v13 control of gene expression

13. Lecture WS 2006/07

Bioinformatics III 1

V13 Control of Gene Expression

A bacterial cell lives in direct contact with its environment.

Its chemical composition may dramatically change from one moment to the other.

Consider bacteria growing either on lactose or tryptophan.

Fig. 2.16 Lactose: di-saccharide from glucose + galactose

oxidation provides cells with metabolic intermediates

and energy.

First step of lactose degradation (catabolism):

hydrolysis of the bond joining the 2 sugars by

-galactosidase

[Karp] Cell & Mol. Biol.



Transfer from minimal medium to lactose medium

When bacterial cells are grown in

a minimal medium, they don‘t

need -galactosidase and

contains < 5 copies and only 1

copy of its mRNA.

What happens when the cells are

transferred to a lactose medium?




lac Operon: an inducible operon

Inducible operon: presence of substance

(lactose) induces transcription of the

structural genes.

lac operon contains 3 tandem structural

genes:

z gene: encodes -galactosidase

y gene: encodes galactoside permease,

a protein that promotes entry of lactose

into the cell

a gene: encodes thiogalactoside

acetyltransferase




positive control by cyclic AMP

Repressors, such as those of the lac and trp operons, exert their influence by

negative control.

lac operon is also under positive control, the „glucose effect“.

If bacterial cells are supplied with glucose (as well as with other substances such as lactose

or galactose), the cells catabolize the glucose and ignore the other compounds.

glucose in the medium suppresses the production of various catabolic enzymes, such as

-galactosidase, needed to degrade the other substrates.

In 1965, cAMP was deteced in E.coli. The higher the glucose concentration, the lower the

cAMP concentration. When adding cAMP to the medium in the presence of glucose, the

catabolic enzymes that were normally absent were suddenly synthesized by the cell.

cAMP binds to CRP. The cAMP-CRP complex recognizes and binds to a specific site in the

lac control region. The presence of bound CRP changes the DNA conformation and allows

RNA polymerase to transcribe the lac operon.




positive control by cyclic AMP

Fig. 12.27




Growth on Trp medium

Trp is required for protein synthesis.

If no Trp is available in the medium, the bacterium must expend energy

synthesizing this amino acid cells contain enzymes and corresponding mRNA

of Trp-synthesis pathway.

If Trp becomes available in the medium, the cells no longer have to synthesize

their own Trp. Within a few minutes, the production of the enzymes of the Trp

pathway stops. In the presence of Trp, the genes encoding these enzymes are

repressed.




trp operon

In a repressible operon, the repressor

is unable to bind to the operator DNA

itself.




eukaryotic gene expression: PEPCK

model case: gene that codes for phosphoenolpyruvate carboxykinase (PEPCK).

This enzyme is one of the key enzymes of gluconeogenesis, the metabolic pathway that

converts pyruvate to glucose.

The enzyme is synthesized in the liver when glucose levels are low, e.g. when considerable

time has passed since your last meal. Synthesis drops sharply after carbohydrate-rich meal.


Level of synthesis of PEPCK mRNA is controlled by a variety of transcription factors,

including several hormone receptors that are involved in regulating carbohydrate

metabolism.

To understand the regulation of PEPCK gene expression, we need to

(1) unravel the functions of the numerous DNA regulatory sequences that residue upstream

from the gene itself

(2) identify the transcription factors that bind these sequences, and

(3) identify the signalling pathways that activate the machinery responsible for selective

gene expression.



eukaryotic gene expression: PEPCK

Fig. 12.32

TATA box followed by core promoter: site of assembly of a pre-initiation complex consisting

of RNA polymerase II and a number of general TFs

CAAT + GC boxes: bind global TFs such as NF1 and SP1; both are typically located 100 –

150 bp upstream proximal promoter elements [Karp] Cell & Mol. Biol.



Responsive elements from PEPCK gene

various hormones affect the expression of

PEPCK gene: insulin, thyroid hormone,

glucagon, glucocorticoid.

All of the act by means of specific TFs

that bind to the DNA.

Fig. shows responsive elements.




Activation of transcription

For example, let us focus on glucocorticoids, a group of steriod hormones (e.g. cortisol) that

are synthesized in response to stress.

Fig. 12.34




Conservation of regulatory elements?

Nature 423, 241 (2003)



Comparative genome analysis

Compare sequences of Saccharomyces paradoxus, S. mikatae, S. bayanus, with

S. cerevisae.

The three new yeast species have

sufficient sequence similarity to

S. cerevisiae to allow orthologous

regions to be aligned reliably, but

sufficient sequence divergence

to allow many functional elements

to be recognized by their greater

degree of conservation

by a four-way species comparison.

Assemble with Arachne program

Align 4 genomes.

