I was reading an important research article recently and encountered a term that I had not see in a while. That word was stochastic. Physical science and engineering undergraduates probably encounter these words with different frequencies - most often as the expression stochastic process. As a chemistry and biology major, the main contact I had with the term was in what is typically considered the most mathematical of undergraduate chemistry courses - Physical Chemistry (PChem). In the days I was an undergraduate we used a text by Moore. In striving to stay in touch with the field I got a copy of a more current PChem text by Atkins several years ago. The main reference to stochastic processes in both is the random walk problem. In Moore it is in the problem set for the chapter on Kinetic Theory and and in Atkins it is in a separate supplement at the end. That supplement is entitled Random Walk, illustrates how a random walk in one dimension can be used to derive an equation that estimates the probability of a particle being at a distance from the origin in a specified time during diffusion. I won't include the equation here since there are a number of books and online sites where the derivation is available.
The authors of the research article were using it to describe a component of neuronal activity in the reward center of rats. In their discussion of the term, they point out that brain complexity precludes the prediction of final outcomes from initial states. In the paper the authors were faced with explaining why a specific population of mice continued to self-stimulate dopaminergic neurons in the ventral tegmental area (VTA) via a optogenetic dopamine- neuron self-stimulation (oDASS) via an optic fiber despite punishment while another group of mice did not. The details are included in the graphic at the top of this post. To quote the authors on this phenomenon:
"Why only a fraction of mice lose control remains to be determined; the emergence of the two groups is even more surprising given the high degree of genetic homogeneity of the mouse line used here (our Datcre (also known as Slc6a3cre) mice were backcrossed for more than ten generations into the C57BL/6J mouse line), and may reflect a case of stochastic individuality" (p. 320)
One of the key elements of this type of experimentation is minimizing variance form genetic and environmental factors. The mice used in this experiment are inbred for several generations and in this case had a homozygous knock-in variation for dopamine transporter (DAT). Colonies are developed to raise heterozygous mice with a greater expression of DAT for experimentation on these systems. The idea behind backcrossing the mice for more than ten generations reduces the phenotypic variation but as noted in reference 2, there have been 30 years of experimentation of inbreeding mice and that reduces the phenotypic variance by 20-30%. Although the C57BL/6J mouse line has its DNA characterized - I could not find any numbers for shared DNA on an individual to individual mouse basis. As an example, in humans the following percentages of shared DNA would be expected identical twins (100%), parent-child (50%), grandparent-grandchild (25%), and first cousins (7.3-13.8%).
The experiment looked at these mice bred for a low degree of phenotypic variation who were all rained in similar environments. All of the mice were trained for oDASS and then subjected to foot shock as a punishment. As noted in the graphic, 60% persevered despite the punishment and 40% renounced or had a marked decrease in oDASS after punishment. Both of these responses were considered distinct behavioral phenotypes. The underlying molecular mechanisms were also studied.
The paper by Honegger and de Bivort (2) takes a more detailed look at examples of stochasticity. From a behavioral standpoint, they define stochastic individuality as non-heritable inter-organism behavioral variation. The lack of concordance between identical twins is cited as a prime example. Beyond genomics they argue that stochastic individuality implies that if we know all about the basis of a trait at the -omics level and all of the relevant environmental factors – the behaviors will remain "beyond reliable prediction". They review some examples from the animal kingdom. Marbled crayfish and pea aphids reproduce by apomictic thelytoky - that is all of the individuals are female and reproduction is clonal - therefore all individuals have the same genome. Despite this individual display significant variation in locomotion and social behavior. They consider nutritional variances, self reinforcing circuits involving nutrition and behavior, and variation in biophysical developmental processes as possible mechanisms. In the case of mice, highly inbred mice raised in the same environment vary significantly in their exploration of the environment. Individual mice that actively explore the environment have more robust hippocampal neurogenesis.
The authors detail and number of possible mechanisms underlying stochastic individuality including:
1. A small number of effects at the molecular level promotes stochasticity. Random fluctuations in RNA polymerase binding to DNA over time leads to fluctuating mRNA in the cell over time. There are also a host of possible mechanisms operating on small gene sets that lead to large combinations of possible outcomes. An example given is T-cell biology in humans. T-cells are essential for normal immunity in humans and the system can use a number of genetic mechanisms to generate a a very large number of T-cell receptor types (1015 to 1020 ) from a small number of genes (4). The authors of this article discuss the fact that T-cell receptor diversity cannot be estimated by a priori assumptions suggesting this is a stochastic rather than deterministic process.
2. Positive feedback in gene networks amplify fluctuations and can cause jumping between discrete states or bistability. An example from the literature is cell quiescence, and there is thought to be a stochastic process involving a specific protein (5,6) that leads to the transition from active proliferation ( a number of states) to quiescence and back again.
3. Biological processes are systems that are non-linear, multidimensional, and have significant feedback and therefore are often chaotic. Initial small differences will be amplified. There are several disorders that occur with different concordance in identical twins (seizure disorders, cardiac arrhythmias) that could occur as the consequence of this process. Biological systems that move large amounts of information across these systems are most susceptible.
