Lately I've been writing on the website Helium. See - Helium
for some examples of this site and my writing.
Saturday, May 24, 2008
Tuesday, May 20, 2008
The Devilish Complexity of Cysteine Modulation in Protein Function
There exists a devilish complexity in the vast array of biological modifications that can alter the free thiol or sulfhydryl group, which is the reactive group of the essential amino acid cysteine an important amino acid of many important biological proteins. The thiol group is vitally important for its ability to form disulfide bonds with other thiol groups and to form either reduced or oxidized (redox) forms that may further interact reversibly or irreversibly with a panoply of other chemical and biological molecules. In addition, many of these forms have their own redox and pH-dependence that determines their successive reactivities with other chemical or biological molecules, which only adds further complexity to this already overly complicated picture.
Unfortunately the experimental expertise necessary to deal with this burgeoning complexity has fallen behind. Experiments often control for temperature and pH and occasionally for the redox environment and ionic strength. However, there are further complexities that are much more difficult to measure and control. These complexities include evaluating the previous exposure of thiol groups to thiol modifying agents and conditions that render them either reversibly or irreversibly modified. In addition, there are time-dependent factors such as the release of nitric oxide (NO) from S-nitrosothiols that may function as a storage form of NO (1) and the additional confounding factors that include successive thiol oxidations to sulfenic acids (R-SOH), sulfinic acids (R-SO2H) and sulfonic acids (R-SO3H) (2). These oxidations also change the pK of the thiol group towards successively lower values (3) .
In many important biological and cellular proteins, the free thiol group of cysteinyl side chains is particularly susceptible to oxidative modifications such as the formation of intermolecular or intramolecular disulfides between other protein thiols or other low-molecular-weight thiol molecules such as glutathione (4). This may also occur by thiol-disulfide exchange or disproportionation reactions. The modification of cysteine thiols by incorporation of NO moieties such as S-nitrosylation or incorporation of glutathione moieties (S-glutathionylation) functionally blocks thiol groups from additional oxidation reactions that could irreversibly block their biological functions. Some reversible modifications may be essential in preserving vital intracellular proteins and membrane receptors, thereby allowing them to eventually return to a functional, free thiol state.
Thiol modifications are produced by a number of reactions induced by a vast number of reactive species. These species include nitric oxide-related species, other proteins or organic molecules with or without free thiol groups and metals that can form reversible redox-cycles or that primarily complex with and deplete glutathione levels or directly bond with free thiol groups (5). These reactions all have their own pH and redox dependence, which further complicates experimental efforts to control for thiol reactivities toward these large number of potentially reactive molecules. Measuring how and under what conditions these reactions can be reversed requires much more experimental work.
Altogether, it is a bit like trying to reverse the development of a photographic plate. The photographic reactions leave their history as an imprint on the plate, but just like an incompletely fixed photographic plate, there may exist other areas or reactive groups that can undergo further reactions given the proper set of experimental conditions. Studying the reactivities of the thiol groups of biological tissues may be very similar to the photographic plate analogy. Once they’ve reacted, it is very difficult to bring them back to their functional in vivo state. Currently there is relatively little recognition of these problems and little or no attempts to address them with suitable experimental controls.
Since this is a critical area for future research, suggestions for improving the experimental strategy may entail treating the cells or tissues with sulfhydryl chelating agents at various times during the experimental preparations so that we may begin to understand how successive handling and extraction procedures modify these critical groups. Using a protocol of successive sampling, the relative exposure of thiol groups could be determined at critical steps in experimental protocols that extract and purify biological proteins. Then the effects of these procedures on thiol modifications may become better understood and more readily controlled in future experiments.
Only by careful analysis and systematic experimentation can we begin to understand the role of thiol groups and their contributions toward the finely balanced control of a great number of critical biological functions (6-17).
References (Since this isn’t intended as an extensive review, these are only a minimal number and I apologize if I have left out other important references):
1) Alencar JL, Lobysheva I, Geffard M, Sarr M, Schott C, Schini-Kerth V, Nepveu F, Stoclet JC, Muller B. Role of S-nitrosation of cysteine residues in long-lasting inhibitory effect of NO on arterial tone. Mol Pharmacol 63: 1148–1158 (2003).
2) Kiley PJ, Storz G. Exploiting Thiol Modifications. PLoS Biol 2(11): e400 (2004).
