Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

Computer simulation of glioma growth and morphology.

Despite major advances in the study of glioma, the quantitative links between intra-tumor molecular/cellular properties, clinically observable properties such as morphology, and critical tumor behaviors such as growth and invasiveness remain unclear, hampering more effective coupling of tumor physical characteristics with implications for prognosis and therapy. Although molecular biology, histopathology, and radiological imaging are employed in this endeavor, studies are severely challenged by the multitude of different physical scales involved in tumor growth, i.e., from molecular nanoscale to cell microscale and finally to tissue centimeter scale. Consequently, it is often difficult to determine the underlying dynamics across dimensions. New techniques are needed to tackle these issues. Here, we address this multi-scalar problem by employing a novel predictive three-dimensional mathematical and computational model based on first-principle equations (conservation laws of physics) that describe mathematically the diffusion of cell substrates and other processes determining tumor mass growth and invasion. The model uses conserved variables to represent known determinants of glioma behavior, e.g., cell density and oxygen concentration, as well as biological functional relationships and parameters linking phenomena at different scales whose specific forms and values are hypothesized and calculated based on in vitro and in vivo experiments and from histopathology of tissue specimens from human gliomas. This model enables correlation of glioma morphology to tumor growth by quantifying interdependence of tumor mass on the microenvironment (e.g., hypoxia, tissue disruption) and on the cellular phenotypes (e.g., mitosis and apoptosis rates, cell adhesion strength). Once functional relationships between variables and associated parameter values have been informed, e.g., from histopathology or intra-operative analysis, this model can be used for disease diagnosis/prognosis, hypothesis testing, and to guide surgery and therapy. In particular, this tool identifies and quantifies the effects of vascularization and other cell-scale glioma morphological characteristics as predictors of tumor-scale growth and invasion.

THEORETICAL STUDIES ON THE METHODS OF RECONSTRUCTING PHYLOGENETIC TREES FROM DNA SEQUENCE DATA (MOLECULAR EVOLUTION, HOMINOID EVOLUTION, COMPUTER SIMULATION)

(1) A mathematical theory for computing the probabilities of various nucleotide configurations is developed, and the probability of obtaining the correct phylogenetic tree (model tree) from sequence data is evaluated for six phylogenetic tree-making methods (UPGMA, distance Wagner method, transformed distance method, Fitch-Margoliash's method, maximum parsimony method, and compatibility method). The number of nucleotides (m*) necessary to obtain the correct tree with a probability of 95% is estimated with special reference to the human, chimpanzee, and gorilla divergence. m* is at least 4,200, but the availability of outgroup species greatly reduces m* for all methods except UPGMA. m* increases if transitions occur more frequently than transversions as in the case of mitochondrial DNA. (2) A new tree-making method called the neighbor-joining method is proposed. This method is applicable either for distance data or character state data. Computer simulation has shown that the neighbor-joining method is generally better than UPGMA, Farris' method, Li's method, and modified Farris method on recovering the true topology when distance data are used. A related method, the simultaneous partitioning method, is also discussed. (3) The maximum likelihood (ML) method for phylogeny reconstruction under the assumption of both constant and varying evolutionary rates is studied, and a new algorithm for obtaining the ML tree is presented. This method gives a tree similar to that obtained by UPGMA when constant evolutionary rate is assumed, whereas it gives a tree similar to that obtained by the maximum parsimony tree and the neighbor-joining method when varying evolutionary rate is assumed. ^

Cerebellar mechanisms for motor learning: Testing predictions from a large-scale computer simulation

