Theoretical Biology and Medical Modelling最新文献

Background: A significant body of literature is devoted to modeling developmental mechanisms that create patterns within groups of initially equivalent embryonic cells. Although it is clear that these mechanisms do not function in isolation, the timing of and interactions between these mechanisms during embryogenesis is not well known. In this work, a computational approach was taken to understand how lateral inhibition, differential adhesion and programmed cell death can interact to create a mosaic pattern of biologically realistic primary and secondary cells, such as that formed by sensory (primary) and supporting (secondary) cells of the developing chick inner ear epithelium.

Results: Four different models that interlaced cellular patterning mechanisms in a variety of ways were examined and their output compared to the mosaic of sensory and supporting cells that develops in the chick inner ear sensory epithelium. The results show that: 1) no single patterning mechanism can create a 2-dimensional mosaic pattern of the regularity seen in the chick inner ear; 2) cell death was essential to generate the most regular mosaics, even through extensive cell death has not been reported for the developing basilar papilla; 3) a model that includes an iterative loop of lateral inhibition, programmed cell death and cell rearrangements driven by differential adhesion created mosaics of primary and secondary cells that are more regular than the basilar papilla; 4) this same model was much more robust to changes in homo- and heterotypic cell-cell adhesive differences than models that considered either fewer patterning mechanisms or single rather than iterative use of each mechanism.

Conclusion: Patterning the embryo requires collaboration between multiple mechanisms that operate iteratively. Interlacing these mechanisms into feedback loops not only refines the output patterns, but also increases the robustness of patterning to varying initial cell states.

Background: The diauxic shift in yeast requires cells to coordinate a complicated response that involves numerous genes and metabolic processes. It is unknown whether responses of this type are mediated in vivo through changes in a few "key" genes and enzymes, which are mathematically characterized by high sensitivities, or whether they are based on many small changes in genes and enzymes that are not particularly sensitive. In contrast to global assessments of changes in gene or protein interaction networks, we study here control aspects of the diauxic shift by performing a detailed analysis of one specific pathway-sphingolipid metabolism-which is known to have signaling functions and is associated with a wide variety of stress responses.

Results: The approach uses two components: publicly available sets of expression data of sphingolipid genes and a recently developed Generalized Mass Action (GMA) mathematical model of the sphingolipid pathway. In one line of exploration, we analyze the sensitivity of the model with respect to enzyme activities, and thus gene expression. Complementary to this approach, we convert the gene expression data into changes in enzyme activities and then predict metabolic consequences by means of the mathematical model. It was found that most of the sensitivities in the model are low in magnitude, but that some stand out as relatively high. This information was then deployed to test whether the cell uses a few of the very sensitive pathway steps to mount a response or whether the control is distributed throughout the pathway. Pilot experiments confirm qualitatively and in part quantitatively the predictions of a group of metabolite simulations.

Conclusion: The results indicate that yeast coordinates sphingolipid mediated changes during the diauxic shift through an array of small changes in many genes and enzymes, rather than relying on a strategy involving a few select genes with high sensitivity. This study also highlights a novel approach in coupling data mining with mathematical modeling in order to evaluate specific metabolic pathways.

Background: We introduce the Basic Immune Simulator (BIS), an agent-based model created to study the interactions between the cells of the innate and adaptive immune system. Innate immunity, the initial host response to a pathogen, generally precedes adaptive immunity, which generates immune memory for an antigen. The BIS simulates basic cell types, mediators and antibodies, and consists of three virtual spaces representing parenchymal tissue, secondary lymphoid tissue and the lymphatic/humoral circulation. The BIS includes a Graphical User Interface (GUI) to facilitate its use as an educational and research tool.

Results: The BIS was used to qualitatively examine the innate and adaptive interactions of the immune response to a viral infection. Calibration was accomplished via a parameter sweep of initial agent population size, and comparison of simulation patterns to those reported in the basic science literature. The BIS demonstrated that the degree of the initial innate response was a crucial determinant for an appropriate adaptive response. Deficiency or excess in innate immunity resulted in excessive proliferation of adaptive immune cells. Deficiency in any of the immune system components increased the probability of failure to clear the simulated viral infection.

Conclusion: The behavior of the BIS matches both normal and pathological behavior patterns in a generic viral infection scenario. Thus, the BIS effectively translates mechanistic cellular and molecular knowledge regarding the innate and adaptive immune response and reproduces the immune system's complex behavioral patterns. The BIS can be used both as an educational tool to demonstrate the emergence of these patterns and as a research tool to systematically identify potential targets for more effective treatment strategies for diseases processes including hypersensitivity reactions (allergies, asthma), autoimmunity and cancer. We believe that the BIS can be a useful addition to the growing suite of in-silico platforms used as an adjunct to traditional research efforts.