3) Claus J, Holme AL, Fry FH. The sulfinic acid switch in proteins Org. Biomol. Chem., 2, 1953 - 1956 (2004). DOI: 10.1039/b406180b
4) Berndt C, Lillig CH, Holmgren A. Thiol-based mechanisms of the thioredoxin and glutaredoxin systems: implications for diseases in the cardiovascular system. Am J Physiol Heart Circ Physiol 292: H1227-H1236, (2007). doi:10.1152/ajpheart.
5) Valko M, Morris H, Cronin MT, Metals, toxicity and oxidative stress. Curr Med Chem. 12(10):1161-208 (2005).
6) Smith JG, Cunningham JM Receptor-Induced Thiolate Couples Env Activation to Retrovirus Fusion and Infection. PLoS Pathog 3(12): e198 (2007).
7) Kokkola T, Savinainen JR,Mönkkönen KS, Retamal MD, Laitinen JT. S-Nitrosothiols modulate G protein-coupled receptor signaling in a reversible and highly receptor-specific manner. BMC Cell Biology 6, 21 (2005).
8) Ding Z, Kim S, Dorsam RT, Jin J, Kunapuli SP. Inactivation of the human P2Y12 receptor by thiol reagents requires interaction with both extracellular cysteine residues, Cys17 and Cys270. Blood 101, 3908-3914 (2003).
9) LoPachin RM, Barber DS. Synaptic Cysteine Sulfhydryl Groups as Targets of Electrophilic Neurotoxicants Toxicol. Sci. 94: 240-255 (2006).
10) Martínez-Ruiza A, Lamas S. Signalling by NO-induced protein S-nitrosylation and S-glutathionylation: Convergences and divergences Cardiovascular Research 75(2):220-228, (2007).doi:10.1016/j.cardiores.2007.03.016
11) Held KD, Sylvester FC, Hopcia KL, Biaglow JE. Role of Fenton chemistry in thiol-induced toxicity and apoptosis. Radiat Res.145(5):542-53 (1996).
12) Nagy L, Nagata M, Szabo S. Protein and non-protein sulfhydryls and disulfides in gastric mucosa and liver after gastrotoxic chemicals and sucralfate: possible new targets of pharmacologic agents.World J Gastroenterol.13(14):2053-60 (2007).
13) Lewandowicz AM, Vepsäläinen J, Laitinen JT. The 'allosteric modulator' SCH-202676 disrupts G protein-coupled receptor function via sulphydryl-sensitive mechanisms British Journal of Pharmacology 147: 422–429 (2006). doi:10.1038/sj.bjp.0706624
14) Moriarty-Craige SE, Dean PJ. EXTRACELLULAR THIOLS AND THIOL/DISULFIDE REDOX IN METABOLISM Annual Review of Nutrition 24: 481-509 (2004). (doi:10.1146/annurev.nutr.24.012003.132208)
15) Nozik-Grayck E, Whalen EJ, Stamler JS, McMahon TJ, Chitano P, Piantadosi CA. S-nitrosoglutathione inhibits {alpha}1-adrenergic receptor-mediated vasoconstriction and ligand binding in pulmonary artery. Am J Physiol Lung Cell Mol Physiol 290: L136-L143, 2006. doi:10.1152/ajplung.00230.2005
16) Rubenstein LA, Zauhar RJ, Lanzara RG. Molecular dynamics of a biophysical model for beta-2-adrenergic and G protein-coupled receptor activation. Journal of Molecular Graphics and Modelling 25: 396-409 (2006). http://dx.doi.org/10.1016/j.jmgm.2006.02.008
17) Rubenstein LA, Lanzara RG, Activation of G Protein-Coupled Receptors Entails Cysteine Modulation of Agonist Binding. J. Molecular Structure (Theochem) 430/1-3: 57-71 (1998). http://dx.doi.org/10.1016/S0166-1280(97)00387-4
Unfortunately the experimental expertise necessary to deal with this burgeoning complexity has fallen behind. Experiments often control for temperature and pH and occasionally for the redox environment and ionic strength. However, there are further complexities that are much more difficult to measure and control. These complexities include evaluating the previous exposure of thiol groups to thiol modifying agents and conditions that render them either reversibly or irreversibly modified. In addition, there are time-dependent factors such as the release of nitric oxide (NO) from S-nitrosothiols that may function as a storage form of NO (1) and the additional confounding factors that include successive thiol oxidations to sulfenic acids (R-SOH), sulfinic acids (R-SO2H) and sulfonic acids (R-SO3H) (2). These oxidations also change the pK of the thiol group towards successively lower values (3) .