4. Somatic mosaicism – as cellular differentiation and proliferation occur genomic alteration can occur in new cells or their progeny. Transposons are active mobile DNA elements that can excise and re-insert into new positions in the genome leading to different cell genetics and tissues from the same progenitor cells. In my current neurobiology lecture I discuss various level of brain complexity and give examples of 90 subtypes of potassium channels and significant numbers of vesicle trafficking proteins (7) in neurons. Wilhelm, et al (7) reconstruct a 3D model of a synapse that contains 60 different in varying copy numbers. In the supplementary data they investigate a total of 100 different synaptic proteins and show that the copy numbers of each protein vary from 10 to 22,000 (Fig. S5).
The complexity of the synaptic proteins and their number may seem impressive and have the complexity to produce an apparent stochastic result. Looking at what might happen if these proteins are all modifiable by one of the mechanisms in the Honegger and de Bivort paper is more impressive. The authors discuss alternative gene splice forms using a Drosophila example. Proteins are typically formed in eukaryotic cells when the exon portions of the gene are cut and spliced from the intron or noncoding segment of a DNA or corresponding RNA transcript. Alternative splicing involves splicing that occurs in a way that some segments are altered or skipped. The result is multiple proteins being encoded by the same gene. A few examples are illustrated in the following graphic.
The nervous system implications of alternative splicing include recognizing that this occurs at every level of neuronal organization (8) and it has already been implicated in neurological diseases like amyotropic lateral sclerosis (ALS). To get a quick look at what research may have already been done in this area I surveyed Medline for references to "alternative splicing" and "protein isoforms" for all of the neuronal proteins listed in the table of neuronal proteins listed in table S2 from reference 7. As noted in the table there are probably over a thousand references unevenly distributed across these proteins indicating a significant amount of research on both the mechanism and classification of neuronal protein isoforms - many of which impact neuronal function and may be responsible for stochastic outcomes.
Research On Neuronal
Protein Alternative Splicing and Isoforms
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Protein
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Alternative Splicing
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Isoforms"[MeSH Terms] + Protein references?
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SNAP 25
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VAMP 2
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α-SNAP
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α/β-Synuclein
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AP 180
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AP 2 (mu2)
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CALM
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Calmodulin
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Clathrin heavy chain
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Clathrin light chain
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Complexin 1,2
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CSP
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Doc2A/B
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Dynamin 1,2,3
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Endophilin I,II,III
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Epsin 1
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Hsc70
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Intersectin 1
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Munc13a
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Munc18a
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NSF
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PIPKIγ
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Rab3
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Rab5a
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Rab7a
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Septin5
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SGIP1
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Synapsin I.II
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Syndapin 1
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At this point I am wrapping up this post with a list of stochastic mechanisms to follow in subsequent posts. This is an important concept for psychiatrists interested in individual differences in behavior and well as unique conscious states to know about. It has the potential for greatly increasing the explanatory power of why there is so much heterogeneity in presentations of illness and outcomes. It has the potential for providing a clearer understanding of the neurobiological substrates of behavior. The distinct behavioral phenotypes in the experiment noted in the beginning of this post is a clear case in point.
George Dawson, MD, DFAPA
References:
1: Pascoli V, Hiver A, Van Zessen R, Loureiro M, Achargui R, Harada M, Flakowski J, Lüscher C. Stochastic synaptic plasticity underlying compulsion in a model of addiction. Nature. 2018 Dec;564(7736):366-371. doi: 10.1038/s41586-018-0789-4. Epub 2018 Dec 19. PubMed PMID: 30568192.
3: Ponomarenko EA, Poverennaya EV, Ilgisonis EV, Pyatnitskiy MA, Kopylov AT, Zgoda VG, Lisitsa AV, Archakov AI. The Size of the Human Proteome: The Width and Depth. Int J Anal Chem. 2016;2016:7436849. doi: 10.1155/2016/7436849. Epub 2016 May 19. Review. PubMed PMID: 27298622.
4: Laydon DJ, Bangham CR, Asquith B. Estimating T-cell repertoire diversity:limitations of classical estimators and a new approach. Philos Trans R Soc Lond B Biol Sci. 2015 Aug 19;370(1675). pii: 20140291. doi: 10.1098/rstb.2014.0291. Review. PubMed PMID: 26150657.
7: Wilhelm BG, Mandad S, Truckenbrodt S, Kröhnert K, Schäfer C, Rammner B, KooSJ, Claßen GA, Krauss M, Haucke V, Urlaub H, Rizzoli SO. Composition of isolated synaptic boutons reveals the amounts of vesicle trafficking proteins. Science. 2014 May 30;344(6187):1023-8. doi: 10.1126/science.1252884. PubMed PMID:24876496.
8: Vuong CK, Black DL, Zheng S. The neurogenetics of alternative splicing. NatRev Neurosci. 2016 May;17(5):265-81. doi: 10.1038/nrn.2016.27. Review. PubMedPMID: 27094079.
Supplementary:
The Kyoto Encyclopedia of Genes and Genomes (KEGG) currently lists 40 alternative splicing factors. Link
Graphics Credit:
1: Top graphic -> me.
2: Alternate splicing graphic from VisiScience per their purchasing agreement.
Click on either graphic to enlarge.
1: Top graphic -> me.
2: Alternate splicing graphic from VisiScience per their purchasing agreement.
Click on either graphic to enlarge.
