Hematopoiesis and its disorders: a systems biology approach
- ^{1}Departments of Pediatrics and Cell and Molecular Biology, Children's Memorial Hospital and the Robert H. Lurie Comprehensive Cancer Center, Northwestern University School of Medicine, Chicago, IL;
- ^{2}Departments of Bioengineering and Chemical and Biomolecular Engineering, University of Pennsylvania, Philadelphia;
- ^{3}Department of Statistics, Rice University, Houston, TX; and
- ^{4}Systems Engineering Group, Silesian University of Technology, Gliwice, Poland
Abstract
Scientists have traditionally studied complex biologic systems by reducing them to simple building blocks. Genome sequencing, high-throughput screening, and proteomics have, however, generated large datasets, revealing a high level of complexity in components and interactions. Systems biology embraces this complexity with a combination of mathematical, engineering, and computational tools for constructing and validating models of biologic phenomena. The validity of mathematical modeling in hematopoiesis was established early by the pioneering work of Till and McCulloch. In reviewing more recent papers, we highlight deterministic, stochastic, statistical, and network-based models that have been used to better understand a range of topics in hematopoiesis, including blood cell production, the periodicity of cyclical neutropenia, stem cell production in response to cytokine administration, and the emergence of imatinib resistance in chronic myeloid leukemia. Future advances require technologic improvements in computing power, imaging, and proteomics as well as greater collaboration between experimentalists and modelers. Altogether, systems biology will improve our understanding of normal and abnormal hematopoiesis, better define stem cells and their daughter cells, and potentially lead to more effective therapies.
- Analytical solution:
- A solution to an equation or set of equations that can be explicitly written in terms of known functions and constants (ie, in “closed form”).
- Bayesian network:
- A statistical model in a form of a tree based on existing data that correlates values of given input parameters with probabilities of certain outputs.
- Bistability:
- A property of 1 or more equations for which 2 stable solutions exist. The existence of multiple stable solutions is known as multistability.
- “Black box” model:
- A model that aims to determine the functional relationship between known system input and output when the specifics of the system structure are unknown. “Black box” models are often built from existing data using some form of regression analysis.
- Boolean network:
- A directed graph where nodes can take 2 possible states (1 or 0) and edges represent causal relationships between nodes. The state of a given node depends on the states of its input nodes through a logic (boolean) function that specifies the causal relationship between nodes. Boolean networks are often used to model genetic regulatory networks in which nodes are genes that can be active or inactive depending on the states of the genes (or gene products) that regulate them.
- Deterministic model:
- A model in which future states are fully determined by the past and present states, frequently built using differential equations.
- Edge:
- A line or arrow between 2 nodes in a graph that indicates a relationship between elements in the system.
- Emergent properties:
- Properties of a system that arise from the interactions among its components that cannot be deduced from their individual behavior.
- Empirical model:
- A nonmechanistic model that shows good agreement with existing experimental data and can be used to predict outcomes in separate but similar datasets.
- Feedback loop:
- A loop structure in which the output signal B produced by an element upon receiving an input signal A is also an input signal to the element generating signal A producing a down-regulation/up-regulation of signal A.
- Feed-forward loop:
- A loop structure in which 2 signals generated by a system element converge on an element downstream from this origin. Feed-forward control can either speed up a system's dynamics or destabilize it.
- Graph:
- A collection of nodes and edges that indicate relationships between nodes. Edges can be directed or undirected. Graphs (or networks) are a useful representation of a system in which each node corresponds to a functional element of the system (eg, state of a molecule, protein, or gene) and an edge represents the relevant interactions between functional units (eg, conformational changes, physical interactions, or regulatory interactions). Graph and network are often used interchangeably in systems biology literature and have acquired essentially the same meaning.
- Hysteresis:
- A property that arises from the existence of multiple stable states/solutions in which the system can get trapped depending on its previous history.
- In silico:
- A term used in reference to systems created, solved, or simulated using a computer.
- Loop:
- A structure in a graph or network that is characterized by a cyclical relationship among system elements.
- Mechanistic model:
- A model that describes the physical processes that give rise to observed properties of the system. Variables and parameters of the system correspond to physical quantities and rates that can be measured empirically.
- Michaelis-Menten kinetics:
- A mechanistic description of the rate of product formation in an enzymatic reaction that is based on the law of mass action but assumes that the concentration of the enzyme-substrate complex intermediate is essentially invariant during the timescale of interest. The enzyme and substrate bind to form a complex at a rate k_{1}, dissociate back into reactants at a rate k_{−1} and turn from a complex to products and enzyme at a rate k_{2}. The Michaelis-Menten equation describes the rate of the reaction and is written as, where v_{0} is the initial reaction rate, v_{max} is the maximum reaction rate, and K_{M}=(k_{−1} + k_{2})/k_{1}, the rate of complex dissociation and product production relative to the rate of complex formation.
- Monte Carlo simulation:
- A widespread method used to obtain observable quantities that depend on random variables whose probability distributions are known. MC methods can be used to introduce stochasticity into a model but are also used to sample the parameter space of deterministic models.
- Network:
- See definition of Graph.
- Neural network:
- A computational framework used to make predictions of an output quantity given some inputs. In a neural network the internal elements (or neurons) are connected to each other with different weights such that the correlation between predicted and known outputs for a specific training set of input signals is high. Neurons and weights do not represent any real process happening in the system thus neural networks are useful when internal relationships between model components are unknown.
- Node:
- Element of a graph or network that is used to represent a functional entity or interacting unit within a system (eg, a protein or transcription factor in a signaling network, a molecular species in a chemical reaction).
- Noise:
- Randomness that is an inherent part of a system.
- Numerical solution:
- Computationally determined solution to an equation or system of equations, typically necessary when an analytical solution is intractable. A numerical solution is approximation of the closed-form solution, but it can be calculated to any desired level of precision, given enough time and computational power.
- Principal component analysis (PCA):
- Statistical analysis technique aimed at determining which parameters of a model have the largest impact on model output. PCA can be used to examine the effect of varying multiple parameters at once on one or more functions of output parameters. PCA is useful when trying to identify a minimal set of transformed variables, or principal components, that can account for most of the variability in a dataset.
- Regression analysis:
- A method used to determine the functional relationship between a system's output and one or more input parameters. Linear regression models are the most common form of regression analysis. In such models the function is assumed to be a linear combination of the input parameters. Various methods exist to determine this function, the earliest being the method of least squares.
- Sensitivity analysis:
- A tool used during the model-making process to determine the quantity of variation in the observable quantities that can be attributed to variation in each input parameter.
- State space:
- The collection of all possible states a system can be in. For example, one's location on earth is described by 3 parameters: longitude, latitude, and altitude. This is one's spatial state. Spatial state space is the collection of all possible combinations of longitude, latitude, and altitude. Extending this to N parameters, one can imagine the space as an N-dimensional grid where each vertex represents a different parameter combination and thus a different spatial state.
- Steady-state solution:
- The solution to a kinetic equation or set of equations that is obtained by setting all time derivatives to zero, a justifiable assumption for equilibrated systems.
- Stochastic model:
- A model that incorporates random fluctuations in model parameters or model structure.
- Submitted August 26, 2009.
- Accepted November 25, 2009.
- © 2010 by The American Society of Hematology