Studies From The Perspective Of Physical Chemistry On Nonlinear Problems In Biochemical Systems

Synthetic biology is a new branch of life sciences, which is developed in the21st century. We can take advantage of synthetic biological technology to construct kinds of artificial gene regulatory networks (GRNs) in biological systems. Such GRNs are used for engineering applications or scientific researches. The GRNs constructed in this work that base on genetic toggle-switch framework can demonstrate cellular differentiation or uniformization, which have both practical and theoretical important significance. For example, the differentiation in an individual of multi-cellular organisms drives the development from stem-cells to tissues and organs, then finally results in a whole multi-cellular organism that is formed by different kinds of cells. On the other hand, the differentiation between organisms brings on individual differences, subspecies, and even new biological species; thereby this strengthens the environment adaptability of biological populations.From the chemical point of view, GRNs are a kind of chemical reaction networks composed of genes and relative substances in the cell. Genetic toggle switch is a bistable or multistable element in GRN, which has been investigated in cell differentiation, bio-circuits, cellular memory, epigenetics and development, etc. There is a kind of genetic toggle switches based only on mutual inhibition regulation; and such mutual-inhibition genetic toggle switches were mentioned commonly over the past decade.The reaction kinetic characteristics of these switches might simply be described by a pair of ordinary differential equations (ODEs), which contain two key variables. These two variables form a two dimensional nonlinear dynamical system. The differential-equation model predicts that the system should have at most two stable steady states (SSS) and one unstable steady state (USS), as shown in the top layer of the figure. This dynamical system has at most two SSS points under appropriate conditions, thus it is called’bistable’; of course, under some other conditions it might have only one SSS point or even none. Previous contributions have proven that it does have two SSS points by deterministic simulations and biology experiments. Stochastic simulations show some differences more or less to deterministic results, however there are only two SSSs at most, consistent with experiments and differential-equation models. Here we’ve constructed a GRN module containing such a mutual-inhibition switch, and surprisingly found that under some certain conditions this system might have extra stability at or nearby the traditionally regarded USS point, where all the genes are silent (i.e. rarely expressing). The whole system could be from monostable to tristable in different certain conditions. Experimental results are shown in the middle layer of the figure (FACS scatter plots, the left half presents monostability and the right half presents tristability):all the regions where the real system converges toward are stable in practical sense. This kind of regions could be found around theoretical deterministic USS points.Particle-based stochastic kinetic simulation results (exact stochastic simulation algorithm) are shown in the bottom layer of the figure. These two-dimensional probability density surface charts of simulation results are semi-quantitatively consistent with the experimental results. Fluctuation analysis and statistical analysis have been done to reveal the source of this additional stable state. Our results are mathematically in agreement with some correlative theoretical works:discrete and fluctuant nature of molecule numbers is the origin of extra stability. Especially, if in a chemical reaction network there are pivotal chemical species whose molecule numbers are often very close to or equal to zero, their discreteness together with fluctuations might result in dramatic phenomena. This kind of small-number effects cannot be treated by ODE model or its simple stochastic variant:chemical Langevin equations (CLEs) with Gaussian noise terms. The stochastic simulation results via CLEs are drawn by green scatter points in the top layer, which only tend to surround deterministic SSS points.Our experimental findings provide a clear example of theoretical hypothesis that stochasticity, particularly at low molecular concentrations, might lead to additional stable states in mesoscopic nonlinear systems. In our view, the subtle role of discreteness and fluctuation has general importance not only in GRN, but also in other kinds of chemical reaction networks in small systems that have pivotal molecules fluctuating on the verge of extinction. These can be natural chemical reaction networks in a single cell, or be artificial ones in microreactors and vesicles. Furthermore, this novel phenomenon might be taken advantage of to achieve special functions that a macroscopic system could not achieve conveniently. A function we’ve demonstrated by experiments is supersensitivity, which might be found in natural GRNs, and might also be used in artificial GRN for constructing biosensor.From the perspective of synthetic biology, tri-state genetic element with ’silent state’ is just like tri-state electronic element that has a high impedance state. It is naturally to implement tri-state elements in bio-circuits as in electro circuits, for keeping a no-output state (’silent state’). For instance, stem cells and other kinds of multipotent cells might have its genes interlock in this no-output state before differentiation. Our work has given a possible mechanism that how it traps several mutually exclusive genes all in low expression level just by mutual inhibition.On the other hand, we have investigated a problem which should be seriously taken into account in future synthetic biology design and chemical kinetic simulation. That is to say:for the small systems whether in vivo or in vitro, chemical kinetic simulations should be checked carefully by particle-based stochastic simulation, rather than concentration-based differential equations. Such a check is particularly important in the case when molecule numbers are so small that continuity assumption breaks down; thus ’concentration’ loses its meaning. This work also has theoretical significance of chemical kinetic simulation and statistical physics in small systems.