N?lting B. Methods in Modern Biophysics

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10.5 Detection of biological agents 195

bution of biological agents offers little information about the precise nature of the

agent. That is why biological agents are pyrolyzed prior to analysis in the IMS

(Fig. 10.27). Pyrolysis (see also Sect. 3.2) decomposes and vaporizes biological

agents and can be applied on bacteria and viruses (Fig. 10.28). The low vapor

pressure of most biological compounds requires an operation of the IMS at a

sufficiently high temperature (Fig. 10.29). The set-up virtual impactor / pyrolyzer

/ GC / IMS (Fig. 10.27) is capable to detect a few bacterial spores in a volume of

several 1000 liters.

-Value analysis

In Chap. 1 some inter-residue contact maps of protein transition states were

presented. Here, the method of

-value analysis underlying such maps and some

of its high-resolution applications are presented in more detail: the correlation of

inter-residue contacts with

-values (see Fig. 1.9) is the currently available

method with the highest resolution for protein folding transition states (Nölting,

1998, 1999a, b; Nölting and Andert, 2000).

The transition state corresponds to the state with the highest free energy in the

course of the reaction. Since it is only extremely short-living, at present its

structural resolution can not be carried out with NMR or X-ray crystallographic

analysis.

-Value analysis uses mutants as structural reporters and a combination

of equilibrium thermodynamics and kinetics methods (Nölting, 2005).

11.1 The method

Fig. 11.1 shows the free energy changes in the folding reaction for a wild-type

protein and a mutant of this protein. One can see that in the course of the reaction

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Fig. 11.1

Energy landscape along the reaction coordinate for the folding reaction of a

wild-type protein (top curve) and a mutant of this protein (bottom curve)

198 11

-Value analysis

Fig. 11.2

Built-up of an energy difference,

∆∆

G, between wild-type protein and a mutant

in the course of the folding reaction.

∆∆

F–U

is the energy difference between wild-type

and mutant protein in the folded state

an energy difference,

∆∆

G, builds up between wild-type and mutant protein. This

build-up of

∆∆

G corresponds to the build-up of structure in the molecule. In

particular, the time point in the reaction at which

∆∆

G becomes significant

depends on the time at which the interactions probed by the mutation build up in

the molecule: If the interactions altered by the mutagenesis form early in the

folding reaction (left curve in Fig. 11.2), one usually observes an early increase of

∆∆

G|. In contrast, if the interactions probed by mutagenesis are formed late in the

folding reaction, there is usually no significant

∆∆

G till late in the reaction (right

curve in Fig. 11.2). So, by measuring

∆∆

G at the different stages of the folding

reaction one can find out when certain interactions in the molecule are becoming

formed. For the methods of measurement of

∆∆

G see Nölting (2005).

The formation of stable interactions in the molecule is usually expressed by the

-value which is a measure of the structure consolidation at the position of the

mutation on a scale from 0 to 1.

is defined as

∆∆

G /

∆∆

F–U

, where

∆∆

F–U

is the

∆∆

G in the folded state (Nölting, 2005). A

of 0 at a certain stage of the

folding reaction suggest the absence of stable structure at the position of the

mutation at this time. If structure is completely formed at the position of the

mutation at this stage of the reaction, one would expect a

-value of 1. Possible

sources of error in this analysis, e.g., the effect of non-native interactions, can be

decreased by using several mutants for the same part of the molecule.

So, in order to obtain information on the structure of a transition state one

simply needs to measure

of the transition state for many mutants and correlate

the data with the inter-residue contacts in the molecule (Nölting, 1998, 1999a, b).

11.2 High resolution of six protein folding transition states 199

11.2 High resolution of six protein folding transition states

This section presents the structural characteristics of the main transition states of

six proteins obtained by correlation of inter-residue contacts with

-values (see

also Sect. 11.1; Chap. 1; Nölting and Andert, 2000). The first four proteins,

barstar, barnase, chymotrypsin inhibitor 2 (CI2), and src SH3 domain are mono-

meric in the native state. Arc repressor is dimeric, and p53 is a tetramer with the

structure of a dimer of dimers. In the first five main transition states (Figs. 11.3–

11.7) one can see a very non-uniform consolidation of structure. It has been

shown that for all five proteins the most consolidated clusters (highlighted as

ribbons in Figs. 11.3–11.7; unconsolidated structure is displayed as wires) contain

a relatively higher content of residues which belong to secondary structure

elements than the non-consolidated parts of the molecules. On the other hand, all

six transition states with the exception of the src SH3 domain (Figs. 11.3–11.5,

11.7, 11.8) contain on average a similar content of secondary and tertiary structure

interactions (Nölting and Andert, 2000). This high resolution of folding transition

states led to an understanding of the mechanism of protein folding and of its

astonishing efficiency: folding of many proteins proceeds similar as the growth of

a crystal – largely driven by the propensity of secondary structure formation, but

also by the hydrophobic effect and other forces, a folding nucleus forms early in

the folding reaction. This nucleus then restricts the number of possible confor-

mations and enables further structure growth around it (Nölting and Andert, 2000;

Nölting et al., 2003; Nölting, 2005).