In many important biological and cellular proteins, the free thiol group of cysteinyl side chains is particularly susceptible to oxidative modifications such as the formation of intermolecular or intramolecular disulfides between other protein thiols or other low-molecular-weight thiol molecules such as glutathione (4). This may also occur by thiol-disulfide exchange or disproportionation reactions. The modification of cysteine thiols by incorporation of NO moieties such as S-nitrosylation or incorporation of glutathione moieties (S-glutathionylation) functionally blocks thiol groups from additional oxidation reactions that could irreversibly block their biological functions. Some reversible modifications may be essential in preserving vital intracellular proteins and membrane receptors, thereby allowing them to eventually return to a functional, free thiol state.
Thiol modifications are produced by a number of reactions induced by a vast number of reactive species. These species include nitric oxide-related species, other proteins or organic molecules with or without free thiol groups and metals that can form reversible redox-cycles or that primarily complex with and deplete glutathione levels or directly bond with free thiol groups (5). These reactions all have their own pH and redox dependence, which further complicates experimental efforts to control for thiol reactivities toward these large number of potentially reactive molecules. Measuring how and under what conditions these reactions can be reversed requires much more experimental work.
Altogether, it is a bit like trying to reverse the development of a photographic plate. The photographic reactions leave their history as an imprint on the plate, but just like an incompletely fixed photographic plate, there may exist other areas or reactive groups that can undergo further reactions given the proper set of experimental conditions. Studying the reactivities of the thiol groups of biological tissues may be very similar to the photographic plate analogy. Once they’ve reacted, it is very difficult to bring them back to their functional in vivo state. Currently there is relatively little recognition of these problems and little or no attempts to address them with suitable experimental controls.
Since this is a critical area for future research, suggestions for improving the experimental strategy may entail treating the cells or tissues with sulfhydryl chelating agents at various times during the experimental preparations so that we may begin to understand how successive handling and extraction procedures modify these critical groups. Using a protocol of successive sampling, the relative exposure of thiol groups could be determined at critical steps in experimental protocols that extract and purify biological proteins. Then the effects of these procedures on thiol modifications may become better understood and more readily controlled in future experiments.
Only by careful analysis and systematic experimentation can we begin to understand the role of thiol groups and their contributions toward the finely balanced control of a great number of critical biological functions (6-17).
References (Since this isn’t intended as an extensive review, these are only a minimal number and I apologize if I have left out other important references):
1) Alencar JL, Lobysheva I, Geffard M, Sarr M, Schott C, Schini-Kerth V, Nepveu F, Stoclet JC, Muller B. Role of S-nitrosation of cysteine residues in long-lasting inhibitory effect of NO on arterial tone. Mol Pharmacol 63: 1148–1158 (2003).
2) Kiley PJ, Storz G. Exploiting Thiol Modifications. PLoS Biol 2(11): e400 (2004).
3) Claus J, Holme AL, Fry FH. The sulfinic acid switch in proteins Org. Biomol. Chem., 2, 1953 - 1956 (2004). DOI: 10.1039/b406180b
4) Berndt C, Lillig CH, Holmgren A. Thiol-based mechanisms of the thioredoxin and glutaredoxin systems: implications for diseases in the cardiovascular system. Am J Physiol Heart Circ Physiol 292: H1227-H1236, (2007). doi:10.1152/ajpheart.
5) Valko M, Morris H, Cronin MT, Metals, toxicity and oxidative stress. Curr Med Chem. 12(10):1161-208 (2005).
6) Smith JG, Cunningham JM Receptor-Induced Thiolate Couples Env Activation to Retrovirus Fusion and Infection. PLoS Pathog 3(12): e198 (2007).
7) Kokkola T, Savinainen JR,Mönkkönen KS, Retamal MD, Laitinen JT. S-Nitrosothiols modulate G protein-coupled receptor signaling in a reversible and highly receptor-specific manner. BMC Cell Biology 6, 21 (2005).
8) Ding Z, Kim S, Dorsam RT, Jin J, Kunapuli SP. Inactivation of the human P2Y12 receptor by thiol reagents requires interaction with both extracellular cysteine residues, Cys17 and Cys270. Blood 101, 3908-3914 (2003).