Nature 423, 241 (2003)



Conservation of the Gal4-binding site

We first studied the binding site for one of the best-studied transcription factors,

Gal4, whose sequence motif is CGGn(11)CCG (which contains 11 unspecified

bases).

Gal4 regulates genes involved in galactose metabolism, including the GAL1 and

GAL10 genes, which are divergently transcribed from a common intergenic

region (Fig. 6).

The Gal4 motif occurs three times in this intergenic region, and all three instances

show perfect conservation across the four species.

In addition, there is a fourth experimentally validated binding site for Gal4 that

differs from the consensus by one nucleotide in S. cerevisiae.

This variant site is also perfectly preserved across the species.

Nature 423, 241 (2003)



Conservation of the Gal4-binding site

We then examined the frequency and conservation of Gal4-binding sites across the aligned

genomes. In S. cerevisiae, the Gal4 motif occurs 96 times in intergenic regions and 415

times in genic (protein-coding) regions.

The motif displays certain marked conservation properties:

(1) occurrences of the Gal4 motif in intergenic regions have a conservation rate (proportion

conserved across all four species) that is about fivefold higher than for equivalent random

motifs.

(2) intergenic occurrences of the Gal4 motif are more frequently conserved than genic

occurrences. By contrast, random motifs are less frequently conserved in intergenic regions

than in genic regions, reflecting the lower overall level of conservation in intergenic regions.

Thus, the relative conservation rate in intergenic compared with genic regions is about 11-

fold higher for Gal4 than for random motifs.

(3) the Gal4 motif shows a higher conservation rate in divergent compared with convergent

intergenic regions (those that lie upstream compared with downstream of both flanking

genes); no such preferences are seen for control motifs. These three observations suggest

various ways to discover motifs based on their conservation properties.

Nature 423, 241 (2003)



Assign function

Assign candidate functions to these discovered motifs by the genes adjacent to conserved

occurrences of the motif with known gene categories.

Test for Gal4 motif. Given the biological role of Gal4, we considered the set of genes

annotated to be involved in carbohydrate metabolism (126 genes according to the Gene

Ontology classification) with the set of genes that have a Gal4-binding motif upstream. The

intergenic regions adjacent to carbohydrate metabolism genes comprise only 2% of all

intergenic regions, but 7% of the occurrences of the Gal4 motif in S. cerevisiae and 29% of

the conserved occurrences across the four species.

suggests that a function of the Gal4 motif could be inferred from the function of the genes

adjacent to its conserved occurrences. Such putative functional assignments can be useful

in directing experimentation for understanding the precise function of a motif.

Such considerations indicate that it should be possible to use comparative analysis, such

as explored here for yeast, to identify directly many functional elements in the human

genome that are common to mammals. More generally, comparative analysis offers a

powerful and precise initial tool for interpreting genomes.

Nature 423, 241 (2003)



Hybrid-methods for macromolecular complexes

Structural Bioinformatics

(a) Integration of

structures of various

protein components into

one large complex.

What to do if density is

too small or too large?

Sali et al. Nature 422, 216 (2003)



Example of EM/X-ray hybrid

docking of atomic X-ray structure of tubulin (3.5 Å resolution)

into 8Å-EM-structure of microtubuli.

Sali et al. Nature 422, 216 (2003)



Overview: Various Techniques

(a) Linear correlation of densities

(b) Density filtering (Laplace correlation)

(c) Core weighting of densities

(d) Surface overlap matching (SOM) of densities

(e) Electron tomography: detect particle densities in whole cells

Wriggers, Chacon, Structure 9, 779 (2001)



Situs: Automatic fitting package X-ray / EM

Chacon et al. Acta Cryst D 59, 1371 (2003)

Situs was developed for automatic

fitting of high-resolution X-ray structures

into low-resolution EM maps.

http://biomachina.org

see also database for animations of the

slow dynamics of low-resolution

proteins:http://emotion.biomachina.org/

Willy Wriggers

http://biomachina.org/

http://biomachina.org/



Fourier Series

The Fourier series is named after Joseph Fourier

A Fourier series is a representation of a periodic function

with period 2 as a sum of periodic functions of the form

www.wikipedia.org

inxex

which are the harmonics of eix.

Euler‘s formula states

xixeix sincos

It follows that

2sin

2cos

ixix

ixix

eex

eex

Joseph Fourier (1768 – 1830)

Using cos (-x) = cos x and sin (-x) = - sin x



Proof of Euler’s formula

Cz ln

Cixz

idxdzz

izxixixixidx

dz

xixdx

dz

xixz

ln

1

sincoscossin

cossin

sincos

2

Define the complex number z such that

Differentiating z with respect to x

Using the fact that i2 = -1

Separating variables and integrating both sides:

where C is the integration constant.

Now we need to show that C must be zero.

Set x = 0.

