Related Experiment Video
Updated: Dec 23, 2025
06:42
Generation and Coherent Control of Pulsed Quantum Frequency Combs
Published on: June 8, 2018
9.5K
Structural conserved moiety splitting of a stoichiometric matrix
Susan Ghaderi1, Hulda S Haraldsdóttir1, Masoud Ahookhosh2
1Luxembourg Centre for Systems Biomedicine, University of Luxembourg, 6 Avenue du Swing, Belvaux L-4362, Luxembourg.
Journal of Theoretical Biology
|April 26, 2020
Summary
Biochemical network structure can be mathematically defined using reaction stoichiometry. This study reveals that stoichiometric matrices can be decomposed into moiety transition matrices, revealing network subnetworks.
Area of Science:
- Biochemistry
- Systems Biology
- Computational Biology
Background:
- Understanding biochemical reaction networks is crucial for inferring functional consequences.
- Network structure can be represented by reaction stoichiometry or molecular transformations.
- Stoichiometric matrices (N∈Zm×n) capture molecule-reaction relationships.
Purpose of the Study:
- To mathematically characterize biochemical reaction network structure.
- To explore the relationship between network structure and functional consequences.
- To develop new mathematical approaches for analyzing biochemical networks.
Main Methods:
- Representing biochemical networks using stoichiometric matrices.
- Decomposing stoichiometric matrices into moiety transition matrices.
- Analyzing subnetworks accessible to structurally identifiable conserved moieties.
Main Results:
- Demonstrated that a stoichiometric matrix can be decomposed into m-rank(N) moiety transition matrices.
- Showed that this moiety matrix splitting is a unique property of stoichiometric matrices.
- Identified subnetworks corresponding to structurally identifiable conserved moieties.
Conclusions:
- Mathematical characterization of biochemical networks enables functional inference.
- Stoichiometric matrix decomposition reveals fundamental network properties.
- The moiety matrix splitting property distinguishes biochemical network matrices from general matrices.
Related Concept Videos
01:13¹H NMR: Complex Splitting
1.7K
A proton M that is coupled to a proton X results in doublet signals for M. However, NMR-active nuclei can be simultaneously coupled to more than one nonequivalent nucleus. When M is coupled to a second proton A, such as in styrene oxide, each peak in the doublet is split into another doublet.
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
Splitting diagrams or splitting tree diagrams are routinely used to depict such complex couplings. While drawing splitting diagrams, the splitting with the larger coupling constant is usually applied...
1.7K
01:10Interpreting ¹H NMR Signal Splitting: The (n + 1) Rule
2.3K
In the AX proton spin system, proton A can sense the two spin states of a coupled proton X, resulting in a doublet NMR signal with two peaks of equal (1:1) intensity. When proton A is coupled to two equivalent protons (AX2 spin system), the spin states of each X can be aligned with or against the external field, creating three possible scenarios. This results in a 1:2:1 triplet signal, where the central peak corresponds to the chemical shift of A and is twice as large or intense as the...
2.3K
02:52Stereoisomerism
13.7K
Isomerism in Complexes
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...
Isomers are different chemical species that have the same chemical formula.
Transition metal complexes often exist as geometric isomers, in which the same atoms are connected through the same types of bonds but with differences in their orientation in space. Coordination complexes with two different ligands in the cis and trans positions from a ligand of interest form isomers. For example, the octahedral [Co(NH3)4Cl2]+ ion has two isomers (Figure 1) In the cis...
13.7K
02:25Molecules with Multiple Chiral Centers
14.6K
Molecules that possess multiple chiral centers can afford a large number of stereoisomers. For instance, while some molecules like 2-butanol have one chiral center, defined as a tetrahedral carbon atom with four different substituents attached, several molecules like butane-2,3-diol have multiple chiral centers. A simple formula to predict the number of stereoisomers possible for a molecule with n chiral centers is 2n. However, there can be a lower number where some of the stereoisomers are...
14.6K
02:40MO Theory and Covalent Bonding
13.3K
The molecular orbital theory describes the distribution of electrons in molecules in a manner similar to the distribution of electrons in atomic orbitals. The region of space in which a valence electron in a molecule is likely to be found is called a molecular orbital. Mathematically, the linear combination of atomic orbitals (LCAO) generates molecular orbitals. Combinations of in-phase atomic orbital wave functions result in regions with a high probability of electron density, while...
13.3K
02:16Resonance and Hybrid Structures
24.2K
According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
Resonance Structures and Resonance Hybrids
The Lewis structure of a nitrite anion (NO2−) may actually be drawn in two different ways, distinguished by the locations of the N–O and N=O bonds.
24.2K