9) LoPachin RM, Barber DS. Synaptic Cysteine Sulfhydryl Groups as Targets of Electrophilic Neurotoxicants Toxicol. Sci. 94: 240-255 (2006).
10) Martínez-Ruiza A, Lamas S. Signalling by NO-induced protein S-nitrosylation and S-glutathionylation: Convergences and divergences Cardiovascular Research 75(2):220-228, (2007).doi:10.1016/j.cardiores.2007.03.016
11) Held KD, Sylvester FC, Hopcia KL, Biaglow JE. Role of Fenton chemistry in thiol-induced toxicity and apoptosis. Radiat Res.145(5):542-53 (1996).
12) Nagy L, Nagata M, Szabo S. Protein and non-protein sulfhydryls and disulfides in gastric mucosa and liver after gastrotoxic chemicals and sucralfate: possible new targets of pharmacologic agents.World J Gastroenterol.13(14):2053-60 (2007).
13) Lewandowicz AM, Vepsäläinen J, Laitinen JT. The 'allosteric modulator' SCH-202676 disrupts G protein-coupled receptor function via sulphydryl-sensitive mechanisms British Journal of Pharmacology 147: 422–429 (2006). doi:10.1038/sj.bjp.0706624
14) Moriarty-Craige SE, Dean PJ. EXTRACELLULAR THIOLS AND THIOL/DISULFIDE REDOX IN METABOLISM Annual Review of Nutrition 24: 481-509 (2004). (doi:10.1146/annurev.nutr.24.012003.132208)
15) Nozik-Grayck E, Whalen EJ, Stamler JS, McMahon TJ, Chitano P, Piantadosi CA. S-nitrosoglutathione inhibits {alpha}1-adrenergic receptor-mediated vasoconstriction and ligand binding in pulmonary artery. Am J Physiol Lung Cell Mol Physiol 290: L136-L143, 2006. doi:10.1152/ajplung.00230.2005
16) Rubenstein LA, Zauhar RJ, Lanzara RG. Molecular dynamics of a biophysical model for beta-2-adrenergic and G protein-coupled receptor activation. Journal of Molecular Graphics and Modelling 25: 396-409 (2006). http://dx.doi.org/10.1016/j.jmgm.2006.02.008
17) Rubenstein LA, Lanzara RG, Activation of G Protein-Coupled Receptors Entails Cysteine Modulation of Agonist Binding. J. Molecular Structure (Theochem) 430/1-3: 57-71 (1998). http://dx.doi.org/10.1016/S0166-1280(97)00387-4
Friday, May 9, 2008
One Consuming Interest
Over the last several years, one of my consuming interests has been to understand how our cellular receptors function on the molecular level. Somewhat surprisingly, there is a rather simple two-state, acid-base model that accounts for a remarkable number of experimental findings.
These include everything from the Weber-Fechner law (see link) to the redox sensitivities of many receptors (see
Activation of G Protein-Coupled Receptors Entails Cysteine Modulation of Agonist Binding, J. Molecular Structure (Theochem), 430/1-3: 57-71 (1998) and Molecular dynamics of a biophysical model for beta-2-adrenergic and G protein-coupled receptor activation Journal of Molecular Graphics and Modelling 25: 396-409 (2006), for a picture of this model - Click here then also click on the picture). Over several years, I've tested many of the predictions from this model and found that it predicts and continues to explain a number of interesting findings. These include rapid receptor desensitization or tachyphylaxis (see link) and a method for preventing this desensitization (see link) and the phenomenon of "spare receptors", which is an old conundrum in pharmacology (see link).
Understanding how our receptors work at the molecular level is an awe inspiring undertaking, because these are the molecules that link our thoughts and senses to the universe. Understanding how they function may open new frontiers for us to truly understand our place in the cosmos.
These include everything from the Weber-Fechner law (see link) to the redox sensitivities of many receptors (see
Activation of G Protein-Coupled Receptors Entails Cysteine Modulation of Agonist Binding, J. Molecular Structure (Theochem), 430/1-3: 57-71 (1998) and Molecular dynamics of a biophysical model for beta-2-adrenergic and G protein-coupled receptor activation Journal of Molecular Graphics and Modelling 25: 396-409 (2006), for a picture of this model - Click here then also click on the picture). Over several years, I've tested many of the predictions from this model and found that it predicts and continues to explain a number of interesting findings. These include rapid receptor desensitization or tachyphylaxis (see link) and a method for preventing this desensitization (see link) and the phenomenon of "spare receptors", which is an old conundrum in pharmacology (see link).