But z is just equal to

Now we exponentiate:

10sin0cossincos ixixz

0

1ln

C

C

xixe

ez

ee

ixz

ix

ix

ixz

sincos

lnln



Definition of a Fourier Series

Suppose that f(x), a complex-valued function of a real variable, is periodic with

period 2, and is square-integrable over the interval from 0 to 2. Let

dxexfF inx

n 2

1

Each Fn is called a Fourier coefficient.

Then, the Fourier series representation of f(x) is given by

n

inxneFxf

Using Euler‘s formula

one can also express f(x) as an infinite linear combination of cos and sin functions:

nxinxeinx sincos

dxnxxfb

dxnxxfa

nxbnxaaxf

n

n

nnn

sin1

cos1

,sincos2

1

10



Fourier transform

Fourier transforms are generalizations of Fourier series.

Most often, the term „Fourier transform“ refers to the continuous Fourier

transform, representing any square-integrable function f(t) as a sum of complex

exponentials with angular frequencies and complex amplitudes F():


deFtFtf ti

2

11-F



Fourier Transform

Combine a sine function with frequency of 2,one with frequency of 3, and one with frequency of 5,

The amplitudes and phases are suitably chosen so that the sum of the three sine functions (red) gives a nice match to the original signal.

The lowest panel shows the Fourier Transform of the original signal. It consists of a series of peaks. The largest peaks are at 2, 3 and 5 on the x-axis. These correspond exactly to the sine-wave frequencies which we used to reconstruct the unit cell. The heights of the peaks correspond to the amplitudes of the three waves: The smaller peaks in the Fourier transform correspond to additional smaller waves which would have to be added to get a perfect fit to the original density. The Fourier Transform tells us what mixture of sine-waves is required to make up any function.



Convolution theorem

If h(t) is the cyclic convolution of f(t) and g(t):


''' dtttgtfth

where g(t) = g(t + 2n), then the Fourier series transforms are related by:

nnn GFH 2

Conversely, if Hn = 2 FnGn, then h(t) will be the cyclic convolution of f(t) and g(t).

In the discrete space, if Hn is the discrete convolution of Fn and Gn:

nnknk GFH

then the inverse transforms are related by:

tgtfth Conversely, if h(t) = f(t)g(t), then Hn will be the discrete convolute of Fn and Gn.



Convolution theorem


Computing the product of two functions f g is simple - the values of the two

functions are simply multiplied at every point f(x) g(x).

The convolution of two functions is more complex.

To convolute two functions, the first function must be superimposed on the

second at every possible position, and multiplied by the value of the second

function at that point. The convolution is the sum of all of these superpositions.



The Convolution Theorem


For example, here is a line, and its Fourier transform:

The line can be convoluted with a circle:

The result is a circle spread by moving it along the line, or alternatively a line

spread by moving it around the circle. It is clear that the Fourier transform of the

convolution is equal to the product of the transforms of the functions themselves.



Docking approaches for Multiresolution Structures I

Fourier space refinement.

Fem and Fcalc are the Fourier

coefficients (structure

factors) of the EM map and

the probe molecule.


Aim: modify structure/orientation of probe molecule to optimize match

of Fem and Fcalc.

Structure factor

rj represents the position of a general atom in the unit cell relative to a lattice point;

G corresponds to a specific Miller plane.

j

jjhkl fS rGexp

h: coordinates in Fourier

space.

R,T: rotational and

translational parameters of

the model.



Direct space vector quantization II


Direct space refinement is WYSIWYG method.- it is e.g. straightforward to combine EM-based

refinement with constraints from biochemistry

or molecular force fields.

Advantage: very fast!

Disadvantage: all density must be accounted for.

See following example how these limitations can be (partly) overcome.



Direct Space Flexible Fitting with Skeletons


Flexible refinement of T. aquaticus crystal

structure of RNA polymerase (RNAP)

against E.coli EM data.

(a) original EM reconstruction. RNAP and lipid are

arranged in tubular crystals.

(b) single RNAP strand extracted. Docking of single

RNAP (white) into the density using Laplacian

correlation coefficient Fit not optimal!

(c) Discrepancy mapping = resulting map of fitted

molecule was subtracted from map (b).

(d) Segmentation of foreign densities (pink and yellow).

(e) Single-molecule skeleton after subtracting foreign

densities from (b)

(f) Parametrization of skeleton. Connectivities and

vector distances are based on a vector quantization.

(g) Flexible fitting of RNAP.

(h) Comparison of flexibly fitted model with single-

molecule map of (e).



additional slides (not used)



Bragg Law

www.chemsoc.org/exemplarchem/entries/2003/bristol_cook/diffraction.htm

Bombard a crystal being studied with

photons, electrons or neutrons with

an associated wavelength comparable to

the interatomic spacing.

A single atom (theoretically) scatters the

incident waves equally in all directions, but

in a crystal cancellation due to destructive

interference gives zero in most directions.

