Team:LCG-UNAM-Mexico/Notebook/2008-October

LCG-UNAM-Mexico:Notebook/October   

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The two known critical concentrations of NiSO4 are 2.2 mM, the minimum inhibitory, and 500uM the minimun  needed to repress RcnR activity.

Planned methodology:

-Establishment of a place to do the measurements.

-We expect to have a constant temperature during the measurement process.

-Test the sensitivity of the measurement dispositive. To achieve this, measurements will be done in agitation of:     Just LB  LB with NiSO4  LB with cells </li> </ul> </ul> </ul> </ul> <ul> <ul> <ul> <ul> <ul> (,001) Dilución de 10 microlitros de 0.1 M en 1 mililitro </li> (,00001) Dilución de 10 microlitros de 0.001M en 1 mililitro </li> (0,0000001) Dilución de 10 microlitros de 0.00001   M en un mililitro </li> </ul> </ul> </ul> </ul> </ul> Internalization -Grow the strain YohM- in LB medium until reach an OD(optical density) of 0.4 to ensure that the  cells are in exponential phase. (Later this was changed to an OD of 0.5 at a lambda of 600nm). -Plot concentration vs  time and calculate the slope

slope= Internalization rate of Ni2+ Extrusion

The following steps were performed in order to prove the RcnA activity, and to get the enough data to  calculate conductivity  from the resistivity measurements. These conductivity data will be useful to get the extrusion rate of RcnA. -          Grow the strains YohM-, YohM- + pBBMICS-5+RcnA, YohM- + pBBMICS-5 and YohM+  in LB medium until reach an OD(optical density) of  0.4 to ensure that the cells are in exponential phase. (Later this was changed to an OD of 0.5 at a lambda of 600nm).

-          Take 1ml  from each culture for each of the next nickel  concentrations:

- The measurements will be performed during three minutes for each one strain <td class="subHeader" bgcolor="#99CC66" id="12">2008-10-12 <td class="bodyText"> WET LAB

Some measurements were done in LB with and without nickel in order to calibrate and prove the apparatus. Initially the measurement dispositive included a gold electrode which seemed to be working properly. <td class="subHeader" bgcolor="#99CC66" id="13">2008-10-13 <td class="bodyText"> WET LAB Solutions nickel 500uM and without nickel at all were prepared from samples of LB, and the strains YohM-, YohM- + pBBIMRCS-5 and YohM- + pBBIMRCS-5 + RcnA. <td class="subHeader" bgcolor="#99CC66" id="14">2008-10-14 <td class="bodyText"> WET LAB

The OD that the cells must reach was changed to 0.5 at a lambda of 600nm(This was due to the finding of the proper OD measurement in the strain  W3110).

Some adjusts were done to the measurement dispositive in order to increase its sensibility. <td class="subHeader" bgcolor="#99CC66" id="15">2008-10-15 <td class="bodyText"> WET LAB

Preparation of the strains YohM-, YohM- + pBBIMRCS-5, and YohM- + pBBIMRCS-5 + RcnA for the measurements. An overnight of each strain was grown in LB. Samples of YohM- + pBBIMRCS-5, and YohM- + pBBIMRCS-5 + RcnA were  prepared with different concentrations of NiSO4. That concentrations includes a gradient from 1x10-3 M – 1X10-10M. And the two critical concentrations 500uM and 2.2mM. <td class="subHeader" bgcolor="#99CC66" id="16">2008-10-16 <td class="bodyText"> WET LAB

Strains were prepared in pursuit to perform some new measurements. Samples of LB, LB+ sulfate, and YohM-+RCNA+PBB were read.

Measurement intervals (100 milliseconds) semeed to be quite large, so its correction was proposed.

<td class="subHeader" bgcolor="#99CC66" id="17"> </a>2008-10-17 <td class="bodyText"> MODELING: Stoichiometric Matrix: Palsson, 2006 Flux vector                   -&gt;         v =(v1, v2, …, vn)

Concentration vector      -&gt;         x =(x1, x2, …, xm)

-&gt;         δ x /δt = S· v δxi/δt=∑Sikvk The four fundamental subspaces <div id="q_q6"><img src="http://2008.igem.org/wiki/images/2/23/FromPalssonM1.jpg" width="500" /> Image from Systems Biology: Properties of Reconstructed Networks by Bernhard O. Palsson

The vector produced by a linear transformation is in two orthogonal spaces (the column and left null spaces), called the domain, and the vector being mapped is also in two orthogonal  spaces (the row and null spaces), called the codomain or the range of  the transformation. The vectors in the left null space (l i ) represent mass conservation. The flux vector can be decomposed into a dynamic component and a steady-state component:

v = vdyn + vss The steady state component satisfies Svss=0 and v</si>ss is thus in the null space  of <i>S. <td class="subHeader" bgcolor="#99CC66" id="18">2008-10-18 <td class="bodyText"> WET LAB

Prosecution of correction of measurement intervals. <td class="subHeader" bgcolor="#99CC66" id="19">2008-10-19 <td class="bodyText"> WET LAB

Due to the great variation observed in the data, some aspects of the samples, measurements and electrodes were reconsidered. As the variations could be caused by the ions present in the medium it was proposed to use a buffer  instead of LB medium.

