. 59: 631-660), which in turn determines the interactions that the protein will have with other macromolecules, and the relative mobilities of domains that allow the protein to function properly.
Biological macromolecules are either polymers or complexes of polymers. Different types of macromolecules are composed of different types of monomers, i.e., twenty amino acids in the case of proteins and four major nucleobases in the case of nucleic acids. A wealth of information can be obtained from a determination of the linear, or primary, sequence of the monomers in a polymer chain. For example, by determining the primary sequence of a nucleic acid, it is possible to determine the primary sequences of proteins encoded by the nucleic acid, to generate expression maps for the determination of mRNA expression patterns, to determine protein expression patterns, and to understand how mutations in genes correspond to a disease state. Furthermore, the characteristic pattern of distribution of specific nucleobase sequences along a particular DNA polymer can be used to unequivocally identify the DNA, as in forensic analysis. To this end, fast, accurate and inexpensive methods of characterizing polymers, and particularly nucleic acids, are being developed as a result of the endeavor of the Human Genome Project to sequence the human genome.
A challenge to the characterization of the linear sequence of monomers in a polymer chain has come from the natural tendency of polymers in most media to adopt unpredictable, coiled conformations. The average amount of such coiling is dependent on the interaction of the polymer with the surrounding solution, the rigidity of the polymer, and the energy of interaction of the polymer with itself. In most cases, the coiling is quite significant. For example, a&lgr;-phage DNA, theoretically 16 &mgr;m long when stretched out so that the DNA is in the B conformation, has a random coil diameter of approximately 1 &mgr;m (Smith et al. (1989) Science 243:203-206).
DNA and many other biopolymers can be modeled as uniform elastic rods in a worm-like chain in order to determine their random coil properties (Austin et al. (1997) Physics Today 50(2):32-38). One relevant parameter is the persistence length, P, the length over which directionality is maintained, which is given by:
P=&kgr;/k
B
T
  (1)
where &kgr; is the elastic bending modulus (Houseal et al. (1989) Biophys. J. 56:507-516), k
B
is the Boltzmann constant, and T is temperature (Austin et al. (1997) Physics Today 50(2):32-38). A longer persistence length means that the polymer is more rigid and more extended. Under physiological conditions, P≅50 nm for DNA. While larger than the molecular diameter of 2.5 nm, the persistence length is many orders of magnitude smaller than the actual length of a typical DNA molecule such as a human chromosome, which is about 50 mm long. From the persistence length, the overall coil size, R, can be calculated (Austin et al. (1997) Physics Today 50(2):32-38) as follows:
(
R
2
)=2
PL
  (2)
where L is the contour length of the DNA molecule. In the case of chromosomal DNA, R≅70 &mgr;m. Clearly, it is much easier to analyze information on an extended piece of DNA that is 5 cm long than on a piece of DNA that has a coil size of 70 &mgr;m.
The force necessary to stretch polymers such as DNA is not very large. The worm-like chain model allows the polymer to be considered to be like a spring, and the force (F
s
) needed to extend it close to its full natural length can be calculated (Austin et al. (1997) Physics Today 50(2):32-38) as follows:
F
s
≅k
B
T/P
  (3)
where all of the parameters are defined as above. Below F
s
, the relationship between the force applied and the amount of stretching is roughly linear; above F
s
, applying more force results in little change in the stretching (Smith et al. (1992) Science 258:1122-1126; Bustamante (1994) Science 265:1599-1600). Hence, full stretching is essentially attained by applying F
s
. In the case of DNA, the force required to stretch it from its coiled conformation to its full length, which stretched conformation retains the B conformation is about 0.1 pN. Such a small force could, in principle, be obtained from virtually any source, including shear forces, electrical forces, and gravitational forces.
The danger in stretching DNA comes not in breaking the covalent bonds, which requires at least 1 nN of force (Grandbois et al. (1999) Science 283:1727-1730), but in over-stretching. It has been observed that, when 70 pN of force is applied, DNA adopts a super-relaxed form, called “S-DNA”, having nearly twice the length of normal B-form DNA having the same number of base pairs (Austin et al. (1997) Physics Today 50(2):32-38). Others have reported this transition at a force of 50 pN (Marko & Siggia (1995) Macromolecules 28:8759-8770). The length of S-DNA is less consistent than that of B-DNA stretched to its natural length and is more dependent on the exact force applied (Cluzel et al. (199
6
) Science 271:792-794), varying linearly with applied force from 1.7 to 2.1 times the length of B-DNA. Since it may not be possible to know the exact force applied, it is desirable to avoid stretching DNA into its S-form. Therefore, a force having a range of about two orders of magnitude, from about 0.1 pN to 25 pN, is capable of consistent and predictable stretching of DNA to its fully extended B-form.
In addition, the force must be applied fast enough to keep the polymer from recoiling. The natural relaxation time of a polymer, &tgr;, depends on the solvent, as follows (Marko (1998) Physical Review E 27:2134-2149):
&tgr;≈
L
2
P&mgr;/k
B
T
  (4)
where &mgr; is the viscosity of the solvent and the other parameters are as defined above. In the case of DNA at physiological conditions, the relaxation time is about 6 seconds, which can be increased to 20 seconds in a solution with a viscosity of 220 cp (Smith et al. (1999) Science 283:1724-1727) or by running the DNA in a confined space to lengthen P and change the viscous drag (Bakajin et al. (1998) Phys. Rev. Let. 80:2737-2740). Relaxation time is also a function of the extent of stretching (Hatfield & Quake (1999) Phys. Rev. Let. 82:3548-3551), so the values calculated above are a lower bound on the actual relaxation time.
Regardless of the exact value of the relaxation time, the polymer must be stretched out on a shorter time scale. In the case of flow through a channel, in which the stretching comes from fluid strain on the polymer, the appropriate time scale for stretching is the reciprocal of the strain rate. The strain rate is defined as d&egr;/dt=dv
x
/dx, where x is the flow direction and v
x
is the x-component of the velocity. The multiple of the strain rate and the relaxation time is known as the Deborah number, De=&tgr;d&egr;/dt, and can be used to determine whether the stretching will be maintained (Smith & Chu (1998) Science 281:1335-1340). If De is much greater than one, then the strain force predominates and the polymer will remain stretched. If De is much smaller than one, then the natural relaxation process dominates and the polym

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