In certain directions constructive

interference gives maxima

of intensity, producing a pattern

characteristic of the crystal structure.

For constructive interference, the path

difference between waves reflected from the

2 planes must be an integer number of the

wavelength .

As can be seen in the figure, the path

difference is 2d sin and so the Bragg law is

n = 2d sin



Miller Indices


Miller indices are the standard method for labelling the planes of atoms in a crystal.

First, the directions of the lattice vectors a, b and c are identified as the lattice axes.

The units of a, b and c are the number of lattice points.

For example, the first lattice point lying on the a axis has a value for a of 1.

Having identified the plane of atoms of interest, the points of intersection of this plane with

the lattice axes are located.

The reciprocals of these values are taken to obtain the Miller indices. The planes are then

written in the form (h k l) where h = 1/a, k = 1/b and l = 1/c.

Thus the (1 1 1) plane intercepts all three axes at 1.

The (1 0 0) plane intercepts the a axis at 1 but never

intercepts the b and c axes;

the (1 0 0) plane is perpendicular to the a axis and

lies parallel to the b-c plane.

The (1 1 1) plane of a ccp lattice using the conventional lattice axes



Reciprocal lattice

Although the Bragg law gives a simple and convenient method for calculating the

separation of crystallographic planes, further analysis is necessary to calculate the

intensity of scattering from a spatial distribution of electrons within each cell.

Fourier analysis of the periodic nature of crystal lattices shows the importance of a

set of vectors, G, related to the lattice vectors a, b, and c.

The set of vectors G is called the „reciprocal lattice“. This makes the calculation of

the intensities and positions of peaks much easier.

cba

bac

cba

acb

cba

cba

2

*,2

*,2

*

If a, b, and c are primitive lattice vectors of the crystal lattice, then a*, b*, and c*

are primitive lattice vectors of the reciprocal lattice.




Reciprocal lattice

The reciprocal lattice vectors have the properties

2*0*0*

0*2*0*

0*0*2*

ccbcac

cbbbab

cabaaa

The reciprocal lattice is defined as

*** cbaG lkh where h, k, and l are arbitrary integers.




Reciprocal lattice

As an example of a reciprocal lattice, consider a simple cubic lattice with lattice

parameter a. The most sensible choice of primitive lattice vectors is then:

a = ai b = aj c = ak

The reciprocal lattice vectors are then:

a* = 2/a i b* = 2/a j c* = 2/a k

These lattice vectors correspond to another simple cubic lattice with lattice

parameters 2/a.




Reciprocal lattice

It is no coincidence that the Miller indices identified earlier used the letters h, k and l.

A diffraction pattern represents a map of the reciprocal lattice and this must be converted

back into the crystal lattice.

Diffraction involving the general (h k l) plane in the crystal lattice corresponds to the point in

the reciprocal lattice with the coefficients h, k and l; this reciprocal lattice vector is

perpendicular to the associated (h k l) plane.

Recall that the real lattice vectors R can be represented as ua + vb + wc and the reciprocal

lattice vectors G can be represented as ha* + kb* + lc*.

It follows from the properties above that R · G = 2m (4)

where m is an integer, because h, k, l, u, v and w are all integers.

Further analysis reveals that

hkl

dG

2




Laue condition

http://www.chemsoc.org/exemplarchem/entries/2003/bristol_cook/lauecondition.htm

Laue formulated an alternative theorem to the Bragg law

for diffraction.

This theorem is beneficial because it does not require the

assumptions used by Bragg, that reflection is specular and

involves parallel planes of atoms.

The derivation is based upon an incident wavevector k

being absorbed and re-emitted as an outgoing wavevector

k'. The scattering is assumed to be elastic, i.e. |k| = |k‘|.

Laue's theory, based upon complex exponential phase

factors, states that, for diffraction, the difference in the

2 wavevectors must be equal to a reciprocal lattice vector.

That is:

k' - k = G

This condition is superior to the Bragg law because it rests

only upon the assumption that scattering is elastic.

The 2 conditions are, however, equivalent.



Structure factor

http://www.chemsoc.org/exemplarchem/entries/2003/bristol_cook/lauecondition.htm

Following Fourier analysis it is found that the scattering amplitude is the sum of complex

exponentials.

For a crystal of N cells the amplitude of a Bragg peak is proportional to the 'structure

factor'.

The intensity of a Bragg peak is then proportional to S*S = |S|2.

In this expression, the dot product is taken for a specific value of G corresponding to a

specific Miller plane.

The vector rj represents the position of a general atom in the unit cell relative to a lattice

point. The sum is hence taken over all atoms in the unit cell.

f is the 'atomic form factor', a constant dependent on the atom at position rj. It is necessary

because different atoms scatter containing different numbers of electrons incident radiation

by different amounts.

j

jjhkl fS rGexp

v13 control of gene expression

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