Background: In the past, tasks of model based yield optimization in metabolic engineering were either approached with stoichiometric models or with structured nonlinear models such as S-systems or linear-logarithmic representations. These models stand out among most others, because they allow the optimization task to be converted into a linear program, for which efficient solution methods are widely available. For pathway models not in one of these formats, an Indirect Optimization Method (IOM) was developed where the original model is sequentially represented as an S-system model, optimized in this format with linear programming methods, reinterpreted in the initial model form, and further optimized as necessary.

Results: A new method is proposed for this task. We show here that the model format of a Generalized Mass Action (GMA) system may be optimized very efficiently with techniques of geometric programming. We briefly review the basics of GMA systems and of geometric programming, demonstrate how the latter may be applied to the former, and illustrate the combined method with a didactic problem and two examples based on models of real systems. The first is a relatively small yet representative model of the anaerobic fermentation pathway in S. cerevisiae, while the second describes the dynamics of the tryptophan operon in E. coli. Both models have previously been used for benchmarking purposes, thus facilitating comparisons with the proposed new method. In these comparisons, the geometric programming method was found to be equal or better than the earlier methods in terms of successful identification of optima and efficiency.

Conclusion: GMA systems are of importance, because they contain stoichiometric, mass action and S-systems as special cases, along with many other models. Furthermore, it was previously shown that algebraic equivalence transformations of variables are sufficient to convert virtually any types of dynamical models into the GMA form. Thus, efficient methods for optimizing GMA systems have multifold appeal.

Background: The Differential Adhesion Hypothesis (DAH) is a theory of the organization of cells within a tissue which has been validated by several biological experiments and tested against several alternative computational models.

Results: In this study, a statistical approach was developed for the estimation of the strength of adhesion, incorporating earlier discrete lattice models into a continuous marked point process framework. This framework allows to describe an ergodic Markov Chain Monte Carlo algorithm that can simulate the model and reproduce empirical biological patterns. The estimation procedure, based on a pseudo-likelihood approximation, is validated with simulations, and a brief application to medulloblastoma stained by beta-catenin markers is given.

Conclusion: Our model includes the strength of cell-cell adhesion as a statistical parameter. The estimation procedure for this parameter is consistent with experimental data and would be useful for high-throughput cancer studies.

Background: Propagation of simulated action potentials (APs) was previously studied in short single chains and in two-dimensional sheets of myocardial cells 123. The present study was undertaken to examine propagation in a long single chain of cells of various lengths, and with varying numbers of gap-junction (g-j) channels, and to compare propagation velocity with the cable properties such as the length constant (lambda).

Methods and results: Simulations were carried out using the PSpice program as previously described. When the electric field (EF) mechanism was dominant (0, 1, and 10 gj-channels), the longer the chain length, the faster the overall velocity (theta(ov)). There seems to be no simple explanation for this phenomenon. In contrast, when the local-circuit current mechanism was dominant (100 gj-channels or more), theta(ov) was slightly slowed with lengthening of the chain. Increasing the number of gj-channels produced an increase in theta(ov) and caused the firing order to become more uniform. The end-effect was more pronounced at longer chain lengths and at greater number of gj-channels. When there were no or only few gj-channels (namely, 0, 10, or 30), the voltage change (DeltaV(m)) in the two contiguous cells (#50 & #52) to the cell injected with current (#51) was nearly zero, i.e., there was a sharp discontinuity in voltage between the adjacent cells. When there were many gj-channels (e.g., 300, 1000, 3000), there was an exponential decay of voltage on either side of the injected cell, with the length constant (lambda) increasing at higher numbers of gj-channels. The effect of increasing the number of gj-channels on increasing lambda was relatively small compared to the larger effect on theta(ov). theta(ov) became very non-physiological at 300 gj-channels or higher.

Conclusion: Thus, when there were only 0, 1, or 10 gj-channels, theta(ov) increased with increase in chain length, whereas at 100 gj-channels or higher, theta(ov) did not increase with chain length. When there were only 0, 10, or 30 gj-channels, there was a very sharp decrease in DeltaV(m) in the two contiguous cells on either side of the injected cell, whereas at 300, 1000, or 3000 gj-channels, the voltage decay was exponential along the length of the chain. The effect of increasing the number of gj-channels on spread of current was relatively small compared to the large effect on theta(ov).

Background: Due to the increasing importance of identifying insulin resistance, a need exists to have a reliable mathematical model representing the glucose/insulin control system. Such a model should be simple enough to allow precise estimation of insulin sensitivity on a single patient, yet exhibit stable dynamics and reproduce accepted physiological behavior.