Fig. 11.3

Main transition state structure of barstar (Nölting and Andert, 2000). Consoli-

dated structure is highlighted as ribbons; unconsolidated parts of the molecule are shown

as wires. Amino acid residues with high

-values are highlighted as spheres. This figure

and the following figures in this section were prepared using MOLMOL, Koradi et al., 1996

200 11

-Value analysis

Fig. 11.4

Main transition state structure of barnase (Nölting and Andert, 2000). Consoli-

dated structure is highlighted as ribbons. For further explanation see Fig. 11.3

Fig. 11.5

Transition state structure of CI2 (Nölting and Andert, 2000). Consolidated

structure is highlighted as ribbons. For further explanation see Fig. 11.3

11.2 High resolution of six protein folding transition states 201

Fig. 11.6

Transition state structure of the src SH3 domain (Nölting and Andert, 2000).

Consolidated structure is highlighted as ribbons. For further explanation see Fig. 11.3

Fig. 11.7

Transition state structure of Arc repressor (Nölting and Andert, 2000). Consoli-

dated structure is highlighted as ribbons. For further explanation see Fig. 11.3

202 11

-Value analysis

Fig. 11.8

Main transition state structure of p53 (Nölting and Andert, 2000). In this

transition state essentially all parts of the molecule are highly consolidated. Here the

residues with low

-values are highlighted as small spheres

12 Evolutionary computer programming

12.1 Reasons for the necessity of self-evolving computer

programs

Nature offers a tremendous amount of extremely complicated problems which

cannot easily be rationalized and resolved. Probably one has to accept that there

are scientific and technological problems too complex to be directly rationalized

by humans. A well-known example is the non-periodical movement of many

gravitationally interacting bodies in space. Since we are not able to imagine their

motions with a sufficient degree of perfection, we call it "chaos". Unfortunately,

humans obviously have significant intellectual difficulties to find theoretical

descriptions or models for phenomena which they do not comprehend. Similarly,

as an ape cannot write a mathematical equation beyond its intellectual abilities,

humans are not directly able to establish mathematical structures beyond their

intellectual limits. However, further progression of science and technology

urgently requires to overcome such limits.

One well-known example for a complicated problem is the so-called folding

paradox (see, e.g., Nölting, 2005): how can a protein find its unique native

conformation among the ~10

–10

200

possible conformations of an average small

protein in the unfolded state? One of the major difficulties of complex phenomena

like protein folding is often the lack of an efficient and solvable mathematical

description. Often one is able to write down some equations which describe the

physics of the system while not being able to solve them.

This chapter describes a method which can potentially provide solutions

beyond current human intelligence: in order to overcome the limits of rational

design, one lets a computer program evolve itself. The method is exemplarily

applied on protein folding and structure predictions (Nölting et al., 2004) and the

optimization of optical effects of nanoparticle arrays. In Sect. 12.5 the much

wider scope of this method is discussed.

12.2 General features of the method

Figs. 12.1 and 12.3 show the principle of operation of the method of self-evolving

programs. A so-called wild-type computer program is evolved towards higher

efficiency by mutagenesis and selection in a similar way as species evolve in

204 12 Evolutionary computer programming

nature: First a number of mutants of the wild-type program is created. The

performance of the mutants is then tested and the best performing program serves

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Fig. 12.1

Scheme of the method of evolutionary computer programming. The best perfor-

ming program at a certain stage of the evolution is shown as a filled rectangle. Open

rectangles indicate less-performing mutants which are usually sorted out. Essentially, the

method is based on the mutation and selection of computer programs similarly as for

species in the biological evolution. In this way, an initial program which contains mu-

tatable parts becomes highly optimized in the course of successive rounds of evolution

Fig. 12.2

A suitable structure of a program for self-evolution. The genes are the mutatable

parts of the program. The genes improve the start solution of the given task

12.2 General features of the method 205

Fig. 12.3

Example of evolutionary computer programming

as a template for further mutagenesis (the next evolution step). The pathway of

evolution is highlighted by filled rectangles in Fig. 12.1. Open rectangles

correspond to dead ends of the evolution, e.g., mutants which did not perform best