Stochastic approaches for modelling in vivo reactions

Space as the final frontier in stochastic simulations of biological systems

Recent technological and theoretical advances are only now allowing the simulation of detailed kinetic models of biological systems that reflect the stochastic movement and reactivity of individual molecules within cellular compartments. The behavior of many systems could not be properly understood without this level of resolution, opening up new perspectives of using computer simulations to accelerate biological research. We review the modeling methodology applied to stochastic spatial models, also to the attention of non-expert potential users. Modeling choices, current limitations and perspectives of improvement of current general-purpose modeling/simulation platforms for biological systems are discussed.

Time accelerated Monte Carlo simulations of biological networks using the binomial -leap method

Developing a quantitative understanding of intracellular networks requires simulations and computational analyses. However, traditional differential equation modeling tools are often inadequate due to the stochasticity of intracellular reaction networks that can potentially influence the phenotypic characteristics. Unfortunately, stochastic simulations are computationally too intense for most biological systems. Herein, we have utilized the recently developed binomial tau-leap method to carry out stochastic simulations of the epidermal growth factor receptor induced mitogen activated protein kinase cascade. Results indicate that the binomial tau-leap method is computationally 100-1000 times more efficient than the exact stochastic simulation algorithm of Gillespie. Furthermore, the binomial tau-leap method avoids negative populations and accurately captures the species populations along with their fluctuations despite the large difference in their size.

AVAILABILITY

http://www.dion.che.udel.edu/multiscale/Introduction.html. Fortran 90 code available for academic use by email.

SUPPLEMENTARY INFORMATION

Details about the binomial tau-leap algorithm, software and a manual are available at the above website.

A computational model of mitochondrial deoxynucleotide metabolism and DNA replication

We present a computational model of mitochondrial deoxynucleotide metabolism and mitochondrial DNA (mtDNA) synthesis. The model includes the transport of deoxynucleosides and deoxynucleotides into the mitochondrial matrix space, as well as their phosphorylation and polymerization into mtDNA. Different simulated cell types (cancer, rapidly dividing, slowly dividing, and postmitotic cells) are represented in this model by different cytoplasmic deoxynucleotide concentrations. We calculated the changes in deoxynucleotide concentrations within the mitochondrion during the course of a mtDNA replication event and the time required for mtDNA replication in the different cell types. On the basis of the model, we define three steady states of mitochondrial deoxynucleotide metabolism: the phosphorylating state (the net import of deoxynucleosides and export of phosphorylated deoxynucleotides), the desphosphorylating state (the reverse of the phosphorylating state), and the efficient state (the net import of both deoxynucleosides and deoxynucleotides). We present five testable hypotheses based on this simulation. First, the deoxynucleotide pools within a mitochondrion are sufficient to support only a small fraction of even a single mtDNA replication event. Second, the mtDNA replication time in postmitotic cells is much longer than that in rapidly dividing cells. Third, mitochondria in dividing cells are net sinks of cytoplasmic deoxynucleotides, while mitochondria in postmitotic cells are net sources. Fourth, the deoxynucleotide carrier exerts the most control over the mtDNA replication rate in rapidly dividing cells, but in postmitotic cells, the NDPK and TK2 enzymes have the most control. Fifth, following from the previous hypothesis, rapidly dividing cells derive almost all of their mtDNA precursors from the cytoplasmic deoxynucleotides, not from phosphorylation within the mitochondrion.

Reverse engineering of biochemical equations from time-course data by means of genetic programming

Increased research aimed at simulating biological systems requires sophisticated parameter estimation methods. All current approaches, including genetic algorithms, need pre-existing equations to be functional. A generalized approach to predict not only parameters but also biochemical equations from only observable time-course information must be developed and a computational method to generate arbitrary equations without knowledge of biochemical reaction mechanisms must be developed. We present a technique to predict an equation using genetic programming. Our technique can search topology and numerical parameters of mathematical expression simultaneously. To improve the search ability of numeric constants, we added numeric mutation to the conventional procedure. As case studies, we predicted two equations of enzyme-catalyzed reactions regarding adenylate kinase and phosphofructokinase. Our numerical experimental results showed that our approach could obtain correct topology and parameters that were close to the originals. The mean errors between given and simulation-predicted time-courses were 1.6 x 10(-5)% and 2.0 x 10(-3)%, respectively. Our equation prediction approach can be applied to identify metabolic reactions from observable time-courses.