Results: A new, discrete Single Delay Model (SDM) of the glucose/insulin system is proposed, applicable to Intra-Venous Glucose Tolerance Tests (IVGTTs) as well as to multiple injection and infusion schemes, which is fitted to both glucose and insulin observations simultaneously. The SDM is stable around baseline equilibrium values and has positive bounded solutions at all times. Applying a similar definition as for the Minimal Model (MM) SI index, insulin sensitivity is directly represented by the free parameter KxgI of the SDM. In order to assess the reliability of Insulin Sensitivity determinations, both SDM and MM have been fitted to 40 IVGTTs from healthy volunteers. Precision of all parameter estimates is better with the SDM: 40 out of 40 subjects showed identifiable (CV < 52%) KxgI from the SDM, 20 out of 40 having identifiable SI from the MM. KxgI correlates well with the inverse of the HOMA-IR index, while SI correlates only when excluding five subjects with extreme SI values. With the exception of these five subjects, the SDM and MM derived indices correlate very well (r = 0.93).

Conclusion: The SDM is theoretically sound and practically robust, and can routinely be considered for the determination of insulin sensitivity from the IVGTT. Free software for estimating the SDM parameters is available.

Background: Transcription is the first step in cellular information processing. It is regulated by cis-acting elements such as promoters and operators in the DNA, and trans-acting elements such as transcription factors and sigma factors. Identification of cis-acting regulatory elements on a genomic scale requires computational analysis.

Results: We have used oligonucleotide profiling to predict regulatory regions in a bacterial genome. The method has been applied to the Escherichia coli K12 genome and the results analyzed. The information content of the putative regulatory oligonucleotides so predicted is validated through intra-genomic analyses, correlations with experimental data and inter-genome comparisons. Based on the results we have proposed a model for the bacterial promoter. The results show that the method is capable of identifying, in the E.coli genome, cis-acting elements such as TATAAT (sigma70 binding site), CCCTAT (1 base relative of sigma32 binding site), CTATNN (LexA binding site), AGGA-containing hexanucleotides (Shine Dalgarno consensus) and CTAG-containing hexanucleotides (core binding sites for Trp and Met repressors).

Conclusion: The method adopted is simple yet effective in predicting upstream regulatory elements in bacteria. It does not need any prior experimental data except the sequence itself. This method should be applicable to most known genomes. Profiling, as applied to the E.coli genome, picks up known cis-acting and regulatory elements. Based on the profile results, we propose a model for the bacterial promoter that is extensible even to eukaryotes. The model is that the core promoter lies within a plateau of bent AT-rich DNA. This bent DNA acts as a homing segment for the sigma factor to recognize the promoter. The model thus suggests an important role for local landscapes in prokaryotic and eukaryotic gene regulation.

Background: The phenomenon of switch-like response to graded input signal is the theme involved in various signaling pathways in living systems. Positive feedback loops or double negative feedback loops embedded with nonlinearity exhibit these switch-like bistable responses. Such feedback regulations exist in insulin signaling pathway as well.

Methods: In the current manuscript, a steady state analysis of the metabolic insulin-signaling pathway is presented. The threshold concentration of insulin required for glucose transporter GLUT4 translocation was studied with variation in system parameters and component concentrations. The dose response curves of GLUT4 translocation at various concentration of insulin obtained by steady state analysis were quantified in-terms of half saturation constant.

Results: We show that, insulin-stimulated GLUT4 translocation can operate as a bistable switch, which ensures that GLUT4 settles between two discrete, but mutually exclusive stable steady states. The threshold concentration of insulin required for GLUT4 translocation changes with variation in system parameters and component concentrations, thus providing insights into possible pathological conditions.

Conclusion: A steady state analysis indicates that negative feedback regulation of phosphatase PTP1B by Akt elicits bistability in insulin-stimulated GLUT4 translocation. The threshold concentration of insulin required for GLUT4 translocation and the corresponding bistable response at different system parameters and component concentrations was compared with reported experimental observations on specific defects in regulation of the system.

The method of mathematically controlled comparison provides a structured approach for the comparison of alternative biochemical pathways with respect to selected functional effectiveness measures. Under this approach, alternative implementations of a biochemical pathway are modeled mathematically, forced to be equivalent through the application of selected constraints, and compared with respect to selected functional effectiveness measures. While the method has been applied successfully in a variety of studies, we offer recommendations for improvements to the method that (1) relax requirements for definition of constraints sufficient to remove all degrees of freedom in forming the equivalent alternative, (2) facilitate generalization of the results thus avoiding the need to condition those findings on the selected constraints, and (3) provide additional insights into the effect of selected constraints on the functional effectiveness measures. We present improvements to the method and related statistical models, apply the method to a previously conducted comparison of network regulation in the immune system, and compare our results to those previously reported.