Understanding how our receptors work at the molecular level is an awe inspiring undertaking, because these are the molecules that link our thoughts and senses to the universe. Understanding how they function may open new frontiers for us to truly understand our place in the cosmos.
Tuesday, May 6, 2008
I Could Be Wrong
I could be wrong.
This is something that every true scientist must face directly. Our mental constructs to explain the real world have assisted us greatly over many millennia. Today more than ever, we need to remind ourselves that our ideas can be mistaken. Scientists have a particularly difficult time with this, as they must become their own worst critic. Not everyone can do this.
What I do is to set my work aside for an extended period of time (dear reader, please forgive my blogging mistakes). Any period of time, from a day to years, helps to clarify issues that are initially unrecognized. This rest allows for the injection of new knowledge and a more objective perspective to grasp the larger picture.
Scientists have the additional burden of mathematics. Mathematics is a two-edged sword that can slice the Gordon's knot or cut off our hand. True science needs mathematics to objectively describe its findings. The problem with mathematics arises because there may exist more than one mathematical solution to a real world physical problem. Scientists have recognized this and decided that the simplest way to describe the real world problem is the best. This has been termed Occam's razor (sometimes spelled as "Ockham's razor" attributed to the 14th-century English logician and Franciscan friar William of Ockham).
If a scientist finds a mathematical solution that isn't so simple, then they often have a dilemma. The dilemma often occurs if they try to fit their data to some mathematical equation that fits the data, but only if they use higher and higher exponential powers of a particular parameter within their equation. The problem is that this process begins to lose the physical meaning behind that parameter and the logical connection to the underlying physical process becomes less clear.
Those who aren't scientists don't understand this dilemma and fail to recognize some of the serious implications for today's scientists. The old saying is, "Publish or perish"; however, my former mentor use to say, "Publish and perish!". This is a problem for both the experimental and theoretical scientists today because they have enormous pressures on them to publish their findings before they get scooped, or to get that grant, or to patent a promising technology, or to show a potential boss that they've published many papers. It is no wonder that the cold hard logic underlying the science often gets lost in these scenarios. It is also no wonder that if they have at least one mathematical equation that fits most of their data, then they will publish it without asking themselves what does it mean and what are the implications of using this equation. In other words the bigger picture often gets lost in the rush to publish and a scientist may lose their hand to the mathematical sword.
This leads one to consider the region of what I'll call "hard science". Hard science is the objective modeling of experimental findings using more than one model and then evaluating which model is best. Today this is almost impossible to do within one scientist's lifetime, because almost 90% of the scientists who've ever lived are alive today and they are exponentially adding to the scientific literature in their rush to publish so that there has been an exponential explosion in potential mathematical models in all scientific areas. No one scientist can test them all.
So what can hard science do? There are additional aspects within the mathematical equations to look for. First, the generality of the equation to other experimental findings is an important aspect. Second, the novelty of predictions arising from manipulations of the parameters within the equation and the experimental verification of these predictions. Third, the ability of the parameters within the equation to match with physical entities. This places the burden on the experimentalists to wisely choose the theory that they are testing. Thus are the scientific models that will lead us toward a better understanding of our universe proven true. This involves a lengthy process of give and take between theory and experiment to find the truth behind our scientific discoveries today.
I could be wrong.
This is something that every true scientist must face directly. Our mental constructs to explain the real world have assisted us greatly over many millennia. Today more than ever, we need to remind ourselves that our ideas can be mistaken. Scientists have a particularly difficult time with this, as they must become their own worst critic. Not everyone can do this.
What I do is to set my work aside for an extended period of time (dear reader, please forgive my blogging mistakes). Any period of time, from a day to years, helps to clarify issues that are initially unrecognized. This rest allows for the injection of new knowledge and a more objective perspective to grasp the larger picture.
Scientists have the additional burden of mathematics. Mathematics is a two-edged sword that can slice the Gordon's knot or cut off our hand. True science needs mathematics to objectively describe its findings. The problem with mathematics arises because there may exist more than one mathematical solution to a real world physical problem. Scientists have recognized this and decided that the simplest way to describe the real world problem is the best. This has been termed Occam's razor (sometimes spelled as "Ockham's razor" attributed to the 14th-century English logician and Franciscan friar William of Ockham).