The cerebellum is the major brain structure that contributes to our ability to improve movements through learning and experience. We have combined computer simulations with behavioral and lesion studies to investigate how modification of synaptic strength at two different sites within the cerebellum contributes to a simple form of motor learning—Pavlovian conditioning of the eyelid response. These studies are based on the wealth of knowledge about the intrinsic circuitry and physiology of the cerebellum and the straightforward manner in which this circuitry is engaged during eyelid conditioning. Thus, our simulations are constrained by the well-characterized synaptic organization of the cerebellum and further, the activity of cerebellar inputs during simulated eyelid conditioning is based on existing recording data. These simulations have allowed us to make two important predictions regarding the mechanisms underlying cerebellar function, which we have tested and confirmed with behavioral studies. The first prediction describes the mechanisms by which one of the sites of synaptic modification, the granule to Purkinje cell synapses (gr → Pkj) of the cerebellar cortex, could generate two time-dependent properties of eyelid conditioning—response timing and the ISI function. An empirical test of this prediction using small, electrolytic lesions of the cerebellar cortex revealed the pattern of results predicted by the simulations. The second prediction made by the simulations is that modification of synaptic strength at the other site of plasticity, the mossy fiber to deep nuclei synapses (mf → nuc), is under the control of Purkinje cell activity. The analysis predicts that this property should confer mf → nuc synapses with resistance to extinction. Thus, while extinction processes erase plasticity at the first site, residual plasticity at mf → nuc synapses remains. The residual plasticity at the mf → nuc site confers the cerebellum with the capability for rapid relearning long after the learned behavior has been extinguished. We confirmed this prediction using a lesion technique that reversibly disconnected the cerebellar cortex at various stages during extinction and reacquisition of eyelid responses. The results of these studies represent significant progress toward a complete understanding of how the cerebellum contributes to motor learning. ^

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

A biophysical model of synaptic plasticity and metaplasticity can account for the dynamics of the backward shift of hippocampal place fields.

Hippocampal place cells in the rat undergo experience-dependent changes when the rat runs stereotyped routes. One such change, the backward shift of the place field center of mass, has been linked by previous modeling efforts to spike-timing-dependent plasticity (STDP). However, these models did not account for the termination of the place field shift and they were based on an abstract implementation of STDP that ignores many of the features found in cortical plasticity. Here, instead of the abstract STDP model, we use a calcium-dependent plasticity (CaDP) learning rule that can account for many of the observed properties of cortical plasticity. We use the CaDP learning rule in combination with a model of metaplasticity to simulate place field dynamics. Without any major changes to the parameters of the original model, the present simulations account both for the initial rapid place field shift and for the subsequent slowing down of this shift. These results suggest that the CaDP model captures the essence of a general cortical mechanism of synaptic plasticity, which may underlie numerous forms of synaptic plasticity observed both in vivo and in vitro.

Dynamics of a minimal model of interlocked positive and negative feedback loops of transcriptional regulation by cAMP-response element binding proteins.

cAMP-response element binding (CREB) proteins are involved in transcriptional regulation in a number of cellular processes (e.g., neural plasticity and circadian rhythms). The CREB family contains activators and repressors that may interact through positive and negative feedback loops. These loops can be generated by auto- and cross-regulation of expression of CREB proteins, via CRE elements in or near their genes. Experiments suggest that such feedback loops may operate in several systems (e.g., Aplysia and rat). To understand the functional implications of such feedback loops, which are interlocked via cross-regulation of transcription, a minimal model with a positive and negative loop was developed and investigated using bifurcation analysis. Bifurcation analysis revealed diverse nonlinear dynamics (e.g., bistability and oscillations). The stability of steady states or oscillations could be changed by time delays in the synthesis of the activator (CREB1) or the repressor (CREB2). Investigation of stochastic fluctuations due to small numbers of molecules of CREB1 and CREB2 revealed a bimodal distribution of CREB molecules in the bistability region. The robustness of the stable HIGH and LOW states of CREB expression to stochastic noise differs, and a critical number of molecules was required to sustain the HIGH state for days or longer. Increasing positive feedback or decreasing negative feedback also increased the lifetime of the HIGH state, and persistence of this state may correlate with long-term memory formation. A critical number of molecules was also required to sustain robust oscillations of CREB expression. If a steady state was near a deterministic Hopf bifurcation point, stochastic resonance could induce oscillations. This comparative analysis of deterministic and stochastic dynamics not only provides insights into the possible dynamics of CREB regulatory motifs, but also demonstrates a framework for understanding other regulatory processes with similar network architecture.