<td class="subHeader" bgcolor="#99CC66" id="20">2008-10-20 <td class="bodyText">  MODELING:  The higher the number of independent reaction vectors, the smaller the orthogonal left null space. The higher the number of independent reactions, the fewer the conservation quantities exist. FUNDAMENTAL SUBSPACES OF S The dimensions of both the column and row space is r ( rank ;  number of linearly independent rows and columns that the matrix contains).

dim(Col(S)) = dim(Row(S)) = r

Since the dimension of the concentration vector is m, we have

dim(Left Null(S)) = m− r

Similarly, the flux vector is n-dimensional; thus,

dim(Null(S)) = n – r         Null space. The null space of S contains all the steady-state flux distributions allowable in the network. The steady state is of much interest since most homeostatic states are close to being steady states.</li>        Row space. The row space of S contains all the dynamic flux distributions of a network and thus the thermodynamic driving forces that change the rate of  reaction activity. </li>        Left null space. The left null space of S contains all the conservation relationships, or time invariants, that a network contains. The sum of conserved metabolites or conserved metabolic pools do not change with time and are combinations  of concentration variables.</li>        Column space. The column space of S contains all the possible time derivatives of the concentration vector and thus shows how the  thermodynamic driving forces move the concentration state of the network.</li> Singular Value Decomposition SVD states that for a matrix S of dimension m× n and of rank r, there are orthonormal matrices U (of dimension m  ×m) and V (of dimension n × n) and a matrix with diagonal elements ∑ = diag(σ1,  σ2, ..., σr ) with σ1 ≥ σ2 ≥ ··· ≥  σr &gt; 0 such that S = U∑VT A non-negative real number σ is a singular value for M if and only if there exist unit-length vectors u in Km and v in Kn such that

Mv=σu and M*u=σv

The vectors u and v are called left-singular and right-singular vectors for σ, respectively.

In any singular value decomposition

M=UΣV*

the diagonal entries of Σ are necessarily equal to the singular values of M. The columns of U and V are, respectively, left- and right-singular vectors  for the corresponding singular values. <img src="http://2008.igem.org/wiki/images/b/bf/FromPalssonM2.jpg" width="500"/> Image from Systems Biology: Properties of Reconstructed Networks by Bernhard O. Palsson <img src="http://2008.igem.org/wiki/images/8/86/FromPalssonM3.jpg" width="500" height="280"/> Image from Systems Biology: Properties of Reconstructed Networks by Bernhard O. Palsson The columns of U are called the left singular vectors and the columns of V are the right singular vectors. The columns of U and V give orthonormal bases for all the four fundamental subspaces of S (see  Figure 8.3). The first r columns of U and V give orthonormal bases for the column and row spaces, respectively. The last m − r columns of U give an orthonormal basis for the left null space, and the last n − r columns or V give an  orthonormal basis for the null space. WET LAB

Correction of the measurement intervals to 1 millisecond.

161008         <td class="subHeader" bgcolor="#99CC66" id="21">2008-10-21 <td class="bodyText">  MODELING:  THE (RIGTH) NULL SPACE OF S The right null space of S is defined by

Svss = <i>0

</i>Thus, all the steady-state flux distributions, v ss, are found in the null space. The null space has a dimension of n − r. Note that v ss must be orthogonal to all the rows of S simultaneously and thus represents  a linear combination of flux values on the reaction map that sum to zero. Mathematics versus biology        The null space represents all the possible functional, or phenotypic, states  of a network.</li>        A particular point in the polytope represents one network function or one  particular phenotypic state.</li>        As we will see in Chapter 16, there are equivalent points in the cone  that lead to the same overall functional state of a network. Biologically, such conditions are called silent phenotypes .</li>        The edges of the flux cone are the unique extreme pathways. Any flux state in the cone can be decomposed into the extreme pathways. The unique set of extreme pathways thus gives a mathematical description of the range of flux  levels that are allowed.</li> - The stoichiometric matrix has a null space that corresponds to a linear combination of the reaction vectors  that add up to zero; so-called link-neutral combinations. - The orthonormal basis given by SVD does not yield a useful biochemical interpretation of the null space of the  stoichiometric matrix. THE LEFT NULL SPACE OF S As with the (right) null space, the  choice of basis for the left null space is important  in describing its contents in biochemically and biologically meaningful terms. …may represent mass conservation… THE ROW AND COLUMN SPACE OF S The column and row spaces of the  stoichiometric matrix contain the concentration time derivatives and the  thermodynamic driving forces, respectively. <td class="bodyText"> - <a href="http://2008.igem.org/Team:LCG-UNAM-Mexico/Notebook/2008-September" onMouseOver="hiLite ('Back','a2','Back')" onMouseOut="hiLite('Back','a1','')"> <img name="Back" src="http://igem.org/wiki/images/5/57/BOTON_BACK1.jpg" border=0 width="200" height="40"/></a>

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