If a scientist finds a mathematical solution that isn't so simple, then they often have a dilemma. The dilemma often occurs if they try to fit their data to some mathematical equation that fits the data, but only if they use higher and higher exponential powers of a particular parameter within their equation. The problem is that this process begins to lose the physical meaning behind that parameter and the logical connection to the underlying physical process becomes less clear.
Those who aren't scientists don't understand this dilemma and fail to recognize some of the serious implications for today's scientists. The old saying is, "Publish or perish"; however, my former mentor use to say, "Publish and perish!". This is a problem for both the experimental and theoretical scientists today because they have enormous pressures on them to publish their findings before they get scooped, or to get that grant, or to patent a promising technology, or to show a potential boss that they've published many papers. It is no wonder that the cold hard logic underlying the science often gets lost in these scenarios. It is also no wonder that if they have at least one mathematical equation that fits most of their data, then they will publish it without asking themselves what does it mean and what are the implications of using this equation. In other words the bigger picture often gets lost in the rush to publish and a scientist may lose their hand to the mathematical sword.
This leads one to consider the region of what I'll call "hard science". Hard science is the objective modeling of experimental findings using more than one model and then evaluating which model is best. Today this is almost impossible to do within one scientist's lifetime, because almost 90% of the scientists who've ever lived are alive today and they are exponentially adding to the scientific literature in their rush to publish so that there has been an exponential explosion in potential mathematical models in all scientific areas. No one scientist can test them all.
So what can hard science do? There are additional aspects within the mathematical equations to look for. First, the generality of the equation to other experimental findings is an important aspect. Second, the novelty of predictions arising from manipulations of the parameters within the equation and the experimental verification of these predictions. Third, the ability of the parameters within the equation to match with physical entities. This places the burden on the experimentalists to wisely choose the theory that they are testing. Thus are the scientific models that will lead us toward a better understanding of our universe proven true. This involves a lengthy process of give and take between theory and experiment to find the truth behind our scientific discoveries today.
I could be wrong.
Welcome
Welcome to my blog. First, a bit about what I'd like to share with those of you searching netspace:
I've discovered something truly remarkable. I'll try to explain it by suggesting that you first check out this gedanken experiment at http://www.bio-balance.com/SB_Gedanken_Exp.pdf and then http://www.bio-balance.com/Simple_Balance_PartI.pdf, and then http://www.bio-balance.com/Simple_Balance_PartII.pdf. These simple physical experiments demonstrate something very profound about a two-pan balance that to my knowledge hasn't been adequately explored or addressed before.
Although some of Archimedes' notebooks are lost, this discovery points to a fundamental equation of equilibrium that may have been previously discovered, but was lost (see - http://www.bio-balance.com/Anemone.pdf). This fundamental equation may revolutionize how scientists view everything from cellular receptor activation to complex, nonlinear systems (see - Weber's law or http://www.bio-balance.com/Weber's_Law.pdf and Graphics and http://www.bio-balance.com/A_Question_of_Balance.htm). Digesting this requires some time, but only a basic understanding of algebra. Those who try will be rewarded by the elegant simplicity of the fundamental equation of equilibrium that may hold the key to several complex problems today.
I've discovered something truly remarkable. I'll try to explain it by suggesting that you first check out this gedanken experiment at http://www.bio-balance.com/SB_Gedanken_Exp.pdf and then http://www.bio-balance.com/Simple_Balance_PartI.pdf, and then http://www.bio-balance.com/Simple_Balance_PartII.pdf. These simple physical experiments demonstrate something very profound about a two-pan balance that to my knowledge hasn't been adequately explored or addressed before.
Although some of Archimedes' notebooks are lost, this discovery points to a fundamental equation of equilibrium that may have been previously discovered, but was lost (see - http://www.bio-balance.com/Anemone.pdf). This fundamental equation may revolutionize how scientists view everything from cellular receptor activation to complex, nonlinear systems (see - Weber's law or http://www.bio-balance.com/Weber's_Law.pdf and Graphics and http://www.bio-balance.com/A_Question_of_Balance.htm). Digesting this requires some time, but only a basic understanding of algebra. Those who try will be rewarded by the elegant simplicity of the fundamental equation of equilibrium that may hold the key to several complex problems today.
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