Making minimally invasive THR safe: conclusions from biomechanical simulation and analysis.

The use of smaller surgical incisions has become popularized for total hip arthroplasty (THR) because of the potential benefits of shorter recovery and improved cosmetic appearance. However, an increased incidence of serious complications has been reported. To minimize the risks of minimally invasive approaches to THR, we have developed an experimental approach which enables us to evaluate risk factors in these procedures through cadaveric simulations performed within the laboratory. During cadaveric hip replacement procedures performed via posterior and antero-lateral mini-incisions, pressures developed between the wound edges and the retractors were approximately double those recorded during conventional hip replacement using Charnley retractors (p < 0.01). In MIS procedures performed via the dual-incision approach, lack of direct visualisation of the proximal femur led to misalignment of broaches and implants with increased risk of cortical fracture during canal preparation and implant insertion. Cadaveric simulation of surgical procedures allows surgeons to measure variables affecting the technical success of surgery and to master new procedures without placing patients at risk.

Simulation of Drosophila circadian oscillations, mutations, and light responses by a model with VRI, PDP-1, and CLK.

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest that two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. However, eliminating positive feedback by fixing vri expression altered the oscillation period. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations, of per overexpression, and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. Temperature compensation of oscillation period could be simulated if temperature elevation slowed PER nuclear entry or PER phosphorylation. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.

Predictive oncology: a review of multidisciplinary, multiscale in silico modeling linking phenotype, morphology and growth.

Empirical evidence and theoretical studies suggest that the phenotype, i.e., cellular- and molecular-scale dynamics, including proliferation rate and adhesiveness due to microenvironmental factors and gene expression that govern tumor growth and invasiveness, also determine gross tumor-scale morphology. It has been difficult to quantify the relative effect of these links on disease progression and prognosis using conventional clinical and experimental methods and observables. As a result, successful individualized treatment of highly malignant and invasive cancers, such as glioblastoma, via surgical resection and chemotherapy cannot be offered and outcomes are generally poor. What is needed is a deterministic, quantifiable method to enable understanding of the connections between phenotype and tumor morphology. Here, we critically assess advantages and disadvantages of recent computational modeling efforts (e.g., continuum, discrete, and cellular automata models) that have pursued this understanding. Based on this assessment, we review a multiscale, i.e., from the molecular to the gross tumor scale, mathematical and computational "first-principle" approach based on mass conservation and other physical laws, such as employed in reaction-diffusion systems. Model variables describe known characteristics of tumor behavior, and parameters and functional relationships across scales are informed from in vitro, in vivo and ex vivo biology. We review the feasibility of this methodology that, once coupled to tumor imaging and tumor biopsy or cell culture data, should enable prediction of tumor growth and therapy outcome through quantification of the relation between the underlying dynamics and morphological characteristics. In particular, morphologic stability analysis of this mathematical model reveals that tumor cell patterning at the tumor-host interface is regulated by cell proliferation, adhesion and other phenotypic characteristics: histopathology information of tumor boundary can be inputted to the mathematical model and used as a phenotype-diagnostic tool to predict collective and individual tumor cell invasion of surrounding tissue. This approach further provides a means to deterministically test effects of novel and hypothetical therapy strategies on tumor behavior.

Extended kalman filter for estimation of parameters in nonlinear state-space models of biochemical networks.

It is system dynamics that determines the function of cells, tissues and organisms. To develop mathematical models and estimate their parameters are an essential issue for studying dynamic behaviors of biological systems which include metabolic networks, genetic regulatory networks and signal transduction pathways, under perturbation of external stimuli. In general, biological dynamic systems are partially observed. Therefore, a natural way to model dynamic biological systems is to employ nonlinear state-space equations. Although statistical methods for parameter estimation of linear models in biological dynamic systems have been developed intensively in the recent years, the estimation of both states and parameters of nonlinear dynamic systems remains a challenging task. In this report, we apply extended Kalman Filter (EKF) to the estimation of both states and parameters of nonlinear state-space models. To evaluate the performance of the EKF for parameter estimation, we apply the EKF to a simulation dataset and two real datasets: JAK-STAT signal transduction pathway and Ras/Raf/MEK/ERK signaling transduction pathways datasets. The preliminary results show that EKF can accurately estimate the parameters and predict states in nonlinear state-space equations for modeling dynamic biochemical networks.

Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields.

The discovery of grid cells in the medial entorhinal cortex (MEC) permits the characterization of hippocampal computation in much greater detail than previously possible. The present study addresses how an integrate-and-fire unit driven by grid-cell spike trains may transform the multipeaked, spatial firing pattern of grid cells into the single-peaked activity that is typical of hippocampal place cells. Previous studies have shown that in the absence of network interactions, this transformation can succeed only if the place cell receives inputs from grids with overlapping vertices at the location of the place cell's firing field. In our simulations, the selection of these inputs was accomplished by fast Hebbian plasticity alone. The resulting nonlinear process was acutely sensitive to small input variations. Simulations differing only in the exact spike timing of grid cells produced different field locations for the same place cells. Place fields became concentrated in areas that correlated with the initial trajectory of the animal; the introduction of feedback inhibitory cells reduced this bias. These results suggest distinct roles for plasticity of the perforant path synapses and for competition via feedback inhibition in the formation of place fields in a novel environment. Furthermore, they imply that variability in MEC spiking patterns or in the rat's trajectory is sufficient for generating a distinct population code in a novel environment and suggest that recalling this code in a familiar environment involves additional inputs and/or a different mode of operation of the network.

Cellular dynamic simulator: an event driven molecular simulation environment for cellular physiology.

In this paper, we present the Cellular Dynamic Simulator (CDS) for simulating diffusion and chemical reactions within crowded molecular environments. CDS is based on a novel event driven algorithm specifically designed for precise calculation of the timing of collisions, reactions and other events for each individual molecule in the environment. Generic mesh based compartments allow the creation / importation of very simple or detailed cellular structures that exist in a 3D environment. Multiple levels of compartments and static obstacles can be used to create a dense environment to mimic cellular boundaries and the intracellular space. The CDS algorithm takes into account volume exclusion and molecular crowding that may impact signaling cascades in small sub-cellular compartments such as dendritic spines. With the CDS, we can simulate simple enzyme reactions; aggregation, channel transport, as well as highly complicated chemical reaction networks of both freely diffusing and membrane bound multi-protein complexes. Components of the CDS are generally defined such that the simulator can be applied to a wide range of environments in terms of scale and level of detail. Through an initialization GUI, a simple simulation environment can be created and populated within minutes yet is powerful enough to design complex 3D cellular architecture. The initialization tool allows visual confirmation of the environment construction prior to execution by the simulator. This paper describes the CDS algorithm, design implementation, and provides an overview of the types of features available and the utility of those features are highlighted in demonstrations.

Hybrid stochastic simulations of intracellular reaction-diffusion systems.

With the observation that stochasticity is important in biological systems, chemical kinetics have begun to receive wider interest. While the use of Monte Carlo discrete event simulations most accurately capture the variability of molecular species, they become computationally costly for complex reaction-diffusion systems with large populations of molecules. On the other hand, continuous time models are computationally efficient but they fail to capture any variability in the molecular species. In this study a hybrid stochastic approach is introduced for simulating reaction-diffusion systems. We developed an adaptive partitioning strategy in which processes with high frequency are simulated with deterministic rate-based equations, and those with low frequency using the exact stochastic algorithm of Gillespie. Therefore the stochastic behavior of cellular pathways is preserved while being able to apply it to large populations of molecules. We describe our method and demonstrate its accuracy and efficiency compared with the Gillespie algorithm for two different systems. First, a model of intracellular viral kinetics with two steady states and second, a compartmental model of the postsynaptic spine head for studying the dynamics of Ca+2 and NMDA receptors.