Kinetic Model of the Lysogeny/Lysis Switch of Phage λ

A kinetic model of the interactions between operators and regulators is developed to study the stabilities of genetic states and lysogeny/lysis switch in Eschemchia coli infected by bacteriophage lambda. Using adiabatic approximation, the kinetic evolutions of mRNA and regulator concentrations can be deduced from operators＇ equations. Furthermore, the stability of each state of the system is studied. The results show that the lysogenic state switches to the lytic state through two bifurcations： one from a single stable state to a three-point state, and the other from a three-point state to a single stable state. Then we indicate that the property of the lysogeny/lysis switch satisfies the topological characteristics theorem. Finally, the influence of the left operators on the lysogeny/lysis switch is briefly discussed. The results show that the cooperativity of the CI2 bound to left and right operators makes the lysogenic state more stable.

Entropy Production Rate Changes in Lysogeny/Lysis Switch Regulation of Bacteriophage Lambda

According to the chemical kinetic model of lysogeny/lysis switch in Escherichia coli （E. coil） infected by bacteriophage A, the entropy production rates of steady states are calculated. The resuits show that the lysogenic state has lower entropy production rate than lyric state, which provides an explanation on why the lysogenic state of A phage is so stable. We a/so notice that the entropy production rates of both lysogenic state and lyric state are lower than that of saddle-point and bifurcation state, which is consistent with the principle of minimum entropy production for living organism in nonequilibrium stationary state. Subsequently, the relations between CI and Cro degradation rates at two bifurcations and the changes of entropy production rate with CI and Cro degradation are deduced. The theory and method can be used to calculate entropy change in other molecular network.

Experimental Study of Entropy Production in Cells under Alternating Electric Field

We put forward a new method for measuring the entropy production in the living cell.It involves heating the sample by alternating the electric field and recording the outward heat flow.The entropy production in a normal cell MCF10A and a cancerous cell MDA-MB-231 were measured and compared.The results show that the method is effective for the entropy measurement of a living organism.The scaled electro-induced entropy production rate(SEEP)of MDA-MB-231 monotonically increases with the electric field strength at 5–40 V/cm.While that of MCF10A changes non-monotonically and there exists a peak at 5–30 V/cm.The electro-induced entropy production ratio(EEPR)is smaller than 1 in a large range of field strengths,from 5 to 25 V/cm,which reveals that under 5–25 V/cm electric field exposure,the direction of the entropy flow may be changed from normal tissue to cancerous cells.We present a facile and effective strategy for experimentally investigating the thermodynamic properties of the cell and give a deeper insight into the physical difference between normal and cancerous cells under electric field exposure.

Protein folding as a quantum transition between conformational states

Assuming that the main variables in the life processes at the molecular level are the conforma- tion of biological macromolecules and their frontier electrons a formalism of quantum theory on conformation-electron system is proposed. Based on the quantum theory of conformation-electron system, the protein folding is regarded as a quantum transition between torsion states on polypep- tide chain, and the folding rate is calculated by nonadiabatic operator method. The rate calculation is generalized to the case of frequency variation in folding. An analytical form of protein folding rate formula is obtained, which can be served as a useful tool for further studying protein folding. The application of the rate theory to explain the protein folding experiments is briefly summarized. It includes the inertial moment dependence of folding rate, the unified description of two-state and multistate protein folding, the relationship of folding and unfolding rates versus denaturant concen- tration, the distinction between exergonic and endergonic foldings, the ultrafast and the downhill folding viewed from quantum folding theory, and, finally, the temperature dependence of folding rate and the interpretation of its non-Arrhenius behaviors. All these studies support the view that the protein folding is essentially a quantum transition between conformational states.

The dynamical contact order:Protein folding rate parameters based on quantum conformational transitions

Protein folding is regarded as a quantum transition between the torsion states of a polypeptide chain.According to the quantum theory of conformational dynamics,we propose the dynamical contact order(DCO) defined as a characteristic of the contact described by the moment of inertia and the torsion potential energy of the polypeptide chain between contact residues.Conse-quently,the protein folding rate can be quantitatively studied from the point of view of dynamics.By comparing theoretical calculations and experimental data on the folding rate of 80 proteins,we successfully validate the view that protein folding is a quantum conformational transition.We conclude that(i) a correlation between the protein folding rate and the contact inertial moment exists;(ii) multi-state protein folding can be regarded as a quantum conformational transition similar to that of two-state proteins but with an intermediate delay.We have estimated the order of magnitude of the time delay;(iii) folding can be classified into two types,exergonic and endergonic.Most of the two-state proteins with higher folding rate are exergonic and most of the multi-state proteins with low folding rate are endergonic.The folding speed limit is determined by exergonic folding.