Rules for biological regulation based on error minimization

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.Comment: biological physics, complex networks, systems biology, transcriptional regulation http://www.weizmann.ac.il/complex/tlusty/papers/PNAS2006.pdf http://www.pnas.org/content/103/11/3999.ful

Evolution of a genome-encoded bias in amino acid biosynthetic pathways is a potential indicator of amino acid dynamics in the environment.

Overcoming the stress of starvation is one of an organism's most challenging phenotypic responses. Those organisms that frequently survive the challenge, by virtue of their fitness, will have evolved genomes that are shaped by their specific environments. Understanding this genotype-environment-phenotype relationship at a deep level will require quantitative predictive models of the complex molecular systems that link these aspects of an organism's existence. Here, we treat one of the most fundamental molecular systems, protein synthesis, and the amino acid biosynthetic pathways involved in the stringent response to starvation. These systems face an inherent logical dilemma: Building an amino acid biosynthetic pathway to synthesize its product-the cognate amino acid of the pathway-may require that very amino acid when it is no longer available. To study this potential "catch-22," we have created a generic model of amino acid biosynthesis in response to sudden starvation. Our mathematical analysis and computational results indicate that there are two distinctly different outcomes: Partial recovery to a new steady state, or full system failure. Moreover, the cell's fate is dictated by the cognate bias, the number of cognate amino acids in the corresponding biosynthetic pathway relative to the average number of that amino acid in the proteome. We test these implications by analyzing the proteomes of over 1,800 sequenced microbes, which reveals statistically significant evidence of low cognate bias, a genetic trait that would avoid the biosynthetic quandary. Furthermore, these results suggest that the pattern of cognate bias, which is readily derived by genome sequencing, may provide evolutionary clues to an organism's natural environment

Unrelated toxin-antitoxin systems cooperate to induce persistence.

Persisters are drug-tolerant bacteria that account for the majority of bacterial infections. They are not mutants, rather, they are slow-growing cells in an otherwise normally growing population. It is known that the frequency of persisters in a population is correlated with the number of toxin-antitoxin systems in the organism. Our previous work provided a mechanistic link between the two by showing how multiple toxin-antitoxin systems, which are present in nearly all bacteria, can cooperate to induce bistable toxin concentrations that result in a heterogeneous population of slow- and fast-growing cells. As such, the slow-growing persisters are a bet-hedging subpopulation maintained under normal conditions. For technical reasons, the model assumed that the kinetic parameters of the various toxin-antitoxin systems in the cell are identical, but experimental data indicate that they differ, sometimes dramatically. Thus, a critical question remains: whether toxin-antitoxin systems from the diverse families, often found together in a cell, with significantly different kinetics, can cooperate in a similar manner. Here, we characterize the interaction of toxin-antitoxin systems from many families that are unrelated and kinetically diverse, and identify the essential determinant for their cooperation. The generic architecture of toxin-antitoxin systems provides the potential for bistability, and our results show that even when they do not exhibit bistability alone, unrelated systems can be coupled by the growth rate to create a strongly bistable, hysteretic switch between normal (fast-growing) and persistent (slow-growing) states. Different combinations of kinetic parameters can produce similar toxic switching thresholds, and the proximity of the thresholds is the primary determinant of bistability. Stochastic fluctuations can spontaneously switch all of the toxin-antitoxin systems in a cell at once. The spontaneous switch creates a heterogeneous population of growing and non-growing cells, typical of persisters, that exist under normal conditions, rather than only as an induced response. The frequency of persisters in the population can be tuned for a particular environmental niche by mixing and matching unrelated systems via mutation, horizontal gene transfer and selection

Elucidating the genotype-phenotype map by automatic enumeration and analysis of the phenotypic repertoire.

BackgroundThe gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process.MethodsThe strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters.ResultsOur strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed.ConclusionsStarting with a system's relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy

Introduction to S-systems and the underlying power-law formalism

A novel approach to the development of an appropriate formalism for representing organizationally complex systems began in the mid 1960's with a search for a general systematic formalism that would retain the essential nonlinear features and that would still be amenable to mathematical analysis. The set of nonlinear differential equations that most closely approached this goal was called an "S-system", because it accurately captures the saturable and synergistic properties intrinsic to biological and other organizationally complex systems. In the early 1980's it was found that essentially any nonlinear differential equation composed of elementary functions could be recast exactly as an S-system. Thus, S-systems may be considered a canonical form with the ability to represent an enormous variety of nonlinear differential equations. This has given rise to new strategies for the mathematical modeling of nonlinear systems.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27576/1/0000620.pd

Efficient solution of nonlinear models expressed in S-system canonical form

The S-system is emerging as a general canonical form for analysis of nonlinear models. Models expressed within this regularly structured system of nonlinear ordinary differential equations are obtained by applying either of two different strategies: (A) Direct derivation of an S-system utilizing the Power Law Formalism; or (B) exact recasting of an existing, well established model into S-system form. By capitalizing on the regular structure of S-systems, efficient formulas for numerical solution of this general class have been developed. For any S-system it can be shown that these formulas are more efficient than conventional multistep formulas of the same order. For implemented methods, the actual improvements in efficiency are considerably more than the minimum estimates. Preliminary tests show that time required for solution of S-systems is reduced by one or two orders of magnitude -- the relative improvement in efficiency increases with size and complexity of the problem, and with degree of accuracy required.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/27485/1/0000528.pd

Focused Practice: Exploring the Relationship Between Mindfulness and Empathy Among Clinical Social Workers

This research project explores the impact of mindfulness on the practice of clinical social work as it pertains to building the skill of empathy. Mindfulness, in practice, varies from clinician to clinician; however, mindfulness in general involves having an expanded sense of awareness and attunement to the greater experience of the client. As such, current research (as discussed in the literature review) supports that those clinicians who practice mindfulness develop an increased compassion for self and others and thus are more empathic than those who do not practice mindfulness. This research is important to the field of clinical social work because of the implications for future education to include mindfulness training as part of developing the skill of using empathy with clients. Data collected for this research comes from 121 clinical social workers registered with the Minnesota Board of Social Work (MBOSW) and is based on their responses to the Interpersonal Reactivity Index (IRI) and a seven-question survey. The results of this study point to a relationship between mindfulness and empathy among clinical social workers, indicating that further research exploring this relationship should be done to support these findings